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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. After a successful field test, Heidi is considering deploying a trap along some Corridor, possibly not the first one. She wants to avoid meeting the Daleks inside the Time Vortex, so for abundance of caution she considers placing the traps only along those Corridors that are not going to be used according to the current Daleks' plan – which is to use a minimum spanning tree of Corridors. Heidi knows that all energy requirements for different Corridors are now different, and that the Daleks have a single unique plan which they are intending to use. Your task is to calculate the number E_{max}(c), which is defined in the same way as in the easy version – i.e., the largest e ≀ 10^9 such that if we changed the energy of corridor c to e, the Daleks might use it – but now for every corridor that Heidi considers. Input The first line: number n of destinations, number m of Time Corridors (2 ≀ n ≀ 10^5, n - 1 ≀ m ≀ 10^6). The next m lines: destinations a, b and energy e (1 ≀ a, b ≀ n, a β‰  b, 0 ≀ e ≀ 10^9). No pair \\{a, b\} will repeat. The graph is guaranteed to be connected. All energy requirements e are distinct. Output Output m-(n-1) lines, each containing one integer: E_{max}(c_i) for the i-th Corridor c_i from the input that is not part of the current Daleks' plan (minimum spanning tree). Example Input 3 3 1 2 8 2 3 3 3 1 4 Output 4 Note If m = n-1, then you need not output anything. Submitted Solution: ``` def naiveSolve(): return from types import GeneratorType def bootstrap(f, stack=[]): def wrappedfunc(*args, **kwargs): if stack: return f(*args, **kwargs) else: to = f(*args, **kwargs) while True: if type(to) is GeneratorType: stack.append(to) to = next(to) else: stack.pop() if not stack: break to = stack[-1].send(to) return to return wrappedfunc class UnionFind: def __init__(self, n): self.parent = list(range(n)) def find(self, a): #return parent of a. a and b are in same set if they have same parent acopy = a while a != self.parent[a]: a = self.parent[a] while acopy != a: #path compression self.parent[acopy], acopy = a, self.parent[acopy] return a def union(self, a, b): #union a and b self.parent[self.find(b)] = self.find(a) def main(): n,m=readIntArr() a=[] b=[] c=[] for _ in range(m): aa,bb,cc=readIntArr() a.append(aa); b.append(bb); c.append(cc) idxes=list(range(m)) idxes.sort(key=lambda i:c[i]) uf=UnionFind(n+1) inA=[] # in MST inB=[] inC=[] outA=[] # not in MST outB=[] for i in range(m): aa=a[idxes[i]] bb=b[idxes[i]] cc=c[idxes[i]] if uf.find(aa)!=uf.find(bb): uf.union(aa,bb) inA.append(aa) inB.append(bb) inC.append(cc) else: outA.append(aa) outB.append(bb) # find largest edge between each outA and outB adj=[[] for _ in range(n+1)] # store (edge,cost) assert len(inA)==n-1 for i in range(n-1): u,v,c=inA[i],inB[i],inC[i] adj[u].append((v,c)) adj[v].append((u,c)) @bootstrap def dfs(node,p,cost): up[node][0]=p maxEdge[node][0]=cost tin[node]=time[0] time[0]+=1 for v,c in adj[node]: if v!=p: yield dfs(v,node,c) tout[node]=time[0] time[0]+=1 yield None time=[0] tin=[-1]*(n+1) tout=[-1]*(n+1) # binary lifting to find LCA maxPow=0 while pow(2,maxPow)<n: maxPow+=1 maxPow+=1 up=[[-1 for _ in range(maxPow)] for __ in range(n+1)] maxEdge=[[-inf for _ in range(maxPow)] for __ in range(n+1)] dfs(1,-1,-inf) for i in range(1,maxPow): for u in range(2,n+1): if up[u][i-1]==-1 or up[up[u][i-1]][i-1]==-1: # reached beyond root continue up[u][i]=up[up[u][i-1]][i-1] maxEdge[u][i]=max(maxEdge[u][i-1],maxEdge[up[u][i-1]][i-1]) def isAncestor(u,v): # True if u is ancestor of v return tin[u]<=tin[v] and tout[u]>=tout[v] def findMaxEdgeValue(u,v): # traverse u to LCA, then v to LCA res=0 if not isAncestor(u,v): u2=u while not isAncestor(up[u2][0],v): # still have to move up for i in range(maxPow-1,-1,-1): if up[u2][i]!=-1 and not isAncestor(up[u2][i],v): res=max(res,maxEdge[u2][i]) u2=up[u2][i] # print('u2:{}'.format(u2)) ## # next level up is lca res=max(res,maxEdge[u2][0]) if not isAncestor(v,u): v2=v while not isAncestor(up[v2][0],u): # still have to move up for i in range(maxPow-1,-1,-1): if up[v2][i]!=-1 and not isAncestor(up[v2][i],u): res=max(res,maxEdge[v2][i]) v2=up[v2][i] # print('v2:{} u:{}'.format(v2,u)) ## # if v2==1: # print(isAncestor(v,u)) ## # break # next level up is lca res=max(res,maxEdge[v2][0]) return res # for i in range(1,4): # for j in range(1,4): # if i!=j: # print('i:{} j:{} anc:{}'.format(i,j,isAncestor(i,j))) ans=[] # print(outA,outB) # for u in range(1,n+1): # print('u:{} up:{} maxEdge:{}'.format(u,up[u],maxEdge[u])) ## for i in range(len(outA)): u,v=outA[i],outB[i] ans.append(findMaxEdgeValue(u,v)) multiLineArrayPrint(ans) return import sys input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok) # input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS. def oneLineArrayPrint(arr): print(' '.join([str(x) for x in arr])) def multiLineArrayPrint(arr): print('\n'.join([str(x) for x in arr])) def multiLineArrayOfArraysPrint(arr): print('\n'.join([' '.join([str(x) for x in y]) for y in arr])) def readIntArr(): return [int(x) for x in input().split()] # def readFloatArr(): # return [float(x) for x in input().split()] def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m]) dv=defaultValFactory;da=dimensionArr if len(da)==1:return [dv() for _ in range(da[0])] else:return [makeArr(dv,da[1:]) for _ in range(da[0])] def queryInteractive(r): print('? {}'.format(r)) sys.stdout.flush() return readIntArr() def answerInteractive(adj,n): print('!') for u in range(1,n+1): for v in adj[u]: if v>u: print('{} {}'.format(u,v)) sys.stdout.flush() inf=float('inf') MOD=10**9+7 # MOD=998244353 from math import gcd,floor,ceil # from math import floor,ceil # for Python2 for _abc in range(1): main() ```
instruction
0
102,976
3
205,952
No
output
1
102,976
3
205,953
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. After a successful field test, Heidi is considering deploying a trap along some Corridor, possibly not the first one. She wants to avoid meeting the Daleks inside the Time Vortex, so for abundance of caution she considers placing the traps only along those Corridors that are not going to be used according to the current Daleks' plan – which is to use a minimum spanning tree of Corridors. Heidi knows that all energy requirements for different Corridors are now different, and that the Daleks have a single unique plan which they are intending to use. Your task is to calculate the number E_{max}(c), which is defined in the same way as in the easy version – i.e., the largest e ≀ 10^9 such that if we changed the energy of corridor c to e, the Daleks might use it – but now for every corridor that Heidi considers. Input The first line: number n of destinations, number m of Time Corridors (2 ≀ n ≀ 10^5, n - 1 ≀ m ≀ 10^6). The next m lines: destinations a, b and energy e (1 ≀ a, b ≀ n, a β‰  b, 0 ≀ e ≀ 10^9). No pair \\{a, b\} will repeat. The graph is guaranteed to be connected. All energy requirements e are distinct. Output Output m-(n-1) lines, each containing one integer: E_{max}(c_i) for the i-th Corridor c_i from the input that is not part of the current Daleks' plan (minimum spanning tree). Example Input 3 3 1 2 8 2 3 3 3 1 4 Output 4 Note If m = n-1, then you need not output anything. Submitted Solution: ``` def naiveSolve(): return from types import GeneratorType def bootstrap(f, stack=[]): def wrappedfunc(*args, **kwargs): if stack: return f(*args, **kwargs) else: to = f(*args, **kwargs) while True: if type(to) is GeneratorType: stack.append(to) to = next(to) else: stack.pop() if not stack: break to = stack[-1].send(to) return to return wrappedfunc class UnionFind: def __init__(self, n): self.parent = list(range(n)) def find(self, a): #return parent of a. a and b are in same set if they have same parent acopy = a while a != self.parent[a]: a = self.parent[a] while acopy != a: #path compression self.parent[acopy], acopy = a, self.parent[acopy] return a def union(self, a, b): #union a and b self.parent[self.find(b)] = self.find(a) def main(): n,m=readIntArr() a=[] b=[] c=[] for _ in range(m): aa,bb,cc=readIntArr() a.append(aa); b.append(bb); c.append(cc) idxes=list(range(m)) idxes.sort(key=lambda i:c[i]) uf=UnionFind(n+1) inA=[] # in MST inB=[] inC=[] outA=[] # not in MST outB=[] for i in range(m): aa=a[idxes[i]] bb=b[idxes[i]] cc=c[idxes[i]] if uf.find(aa)!=uf.find(bb): uf.union(aa,bb) inA.append(aa) inB.append(bb) inC.append(cc) else: outA.append(aa) outB.append(bb) # find largest edge between each outA and outB adj=[[] for _ in range(n+1)] # store (edge,cost) for i in range(n-1): u,v,c=inA[i],inB[i],inC[i] adj[u].append((v,c)) adj[v].append((u,c)) @bootstrap def dfs(node,p,cost): up[node][0]=p maxEdge[node][0]=cost tin[node]=time[0] time[0]+=1 for v,c in adj[node]: if v!=p: yield dfs(v,node,c) tout[node]=time[0] time[0]+=1 yield None time=[0] tin=[-1]*(n+1) tout=[-1]*(n+1) # binary lifting to find LCA maxPow=0 while pow(2,maxPow)<n: maxPow+=1 maxPow+=1 up=[[-1 for _ in range(maxPow)] for __ in range(n+1)] maxEdge=[[-inf for _ in range(maxPow)] for __ in range(n+1)] dfs(1,-1,-inf) for i in range(1,maxPow): for u in range(1,n+1): up[u][i]=up[up[u][i-1]][i-1] maxEdge[u][i]=max(maxEdge[u][i-1],maxEdge[up[u][i-1]][i-1]) def isAncestor(u,v): # True if u is ancestor of v return tin[u]<=tin[v] and tout[u]>=tout[v] def findMaxEdgeValue(u,v): # traverse u to LCA, then v to LCA res=0 if not isAncestor(u,v): u2=u while not isAncestor(up[u2][0],v): # still have to move up for i in range(maxPow-1,-1,-1): if up[u2][i]!=-1 and not isAncestor(up[u2][i],v): res=max(res,maxEdge[u2][i]) u2=up[u2][i] # print('u2:{}'.format(u2)) ## # next level up is lca res=max(res,maxEdge[u2][0]) if not isAncestor(v,u): v2=v while not isAncestor(up[v2][0],u): # still have to move up for i in range(maxPow-1,-1,-1): if up[v2][i]!=-1 and not isAncestor(up[v2][i],u): res=max(res,maxEdge[v2][i]) v2=up[v2][i] # print('v2:{} u:{}'.format(v2,u)) ## # if v2==1: # print(isAncestor(v,u)) ## # break # next level up is lca res=max(res,maxEdge[v2][0]) return res # for i in range(1,4): # for j in range(1,4): # if i!=j: # print('i:{} j:{} anc:{}'.format(i,j,isAncestor(i,j))) ans=[] # print(outA,outB) for i in range(len(outA)): u,v=outA[i],outB[i] ans.append(findMaxEdgeValue(u,v)) multiLineArrayPrint(ans) return import sys input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok) # input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS. def oneLineArrayPrint(arr): print(' '.join([str(x) for x in arr])) def multiLineArrayPrint(arr): print('\n'.join([str(x) for x in arr])) def multiLineArrayOfArraysPrint(arr): print('\n'.join([' '.join([str(x) for x in y]) for y in arr])) def readIntArr(): return [int(x) for x in input().split()] # def readFloatArr(): # return [float(x) for x in input().split()] def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m]) dv=defaultValFactory;da=dimensionArr if len(da)==1:return [dv() for _ in range(da[0])] else:return [makeArr(dv,da[1:]) for _ in range(da[0])] def queryInteractive(r): print('? {}'.format(r)) sys.stdout.flush() return readIntArr() def answerInteractive(adj,n): print('!') for u in range(1,n+1): for v in adj[u]: if v>u: print('{} {}'.format(u,v)) sys.stdout.flush() inf=float('inf') MOD=10**9+7 # MOD=998244353 from math import gcd,floor,ceil # from math import floor,ceil # for Python2 for _abc in range(1): main() ```
instruction
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102,977
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205,954
No
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Annie has gotten bored of winning every coding contest and farming unlimited rating. Today, she is going to farm potatoes instead. Annie's garden is an infinite 2D plane. She has n potatoes to plant, and the i-th potato must be planted at (x_i,y_i). Starting at the point (0, 0), Annie begins walking, in one step she can travel one unit right or up (increasing her x or y coordinate by 1 respectively). At any point (X,Y) during her walk she can plant some potatoes at arbitrary points using her potato gun, consuming max(|X-x|,|Y-y|) units of energy in order to plant a potato at (x,y). Find the minimum total energy required to plant every potato. Note that Annie may plant any number of potatoes from any point. Input The first line contains the integer n (1 ≀ n ≀ 800 000). The next n lines contain two integers x_i and y_i (0 ≀ x_i,y_i ≀ 10^9), representing the location of the i-th potato. It is possible that some potatoes should be planted in the same location. Output Print the minimum total energy to plant all potatoes. Examples Input 2 1 1 2 2 Output 0 Input 2 1 1 2 0 Output 1 Input 3 5 5 7 7 4 9 Output 2 Input 10 5 1 4 0 9 6 0 2 10 1 9 10 3 10 0 10 8 9 1 5 Output 19 Input 10 1 1 2 2 2 0 4 2 4 0 2 0 0 2 4 0 4 2 5 1 Output 6 Note In example 1, Annie can travel to each spot directly and plant a potato with no energy required. In example 2, moving to (1,0), Annie plants the second potato using 1 energy. Next, she travels to (1,1) and plants the first potato with 0 energy. Submitted Solution: ``` n=int(input()) lst_x=[] lst_y=[] for i in range(n): x,y=map(int,input().split()) lst_x.append(x) lst_y.append(y) print(0) ```
instruction
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103,124
3
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No
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1
103,124
3
206,249
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. My name is James diGriz, I'm the most clever robber and treasure hunter in the whole galaxy. There are books written about my adventures and songs about my operations, though you were able to catch me up in a pretty awkward moment. I was able to hide from cameras, outsmart all the guards and pass numerous traps, but when I finally reached the treasure box and opened it, I have accidentally started the clockwork bomb! Luckily, I have met such kind of bombs before and I know that the clockwork mechanism can be stopped by connecting contacts with wires on the control panel of the bomb in a certain manner. I see n contacts connected by n - 1 wires. Contacts are numbered with integers from 1 to n. Bomb has a security mechanism that ensures the following condition: if there exist k β‰₯ 2 contacts c1, c2, ..., ck forming a circuit, i. e. there exist k distinct wires between contacts c1 and c2, c2 and c3, ..., ck and c1, then the bomb immediately explodes and my story ends here. In particular, if two contacts are connected by more than one wire they form a circuit of length 2. It is also prohibited to connect a contact with itself. On the other hand, if I disconnect more than one wire (i. e. at some moment there will be no more than n - 2 wires in the scheme) then the other security check fails and the bomb also explodes. So, the only thing I can do is to unplug some wire and plug it into a new place ensuring the fact that no circuits appear. I know how I should put the wires in order to stop the clockwork. But my time is running out! Help me get out of this alive: find the sequence of operations each of which consists of unplugging some wire and putting it into another place so that the bomb is defused. Input The first line of the input contains n (2 ≀ n ≀ 500 000), the number of contacts. Each of the following n - 1 lines contains two of integers xi and yi (1 ≀ xi, yi ≀ n, xi β‰  yi) denoting the contacts currently connected by the i-th wire. The remaining n - 1 lines contain the description of the sought scheme in the same format. It is guaranteed that the starting and the ending schemes are correct (i. e. do not contain cicuits nor wires connecting contact with itself). Output The first line should contain k (k β‰₯ 0) β€” the minimum number of moves of unplugging and plugging back some wire required to defuse the bomb. In each of the following k lines output four integers ai, bi, ci, di meaning that on the i-th step it is neccesary to unplug the wire connecting the contacts ai and bi and plug it to the contacts ci and di. Of course the wire connecting contacts ai and bi should be present in the scheme. If there is no correct sequence transforming the existing scheme into the sought one, output -1. Examples Input 3 1 2 2 3 1 3 3 2 Output 1 1 2 1 3 Input 4 1 2 2 3 3 4 2 4 4 1 1 3 Output 3 1 2 1 3 4 3 4 1 2 3 2 4 Note Picture with the clarification for the sample tests: <image> Submitted Solution: ``` #!/usr/bin/python3 # -*- config:utf-8 -*- import sys import re # exception type for wrong input data class IncorrectDataException(Exception): pass # transform graph without circles to tree def createtree(cnt,data): data=[[int(y) for y in x.split(' ')] for x in data] edges={} backtrace={} for i in range(1,cnt+1): edges[i]={} backtrace[i]={} for edge in data: edges[edge[0]][edge[1]]=1 edges[edge[1]][edge[0]]=1 backtrace[edge[0]][edge[1]]=1 backtrace[edge[1]][edge[0]]=1 stack=[1] while stack: srcvert=stack.pop(-1) for destvert in edges[srcvert].keys(): stack.append(destvert) edges[destvert].pop(srcvert) backtrace[srcvert].pop(destvert) return edges,backtrace # get source data def getSrcData(): f = sys.stdin buf = f.read() sample=re.compile(r'^\d+\n(\d+ \d+\n)+',re.MULTILINE) data=sample.match(buf) if not (data): raise IncorrectDataException("Incorrect source data: %s" % buf) buf=data.group(0) buf=buf.split('\n') cnt=int(buf[0]) src=buf[1:cnt] trg=buf[cnt:(cnt*2-1)] src,srcbacktrace=createtree(cnt,src) trg,trgbacktrace=createtree(cnt,trg) trgbacktrace=None return src,srcbacktrace,trg # find transform src tree to trg tree def getTransform(src,srcbacktrace,trg): result='' srcvert=1 stack=[1] while stack: srcvert=stack.pop(-1) stack.reverse() for destvert in trg[srcvert].keys(): stack.append(destvert) if not destvert in src[srcvert]: src4destvert=list(srcbacktrace[destvert].keys())[0] # get edge <src4destvert,destvert> in src tree # change found edge for <srcvert,destvert> # src[src4destvert][destvert]=0 # src[srcvert][destvert]=1 result+=str(src4destvert)+" "+str(destvert)+" "+str(srcvert)+" "+str(destvert)+"\n" stack.reverse() return result,src # save result def saveResult(result): f = sys.stdout f.write(str(result) + '\n') f.flush() # start def run(): src,srcbacktrace,trg=getSrcData() result,src=getTransform(src,srcbacktrace,trg) cnt=result.count('\n') result=str(cnt)+'\n'+result saveResult(result) if __name__ == '__main__': run() ```
instruction
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104,073
3
208,146
No
output
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104,073
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. My name is James diGriz, I'm the most clever robber and treasure hunter in the whole galaxy. There are books written about my adventures and songs about my operations, though you were able to catch me up in a pretty awkward moment. I was able to hide from cameras, outsmart all the guards and pass numerous traps, but when I finally reached the treasure box and opened it, I have accidentally started the clockwork bomb! Luckily, I have met such kind of bombs before and I know that the clockwork mechanism can be stopped by connecting contacts with wires on the control panel of the bomb in a certain manner. I see n contacts connected by n - 1 wires. Contacts are numbered with integers from 1 to n. Bomb has a security mechanism that ensures the following condition: if there exist k β‰₯ 2 contacts c1, c2, ..., ck forming a circuit, i. e. there exist k distinct wires between contacts c1 and c2, c2 and c3, ..., ck and c1, then the bomb immediately explodes and my story ends here. In particular, if two contacts are connected by more than one wire they form a circuit of length 2. It is also prohibited to connect a contact with itself. On the other hand, if I disconnect more than one wire (i. e. at some moment there will be no more than n - 2 wires in the scheme) then the other security check fails and the bomb also explodes. So, the only thing I can do is to unplug some wire and plug it into a new place ensuring the fact that no circuits appear. I know how I should put the wires in order to stop the clockwork. But my time is running out! Help me get out of this alive: find the sequence of operations each of which consists of unplugging some wire and putting it into another place so that the bomb is defused. Input The first line of the input contains n (2 ≀ n ≀ 500 000), the number of contacts. Each of the following n - 1 lines contains two of integers xi and yi (1 ≀ xi, yi ≀ n, xi β‰  yi) denoting the contacts currently connected by the i-th wire. The remaining n - 1 lines contain the description of the sought scheme in the same format. It is guaranteed that the starting and the ending schemes are correct (i. e. do not contain cicuits nor wires connecting contact with itself). Output The first line should contain k (k β‰₯ 0) β€” the minimum number of moves of unplugging and plugging back some wire required to defuse the bomb. In each of the following k lines output four integers ai, bi, ci, di meaning that on the i-th step it is neccesary to unplug the wire connecting the contacts ai and bi and plug it to the contacts ci and di. Of course the wire connecting contacts ai and bi should be present in the scheme. If there is no correct sequence transforming the existing scheme into the sought one, output -1. Examples Input 3 1 2 2 3 1 3 3 2 Output 1 1 2 1 3 Input 4 1 2 2 3 3 4 2 4 4 1 1 3 Output 3 1 2 1 3 4 3 4 1 2 3 2 4 Note Picture with the clarification for the sample tests: <image> Submitted Solution: ``` #!/usr/bin/python3 # -*- config:utf-8 -*- import sys import re # exception type for wrong input data class IncorrectDataException(Exception): pass # transform graph without circles to tree def createtree(cnt,data,curvert): data=[[int(y) for y in x.split(' ')] for x in data] edges={} backtrace={} for i in range(1,cnt+1): edges[i]={} backtrace[i]={} for edge in data: edges[edge[0]][edge[1]]=1 edges[edge[1]][edge[0]]=1 backtrace[edge[0]][edge[1]]=1 backtrace[edge[1]][edge[0]]=1 if not curvert: cnt=0 for i in edges.keys(): if len(edges[i])>cnt: cnt=len(edges[i]) curvert=i stack=[curvert] while stack: srcvert=stack.pop(-1) for destvert in edges[srcvert].keys(): stack.append(destvert) edges[destvert].pop(srcvert) backtrace[srcvert].pop(destvert) return edges,backtrace,curvert # get source data def getSrcData(): f = sys.stdin buf = f.read() sample=re.compile(r'^\d+\n(\d+ \d+\n)+',re.MULTILINE) data=sample.match(buf) if not (data): raise IncorrectDataException("Incorrect source data: %s" % buf) buf=data.group(0) buf=buf.split('\n') cnt=int(buf[0]) src=buf[1:cnt] trg=buf[cnt:(cnt*2-1)] trg,trgbacktrace,curvert=createtree(cnt,trg,0) src,srcbacktrace,curvert=createtree(cnt,src,curvert) trgbacktrace=None return src,srcbacktrace,trg,curvert # find transform src tree to trg tree def getTransform(src,srcbacktrace,trg,curvert): result='' stack=[curvert] while stack: srcvert=stack.pop(-1) stack.reverse() for destvert in trg[srcvert].keys(): stack.append(destvert) if not destvert in src[srcvert]: src4destvert=list(srcbacktrace[destvert].keys())[0] # get edge <src4destvert,destvert> in src tree # change found edge for <srcvert,destvert> # src[src4destvert][destvert]=0 # src[srcvert][destvert]=1 result+=str(src4destvert)+" "+str(destvert)+" "+str(srcvert)+" "+str(destvert)+"\n" stack.reverse() return result,src # save result def saveResult(result): f = sys.stdout f.write(str(result) + '\n') f.flush() # start def run(): src,srcbacktrace,trg,curvert=getSrcData() result,src=getTransform(src,srcbacktrace,trg,curvert) cnt=result.count('\n') result=str(cnt)+'\n'+result saveResult(result) if __name__ == '__main__': run() ```
instruction
0
104,074
3
208,148
No
output
1
104,074
3
208,149
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,783
3
209,566
Tags: binary search, greedy, two pointers Correct Solution: ``` import sys def input(): return sys.stdin.buffer.readline()[:-1] for T in range(1): n, m = map(int, input().split()) p = list(map(int, input().split())) q = list(map(int, input().split())) ok, ng = 10**11, -1 while ok-ng > 1: x = (ok+ng)//2 flg = True j = 0 for i in range(n): l = max(p[i] - q[j], 0) if l > x: flg = False break while j < m and q[j] < p[i]: j += 1 if j == m: break while j < m: r = q[j] - p[i] if min(l, r)*2 + max(l, r) <= x: j += 1 continue else: break if j == m: break if flg == False or j < m: ng = x else: ok = x print(ok) ```
output
1
104,783
3
209,567
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,784
3
209,568
Tags: binary search, greedy, two pointers Correct Solution: ``` def can(d,a,b): d1=d mi=a[-1] ma=a[-1] while len(a)>0 and len(b)>0: if b[-1]<=mi: if abs(b[-1]-ma)<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] elif b[-1]>=ma: if abs(b[-1]-mi)<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] else: if abs(ma-mi)+min(abs(b[-1]-mi),abs(b[-1]-ma))<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] return len(a)==0 n,m=map(int,input().split()) s=list(map(int,input().split()))[::-1] s1=list(map(int,input().split()))[::-1] high=(10**12)+1 low=0 while high-low>1: mid=(high+low)//2 if can(mid,s1.copy(),s.copy()): high=mid else: low=mid if can(low,s1,s): print(low) else: print(high) ```
output
1
104,784
3
209,569
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,785
3
209,570
Tags: binary search, greedy, two pointers Correct Solution: ``` import sys from itertools import * from math import * def solve(): n, m = map(int, input().split()) h = list(map(int, input().split())) p = list(map(int, input().split())) ss, ll = 0, int(2.2e10) while ss < ll: avg = (ss + ll) // 2 works = True hidx = 0 pidx = 0 while hidx < len(h) and pidx < len(p): leftget = p[pidx] curpos = h[hidx] if curpos - leftget > avg: works = False break getbacktime = max(0, 2*(curpos - leftget)) alsotoright = max(0, avg - getbacktime) leftime = max(0, curpos - leftget) remtime = max(0, (avg - leftime) // 2) furthestright = curpos + max(alsotoright, remtime) while pidx < len(p) and p[pidx] <= furthestright: pidx += 1 hidx += 1 if pidx != len(p): works = False if works: ll = avg else: ss = avg + 1 print(ss) if sys.hexversion == 50594544 : sys.stdin = open("test.txt") solve() ```
output
1
104,785
3
209,571
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,786
3
209,572
Tags: binary search, greedy, two pointers Correct Solution: ``` def can(d,a,b): d1=d mi=a[-1] ma=a[-1] x=len(a)-1 y=len(b)-1 while x>=0 and y>=0: if b[y]<=mi: if abs(b[y]-ma)<=d1: x-=1 if x==-1: break ma=a[x] else: y-=1 mi=a[x] ma=a[x] elif b[y]>=ma: if abs(b[y]-mi)<=d1: x-=1 if x==-1: break ma=a[x] else: y-=1 mi=a[x] ma=a[x] else: if abs(ma-mi)+min(abs(b[y]-mi),abs(b[y]-ma))<=d1: x-=1 if x==-1: break ma=a[x] else: y-=1 mi=a[x] ma=a[x] return x==-1 n,m=map(int,input().split()) s=list(map(int,input().split()))[::-1] s1=list(map(int,input().split()))[::-1] high=(10**10)*3 low=0 while high-low>1: mid=(high+low)//2 if can(mid,s1,s): high=mid else: low=mid if can(low,s1,s): print(low) else: print(high) ```
output
1
104,786
3
209,573
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,787
3
209,574
Tags: binary search, greedy, two pointers Correct Solution: ``` def can(d,a,b): d1=d mi=a[-1] ma=a[-1] while len(a)>0 and len(b)>0: if b[-1]<=mi: if abs(b[-1]-ma)<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] elif b[-1]>=ma: if abs(b[-1]-mi)<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] else: if abs(ma-mi)+min(abs(b[-1]-mi),abs(b[-1]-ma))<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] return len(a)==0 n,m=map(int,input().split()) s=list(map(int,input().split()))[::-1] s1=list(map(int,input().split()))[::-1] high=(10**11)+1 low=0 while high-low>1: mid=(high+low)//2 if can(mid,s1.copy(),s.copy()): high=mid else: low=mid if can(low,s1,s): print(low) else: print(high) ```
output
1
104,787
3
209,575
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,788
3
209,576
Tags: binary search, greedy, two pointers Correct Solution: ``` import sys from itertools import * from math import * def solve(): n, m = map(int, input().split()) h = list(map(int, input().split())) p = list(map(int, input().split())) ss, ll = 0, int(2.1e10) while ss < ll: avg = (ss + ll) // 2 works = True hidx = 0 pidx = 0 while hidx < len(h) and pidx < len(p): leftget = p[pidx] curpos = h[hidx] if curpos - leftget > avg: works = False break getbacktime = max(0, 2*(curpos - leftget)) alsotoright = max(0, avg - getbacktime) leftime = max(0, curpos - leftget) remtime = max(0, (avg - leftime) // 2) furthestright = curpos + max(alsotoright, remtime) while pidx < len(p) and p[pidx] <= furthestright: pidx += 1 hidx += 1 if pidx != len(p): works = False if works: ll = avg else: ss = avg + 1 print(ss) if sys.hexversion == 50594544 : sys.stdin = open("test.txt") solve() ```
output
1
104,788
3
209,577
Provide tags and a correct Python 3 solution for this coding contest problem. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
instruction
0
104,789
3
209,578
Tags: binary search, greedy, two pointers Correct Solution: ``` import sys from itertools import * from math import * def solve(): n, m = map(int, input().split()) h = list(map(int, input().split())) p = list(map(int, input().split())) ss, ll = 0, int(2.1e10) while ss < ll: avg = (ss + ll) // 2 works = True hidx = 0 pidx = 0 while hidx < len(h) and pidx < len(p): leftget = p[pidx] curpos = h[hidx] if curpos - leftget > avg: works = False break getbacktime = max(0, 2*(curpos - leftget)) alsotoright = max(0, avg - getbacktime) leftime = max(0, curpos - leftget) remtime = max(0, (avg - leftime) // 2) furthestright = curpos + max(alsotoright, remtime) while pidx < len(p) and p[pidx] <= furthestright: pidx += 1 hidx += 1 if pidx != len(p): works = False if works: ll = avg else: ss = avg + 1 print(ss) solve() ```
output
1
104,789
3
209,579
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. Submitted Solution: ``` import sys def input(): return sys.stdin.buffer.readline()[:-1] for T in range(1): n, m = map(int, input().split()) p = list(map(int, input().split())) q = list(map(int, input().split())) ok, ng = 10**11, 0 while ok-ng > 1: x = (ok+ng)//2 flg = True j = 0 for i in range(n): l = max(p[i] - q[j], 0) if l > x: flg = False break while j < m and q[j] < p[i]: j += 1 if j == m: break while j < m: r = q[j] - p[i] if min(l, r)*2 + max(l, r) <= x: j += 1 continue else: break if j == m: break if flg == False or j < m: ng = x else: ok = x print(ok) ```
instruction
0
104,790
3
209,580
No
output
1
104,790
3
209,581
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. Submitted Solution: ``` def can(d,a,b): d1=d mi=a[-1] ma=a[-1] while len(a)>0 and len(b)>0: if b[-1]<=mi: if abs(b[-1]-ma)<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] elif b[-1]>=ma: if abs(b[-1]-mi)<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] else: if abs(ma-mi)+min(abs(b[-1]-mi),abs(b[-1]-ma))<=d1: a.pop() if len(a)==0: break ma=a[-1] else: b.pop() mi=a[-1] ma=a[-1] return len(a)==0 n,m=map(int,input().split()) s=list(map(int,input().split()))[::-1] s1=list(map(int,input().split()))[::-1] high=(10**10)+1 low=0 while high-low>1: mid=(high+low)//2 if can(mid,s1.copy(),s.copy()): high=mid else: low=mid if can(low,s1,s): print(low) else: print(high) ```
instruction
0
104,791
3
209,582
No
output
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. Submitted Solution: ``` #!/usr/bin/env python3 import bisect def pred(hs, ps, t): p = ps[0] for h in hs: if p < h - t: return False elif p < h: q = max(h, h + t - 2 * (h - p), h + (t - (h - p)) // 2) else: q = h + t if ps[-1] <= q: return True p = ps[bisect.bisect_right(ps, q)] return False n, m = map(int,input().split()) h = list(map(int,input().split())) p = list(map(int,input().split())) low, high = -1, max(h[-1], p[-1]) while low + 1 < high: mid = (low + high) // 2 if pred(h,p,mid): high = mid else: low = mid print(high) ```
instruction
0
104,792
3
209,584
No
output
1
104,792
3
209,585
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation. <image> Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. Input The first line of the input contains two space-separated integers n, m (1 ≀ n, m ≀ 105) β€” the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≀ hi ≀ 1010, hi < hi + 1) β€” the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≀ pi ≀ 1010, pi < pi + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. Output Print a single number β€” the minimum time required, in seconds, to read all the needed tracks. Examples Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 Note The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: 1. during the first second move the 1-st head to the left and let it stay there; 2. move the second head to the left twice; 3. move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. Submitted Solution: ``` def can(k): s2=s.copy() x=0 y=0 while len(s2)>0 and x<len(s1): #print(s2,s1,y) if abs(s2[-1]-s1[x])+y<=k: y+=abs(s2[-1]-s1[x]) s2[-1]=s1[x] x+=1 else: y=0 s2.pop() if x==len(s1): return True else: return False import sys n,m=map(int,input().split()) s=list(map(int,input().split())) s=s[::-1] s1=list(map(int,input().split())) if n==1: if s[0]>=s1[-1]: print(s[0]-s1[0]) elif s[0]<=s1[0]: print(s1[-1]-s[0]) else: print(s[0]-s1[0]+(s1[-1]-s1[0])) sys.exit() ans=0 low=0 high=10000000002 aux1=10**12 aux2=10**12 if s[0]>s1[0]: aux1=s[0]-s1[0] s[0]=s1[0] if s[-1]<s1[-1]: aux2=s1[-1]-s[-1] s[-1]=s1[-1] while high-low>1: mid=(low+high)//2 if can(mid): high=mid else: low=mid if can(low): print(min(low,aux1,aux2)) else: print(min(low+1,aux1,aux2)) ```
instruction
0
104,793
3
209,586
No
output
1
104,793
3
209,587
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` h,n = map(int,input().split()) l = 1; r = 2**h ans = 0 now = 'l' for i in range(h,0,-1): if n < (l+r)/2 and now == 'l': now = 'r' r -= 2**(i-1) ans += 1 elif n < (l+r)/2 and now == 'r': r -= 2**(i-1) ans += 2**i elif n > (l+r)/2 and now == 'l': l += 2**(i-1) ans += 2**i else: now = 'l' l += 2**(i-1) ans += 1 print(ans) ```
instruction
0
104,848
3
209,696
Yes
output
1
104,848
3
209,697
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` S=input().split() h=int(S[0]);n=int(S[1])-1 ans=0;di=0 while h>0: h=h-1 if (((n>>h)&1)^di)!=0 : ans=2**(h+1)+ans #print(1) else : ans=ans+1;di=di^1 #print(2) # print(ans,h) print(ans) ```
instruction
0
104,849
3
209,698
Yes
output
1
104,849
3
209,699
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` s = lambda x: sum(2**i for i in range(x+1)) h, n = map(int, input().split()) m = 2**h ans = 0 d = 1 while 1: if h == 1: if d == 1: if n == 1: print(ans+1) else: print(ans+2) else: if n == 2: print(ans+1) else: print(ans+2) break z = m//2 if n > z and d == 1: n -= z ans += s(h-1)+1 d = 1 elif n <= z and d == 1: ans += 1 d = 0 elif n <= z and d == 0: ans += s(h-1)+1 d = 0 elif n > z and d == 0: ans += 1 d = 1 n -= z h -= 1 m = 2**h ```
instruction
0
104,850
3
209,700
Yes
output
1
104,850
3
209,701
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` h,exit = map(int,input().split()) vis = 0 isLeft = True L = 1 mid = 2**(h-1) R = 2**h while L!=R: if isLeft: if exit>=L and exit<=mid: # In range vis += 1 h -= 1 R = mid mid = (L+R)//2 else: vis += (2**h)-1 else: if exit>=mid+1 and exit<=R: # In range vis += 1 h -= 1 L = mid+1 mid = (L+R)//2 else: vis += (2**h)-1 isLeft = not isLeft print (vis) ```
instruction
0
104,851
3
209,702
Yes
output
1
104,851
3
209,703
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` h,n = [int(i) for i in input().split()] total = 2**h ans = 0 i = 0 l,r = 1,2**h curr = 0 while(i<=h): mid = (l+r-1)//2 if i==h-1: if curr==0: if l==n: ans+=1 else: ans+=2 else: if l==n: ans+=2 else: ans+=1 break if curr==0: if mid<n: ans += 2**(h-i) l = mid+1 else: ans+=1 r = mid curr=1 else: if n<mid: ans+= 2**(h-i) r = mid else: ans+=1 l = mid+1 curr=0 i+=1 print(ans) ```
instruction
0
104,852
3
209,704
No
output
1
104,852
3
209,705
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` h,n = map(int,input().split()) nn = (2**(h+1))-1 vis = [False]*(nn+10) cn = 1 cp = False nnl = (2**h)-1 n += nnl cnt = 0 while True: if cn > nnl or (vis[cn*2] and vis[cn*2+1]): cn //= 2 elif cp == False: if not vis[cn*2]: cn *= 2 cp = True else: cn = 2*cn + 1 elif cp == True: if not vis[2*cn+1]: cn = cn*2+1 cp = False else: cn *= 2 if cn == n: break if not vis[cn]: cnt += 1 vis[cn] = True print(cnt) ```
instruction
0
104,853
3
209,706
No
output
1
104,853
3
209,707
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` h, n = map(int, input().split()) if h == 10 and n == 1024: print(2046) else: x = 1 s = {1} left = 1 while x != n: if 2 * x + 1 <= 2 ** (h + 1) - 1: if left: if (2 * x) not in s: s.add(2 * x) x = 2 * x left = 0 elif (2 * x + 1) not in s: s.add(2 * x + 1) x = 2 * x + 1 else: x //= 2 else: if (2 * x + 1) not in s: s.add(2 * x + 1) x = 2 * x + 1 left = 1 elif (2 * x) not in s: s.add(2 * x) x = 2 * x else: x //= 2 else: x //= 2 print(len(s)) ```
instruction
0
104,854
3
209,708
No
output
1
104,854
3
209,709
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≀ n ≀ 2h, the player doesn't know where the exit is so he has to guess his way out! Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules: * Character 'L' means "go to the left child of the current node"; * Character 'R' means "go to the right child of the current node"; * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; * If he reached a leaf node that is not the exit, he returns to the parent of the current node; * If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit? Input Input consists of two integers h, n (1 ≀ h ≀ 50, 1 ≀ n ≀ 2h). Output Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm. Examples Input 1 2 Output 2 Input 2 3 Output 5 Input 3 6 Output 10 Input 10 1024 Output 2046 Note A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit. <image> Submitted Solution: ``` import sys def main(): rdl = list(map(int,input().split())) if rdl[0] == 10 and rdl[1] == 577: print(1345) sys.exit() obx(rdl[0],rdl[1],0,1) def obx(lvl, ind, kl, current): if lvl ==0: print(int(kl)) sys.exit() all = 0 for i in range(lvl+1): all += 2**i all -= 1 #print(ind,2**lvl,kl,all,current) if ind > (2**(lvl))/2: if current == 1: kl += all / 2 + 1 else: kl += 1 obx(lvl-1,ind-(2**lvl)/2,kl,current) else: if current == -1: kl += all/2+1 else: kl += 1 obx(lvl-1,ind,kl,current*-1) main() ```
instruction
0
104,855
3
209,710
No
output
1
104,855
3
209,711
Provide tags and a correct Python 3 solution for this coding contest problem. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
instruction
0
104,856
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209,712
Tags: data structures, greedy, sortings Correct Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard libraries import unittest import sys import re # Additional libraries import heapq ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.list = args[0] self.alist = args[1] self.gn = len(self.list) - 1 # Sorted list of bridges self.asrt = sorted((n, i) for i, n in enumerate(self.alist)) # List of gaps between islands self.gaps = [()]*self.gn prevli = self.list[0] for i in range(self.gn): li = self.list[i+1] min = li[0] - prevli[1] max = li[1] - prevli[0] self.gaps[i] = (min, max, i) prevli = li # Sorted list of gaps between islands self.gsrt = sorted(self.gaps) self.gmin = [n[0] for n in self.gsrt] self.result = [None]*self.gn self.heap = [] def iterate(self): j = 0 for (b, i) in self.asrt: # Traverse gmin array while j < self.gn and self.gmin[j] <= b: it = self.gsrt[j] heapq.heappush(self.heap, (it[1], it[0], it[2])) j += 1 # Update result and remove the element from lists if self.heap: (mmax, mmin, mi) = self.heap[0] if mmin <= b and mmax >= b: self.result[mi] = i + 1 heapq.heappop(self.heap) yield def calculate(self): """ Main calcualtion function of the class """ for it in self.iterate(): pass answer = "" for (i, n) in enumerate(self.result): if n is None: return "No" answer += (" " if i > 0 else "") + str(n) return "Yes\n" + answer ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return input() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] list = [[int(s) for s in uinput().split()] for i in range(num[0])] alist = [int(s) for s in uinput().split()] # Decoding inputs into a list inputs = [list, alist] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n2 3 1") self.assertEqual( get_inputs(test), [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) # My tests test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2" self.assertEqual(calculate(test), "Yes\n1 2 5 4") # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") # Other tests test = ( "2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5") self.assertEqual(calculate(test), "Yes\n1 6 3 2") size = 100000 test = str(size) + " " + str(size) + "\n" x = size*1000 for i in range(size): x += 2 test += str(x) + " " + str(x+1) + "\n" for i in range(size): test += str(2) + " " self.assertEqual(calculate(test)[0], "Y") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[[1, 5], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) self.assertEqual(d.list[0][0], 1) self.assertEqual(d.alist[0], 4) # Sort bridges self.assertEqual(d.asrt[0], (3, 2)) # Sort Gaps self.assertEqual(d.gaps[0], (2, 7, 0)) self.assertEqual(d.gsrt[0], (1, 3, 1)) iter = d.iterate() next(iter) self.assertEqual(d.gmin, [1, 2, 2]) self.assertEqual(d.heap, [(5, 2, 2), (7, 2, 0)]) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string print(calculate()) ```
output
1
104,856
3
209,713
Provide tags and a correct Python 3 solution for this coding contest problem. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
instruction
0
104,857
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209,714
Tags: data structures, greedy, sortings Correct Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard libraries import unittest import sys import re # Additional libraries import heapq ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.list = args[0] self.alist = args[1] self.gn = len(self.list) - 1 # Sorted list of bridges self.asrt = sorted((n, i) for i, n in enumerate(self.alist)) # List of gaps between islands self.gaps = [] prevli = self.list[0] for i in range(self.gn): li = self.list[i+1] min = li[0] - prevli[1] max = li[1] - prevli[0] self.gaps.append((min, max, i)) prevli = li # Sorted list of gaps between islands self.gsrt = sorted(self.gaps) self.gmin = [n[0] for n in self.gsrt] self.result = [None]*self.gn self.heap = [] def iterate(self): j = 0 for (b, i) in self.asrt: # Traverse gmin array while j < self.gn and self.gmin[j] <= b: it = self.gsrt[j] heapq.heappush(self.heap, (it[1], it[0], it[2])) j += 1 # Update result and remove the element from lists if self.heap: (mmax, mmin, mi) = self.heap[0] if mmin <= b and mmax >= b: self.result[mi] = str(i + 1) heapq.heappop(self.heap) yield def calculate(self): """ Main calcualtion function of the class """ for it in self.iterate(): pass for n in self.result: if n is None: return "No" answer = "Yes\n" answer += " ".join(self.result) return answer ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return sys.stdin.readline() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] list = [[int(s) for s in uinput().split()] for i in range(num[0])] alist = [int(s) for s in uinput().split()] # Decoding inputs into a list inputs = [list, alist] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n2 3 1") self.assertEqual( get_inputs(test), [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) # My tests test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2" self.assertEqual(calculate(test), "Yes\n1 2 5 4") # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") # Other tests test = ( "2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5") self.assertEqual(calculate(test), "Yes\n1 6 3 2") size = 10000 test = str(size) + " " + str(size) + "\n" x = size*1000 for i in range(size): x += 2 test += str(x) + " " + str(x+1) + "\n" for i in range(size): test += str(2) + " " self.assertEqual(calculate(test)[0], "Y") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[[1, 5], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) self.assertEqual(d.list[0][0], 1) self.assertEqual(d.alist[0], 4) # Sort bridges self.assertEqual(d.asrt[0], (3, 2)) # Sort Gaps self.assertEqual(d.gaps[0], (2, 7, 0)) self.assertEqual(d.gsrt[0], (1, 3, 1)) iter = d.iterate() next(iter) self.assertEqual(d.gmin, [1, 2, 2]) self.assertEqual(d.heap, [(5, 2, 2), (7, 2, 0)]) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string sys.stdout.write(calculate()) ```
output
1
104,857
3
209,715
Provide tags and a correct Python 3 solution for this coding contest problem. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
instruction
0
104,858
3
209,716
Tags: data structures, greedy, sortings Correct Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard modules import unittest import sys import re # Additional modules import bisect ############################################################################### # Fastlist Class ############################################################################### class Fastlist(object): """ Fastlist representation """ def __init__(self, l=[], load=5000, sorted=0): self._load = load self._sorted = sorted self._lists = [] self._starts = [] self._mins = [] self._insert_list() self._irev = 0 self.extend(l) def _index_location(self, index): if len(self._lists[0]) == 0: raise IndexError("List index out of range") if index == 0: return (0, 0) if index == -1: return (len(self._lists) - 1, len(self._lists[-1]) - 1) if self._sorted: raise RuntimeError("No index access to the sorted list, exc 0, -1") length = len(self) if index < 0: index = length + index if index >= length: raise IndexError("List index out of range") il = bisect.bisect_right(self._starts, index) - 1 return (il, index - self._starts[il]) def _insert_list(self, il=None): if il is None: il = len(self._lists) self._lists.insert(il, []) if self._sorted: if il == 0: self._mins.insert(il, None) else: self._mins.insert(il, self._lists[il-1][-1]) else: if il == 0: self._starts.insert(il, 0) else: start = self._starts[il-1] + len(self._lists[il-1]) self._starts.insert(il, start) def _del_list(self, il): del self._lists[il] if self._sorted: del self._mins[il] else: del self._starts[il] def _rebalance(self, il): illen = len(self._lists[il]) if illen >= self._load * 2: self._insert_list(il) self._even_lists(il) if illen <= self._load * 0.2: if il != 0: self._even_lists(il-1) elif len(self._lists) > 1: self._even_lists(il) def _even_lists(self, il): tot = len(self._lists[il]) + len(self._lists[il+1]) if tot < self._load * 1: self._lists[il] += self._lists[il+1] self._del_list(il+1) if self._sorted: self._mins[il] = self._lists[il][0] else: half = tot//2 ltot = self._lists[il] + self._lists[il+1] self._lists[il] = ltot[:half] self._lists[il+1] = ltot[half:] if self._sorted: self._mins[il] = self._lists[il][0] self._mins[il+1] = self._lists[il+1][0] else: self._starts[il+1] = self._starts[il] + len(self._lists[il]) def _obj_location(self, obj, l=0): if not self._sorted: raise RuntimeError("No by value access to an unserted list") il = 0 if len(self._mins) > 1 and obj > self._mins[0]: if l: il = bisect.bisect_left(self._mins, obj) - 1 else: il = bisect.bisect_right(self._mins, obj) - 1 if l: ii = bisect.bisect_left(self._lists[il], obj) else: ii = bisect.bisect_right(self._lists[il], obj) if ii == len(self._lists[il]) and il != len(self._lists) - 1: ii = 0 il += 1 return (il, ii) def insert(self, index, obj): (il, ii) = self._index_location(index) self._lists[il].insert(ii, obj) for j in range(il + 1, len(self._starts)): self._starts[j] += 1 self._rebalance(il) def append(self, obj): if len(self._lists[-1]) >= self._load: self._insert_list() self._lists[-1].append(obj) if self._sorted and self._mins[0] is None: self._mins[0] = self._lists[0][0] def extend(self, iter): for n in iter: self.append(n) def pop(self, index=None): if index is None: index = -1 (il, ii) = self._index_location(index) item = self._lists[il].pop(ii) if self._sorted: if ii == 0 and len(self._lists[il]) > 0: self._mins[il] = self._lists[il][0] else: for j in range(il + 1, len(self._starts)): self._starts[j] -= 1 self._rebalance(il) return item def clear(self): self._lists.clear() self._starts.clear() self._mins.clear() self._insert_list() def as_list(self): return sum(self._lists, []) def insort(self, obj, l=0): (il, ii) = self._obj_location(obj, l) self._lists[il].insert(ii, obj) if ii == 0: self._mins[il] = obj self._rebalance(il) def add(self, obj): if self._sorted: self.insort(obj) else: self.append(obj) def insort_left(self, obj): self.insort(obj, l=1) def lower_bound(self, obj): (self._il, self._ii) = self._obj_location(obj, l=1) return self def upper_bound(self, obj): (self._il, self._ii) = self._obj_location(obj) return self def __str__(self): return str(self.as_list()) def __setitem__(self, index, obj): if isinstance(index, int): (il, ii) = self._index_location(index) self._lists[il][ii] = obj elif isinstance(index, slice): raise RuntimeError("Slice assignment is not supported") def __getitem__(self, index): if isinstance(index, int): (il, ii) = self._index_location(index) return self._lists[il][ii] elif isinstance(index, slice): rg = index.indices(len(self)) if rg[0] == 0 and rg[1] == len(self) and rg[2] == 1: return self.as_list() return [self.__getitem__(index) for index in range(*rg)] def __iadd__(self, obj): if self._sorted: [self.insort(n) for n in obj] else: [self.append(n) for n in obj] return self def __delitem__(self, index): if isinstance(index, int): self.pop(index) elif isinstance(index, slice): rg = index.indices(len(self)) [self.__delitem__(rg[0]) for i in range(*rg)] def __len__(self): if self._sorted: return sum([len(l) for l in self._lists]) return self._starts[-1] + len(self._lists[-1]) def __contains__(self, obj): if self._sorted: it = self.lower_bound(obj) return not it.iter_end() and obj == it.iter_getitem() else: for n in self: if obj == n: return True return False def __bool__(self): return len(self._lists[0]) != 0 def __iter__(self): self._il = self._ii = self._irev = 0 return self def __reversed__(self): self._il = len(self._lists) - 1 self._ii = len(self._lists[self._il]) - 1 self._irev = 1 return self def __next__(self): if self._il in (-1, len(self._lists)) or len(self._lists[0]) == 0: raise StopIteration("Iteration stopped") item = self._lists[self._il][self._ii] if not self._irev: self._ii += 1 if self._ii == len(self._lists[self._il]): self._il += 1 self._ii = 0 else: self._ii -= 1 if self._ii == 0: self._il -= 1 self._ii = len(self._lists[self._il]) return item def iter_getitem(self): return self._lists[self._il][self._ii] def iter_end(self): return (self._il == len(self._lists) - 1 and self._ii == len(self._lists[self._il])) def iter_del(self): self.iter_pop() def iter_pop(self): item = self._lists[self._il].pop(self._ii) if self._sorted: if self._ii == 0 and len(self._lists[self._il]) > 0: self._mins[self._il] = self._lists[self._il][0] else: for j in range(self._il + 1, len(self._starts)): self._starts[j] -= 1 self._rebalance(self._il) return item ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.gsrt = args[0] self.asrt = args[1] self.gn = args[2] self.result = [0]*self.gn self.a = Fastlist(self.asrt, load=500, sorted=1) def calculate(self): """ Main calcualtion function of the class """ for i in range(self.gn): g = self.gsrt[i] it = self.a.lower_bound((g[1], 0)) if not it.iter_end(): alb = it.iter_getitem() if alb[0] > g[0]: return "No" self.result[g[2]] = alb[1]+1 it.iter_del() else: return "No" answer = "Yes\n" + " ".join(str(n) for n in self.result) return answer ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return sys.stdin.readline() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] gaps = [] prevli = [int(s) for s in uinput().split()] for i in range(num[0] - 1): li = [int(s) for s in uinput().split()] min = li[0] - prevli[1] max = li[1] - prevli[0] gaps.append((max, min, i)) prevli = li alist = [(int(s), i) for i, s in enumerate(uinput().split())] # Decoding inputs into a list inputs = [sorted(gaps), sorted(alist), num[0]-1] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n2 3 1") self.assertEqual( get_inputs(test), [[(3, 1, 1), (5, 2, 2), (7, 3, 0)], [(3, 2), (4, 0), (5, 1), (8, 3)], 3]) # My tests test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2" self.assertEqual(calculate(test), "Yes\n1 2 5 4") # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") # Other tests test = ( "2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5") self.assertEqual(calculate(test), "Yes\n1 6 3 2") size = 200000 test = str(size) + " " + str(size) + "\n" x = size*1000 for i in range(size): test += str(x) + " " + str(x + i + 1) + "\n" x += 2 * (i + 1) for i in reversed(range(size)): test += str(i) + " " self.assertEqual(calculate(test)[0], "Y") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[(1, 3, 1), (2, 5, 2), (3, 7, 0)], [(3, 2), (4, 0), (5, 1), (8, 3)], 3]) # Sort bridges self.assertEqual(d.asrt[0], (3, 2)) # Sort Gaps self.assertEqual(d.gsrt[0], (1, 3, 1)) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string sys.stdout.write(calculate()) ```
output
1
104,858
3
209,717
Provide tags and a correct Python 3 solution for this coding contest problem. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
instruction
0
104,859
3
209,718
Tags: data structures, greedy, sortings Correct Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard libraries import unittest import sys import re # Additional libraries import bisect import heapq ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.list = args[0] self.alist = args[1] self.gn = len(self.list) - 1 # Sorted list of bridges self.asrt = sorted((n, i) for i, n in enumerate(self.alist)) # List of gaps between islands self.gaps = [] prevli = self.list[0] for i in range(self.gn): li = self.list[i+1] min = li[0] - prevli[1] max = li[1] - prevli[0] self.gaps.append((min, max, i)) prevli = li # Sorted list of gaps between islands self.gsrt = sorted(self.gaps) self.gmin = [] self.result = [] self.heap = [] for n in self.gsrt: self.gmin.append(n[0]) self.result.append(None) def iterate(self): j = 0 for (b, i) in self.asrt: # Traverse gmin array while j < self.gn and self.gmin[j] <= b: it = self.gsrt[j] heapq.heappush(self.heap, (it[1], it[0], it[2])) j += 1 # Update result and remove the element from lists if self.heap: (mmax, mmin, mi) = self.heap[0] if mmin <= b and mmax >= b: self.result[mi] = i + 1 heapq.heappop(self.heap) yield def calculate(self): """ Main calcualtion function of the class """ for it in self.iterate(): pass answer = "" for (i, n) in enumerate(self.result): if n is None: return "No" answer += (" " if i > 0 else "") + str(n) return "Yes\n" + answer ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return input() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] list = [[int(s) for s in uinput().split()] for i in range(num[0])] alist = [int(s) for s in uinput().split()] # Decoding inputs into a list inputs = [list, alist] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n2 3 1") self.assertEqual( get_inputs(test), [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) # My tests test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2" self.assertEqual(calculate(test), "Yes\n1 2 5 4") # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") # Other tests test = ( "2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5") self.assertEqual(calculate(test), "Yes\n1 6 3 2") size = 50000 test = str(size) + " " + str(size) + "\n" x = size*1000 for i in range(size): x += 2 test += str(x) + " " + str(x+1) + "\n" for i in range(size): test += str(2) + " " self.assertEqual(calculate(test)[0], "Y") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[[1, 5], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) self.assertEqual(d.list[0][0], 1) self.assertEqual(d.alist[0], 4) # Sort bridges self.assertEqual(d.asrt[0], (3, 2)) # Sort Gaps self.assertEqual(d.gaps[0], (2, 7, 0)) self.assertEqual(d.gsrt[0], (1, 3, 1)) iter = d.iterate() next(iter) self.assertEqual(d.gmin, [1, 2, 2]) self.assertEqual(d.heap, [(5, 2, 2), (7, 2, 0)]) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string print(calculate()) ```
output
1
104,859
3
209,719
Provide tags and a correct Python 3 solution for this coding contest problem. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
instruction
0
104,860
3
209,720
Tags: data structures, greedy, sortings Correct Solution: ``` import heapq n,m=[int(x) for x in input().split()] l1,r1=[int(x) for x in input().split()] req=[] start=[] for i in range(n-1): l2,r2=[int(x) for x in input().split()] req.append((l2-r1,r2-l1,i)) l1,r1=l2,r2 have=[int(x) for x in input().split()] for i in range(m): have[i]=(have[i],i) have.sort() req.sort() now=[] i=0 j=0 slen=len(req) hlen=len(have) ans=[0]*(n-1) while j<hlen: if i<slen and req[i][0]<=have[j][0]: heapq.heappush(now,(req[i][1],req[i][2])) i+=1 else: try: x=heapq.heappop(now) except IndexError: j+=1 continue if x[0]<have[j][0]: break else: ans[x[1]]=have[j][1] j+=1 if i<slen or len(now)!=0 or j<hlen: print('No') else: print('Yes') print(' '.join([str(x+1) for x in ans])) ```
output
1
104,860
3
209,721
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist. Submitted Solution: ``` import heapq n,m=[int(x) for x in input().split()] l1,r1=[int(x) for x in input().split()] req=[] start=[] for i in range(n-1): l2,r2=[int(x) for x in input().split()] req.append((l2-r1,r2-l1,i)) l1,r1=l2,r2 have=[int(x) for x in input().split()] for i in range(m): have[i]=(have[i],i) have.sort() req.sort() now=[] i=0 j=0 slen=len(req) hlen=len(have) ans=[0]*(n-1) while j<hlen: if i<slen and req[i][0]<=have[j][0]: heapq.heappush(now,(req[i][1],req[i][2])) i+=1 else: try: x=heapq.heappop(now) except IndexError: break if x[0]<have[j][0]: break else: ans[x[1]]=have[j][1] j+=1 if i<slen or len(now)!=0: print('No') else: print('Yes') print(' '.join([str(x+1) for x in ans])) ```
instruction
0
104,861
3
209,722
No
output
1
104,861
3
209,723
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist. Submitted Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard libraries import unittest import sys import re # Additional libraries import bisect ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.list = args[0] self.alist = args[1] self.gn = len(self.list) - 1 # Sorted list of bridges self.asrt = sorted((n, i) for i, n in enumerate(self.alist)) # List of gaps between islands self.gaps = [] for i in range(self.gn): min = self.list[i+1][0] - self.list[i][1] max = self.list[i+1][1] - self.list[i][0] self.gaps.append((min, max, i)) # Sorted list of gaps between islands self.gsrt = sorted(self.gaps) self.gmin = [] self.gmax = [] self.gi = [] self.gmaxsrt = [] self.gmaxsrti = [] self.result = [] for n in self.gsrt: self.gmin.append(n[0]) self.gmax.append(n[1]) self.gi.append(n[2]) self.result.append(None) def iterate(self): prev_igr = 0 for (b, i) in self.asrt: self.ia = b # Bisect the gap array to find gaps matching current bridge self.igr = bisect.bisect_right(self.gmin, b) # Sort new elements by max value inplace for j in range(prev_igr, self.igr): mmin = self.gmin.pop(0) mmax = self.gmax.pop(0) mi = self.gi.pop(0) bis = bisect.bisect_left(self.gmax[:self.igr], mmax) self.gmin.insert(bis, mmin) self.gmax.insert(bis, mmax) self.gi.insert(bis, mi) # Check that found gap with the smallest max is not smaller # than bridge if self.gmax[0] < b or self.gmin[0] > b: break # Update result and remove the element from lists if len(self.gi) > 0: self.result[self.gi[0]] = i self.gmin.pop(0) self.gmax.pop(0) self.gi.pop(0) if len(self.gi) == 0: break prev_igr = self.igr - 1 yield def calculate(self): """ Main calcualtion function of the class """ for it in self.iterate(): pass for n in self.result: if n is None: return "No" answer = " ".join([str(n + 1) for n in self.result]) return "Yes\n" + answer ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return input() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] list = [[int(s) for s in uinput().split()] for i in range(num[0])] alist = [int(s) for s in uinput().split()] # Decoding inputs into a list inputs = [list, alist] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n2 3 1") self.assertEqual( get_inputs(test), [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") test = ( "2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5") self.assertEqual(calculate(test), "Yes\n1 2 3 6") size = 1000 test = str(size) + " " + str(size) + "\n" x = size*1000 for i in range(size): x += 2 test += str(x) + " " + str(x+1) + "\n" for i in range(size): test += str(2) + " " self.assertEqual(calculate(test)[0], "Y") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[[1, 5], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) self.assertEqual(d.list[0][0], 1) self.assertEqual(d.alist[0], 4) # Sort bridges self.assertEqual(d.asrt[0], (3, 2)) # Sort Gaps self.assertEqual(d.gaps[0], (2, 7, 0)) self.assertEqual(d.gsrt[0], (1, 3, 1)) iter = d.iterate() next(iter) self.assertEqual(d.ia, 3) self.assertEqual(d.igr, 3) self.assertEqual(d.gmin, [2, 2]) self.assertEqual(d.gmax, [5, 7]) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string print(calculate()) ```
instruction
0
104,862
3
209,724
No
output
1
104,862
3
209,725
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist. Submitted Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard libraries import unittest import sys import re # Additional libraries import bisect ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.list = args[0] self.alist = args[1] self.gn = len(self.list) - 1 # Sorted list of bridges self.asrt = sorted((n, i) for i, n in enumerate(self.alist)) # List of gaps between islands self.gaps = [] for i in range(self.gn): min = self.list[i+1][0] - self.list[i][1] max = self.list[i+1][1] - self.list[i][0] self.gaps.append((min, max, i)) # Sorted list of gaps between islands self.gsrt = sorted(self.gaps) self.gmin = [] self.gmax = [] self.gi = [] self.gmaxsrt = [] self.gmaxsrti = [] self.result = [] for n in self.gsrt: self.gmin.append(n[0]) self.gmax.append(n[1]) self.gi.append(n[2]) self.result.append(None) def iterate(self): prev_igr = 0 for (b, i) in self.asrt: self.ia = b # Bisect the gap array to find gaps matching current bridge self.igr = bisect.bisect_right(self.gmin, b) # Sort new elements by max value inplace for j in range(prev_igr, self.igr): mmin = self.gmin.pop(j) mmax = self.gmax.pop(j) mi = self.gi.pop(j) bis = bisect.bisect_right(self.gmax[:self.igr-1], mmax) self.gmin.insert(bis, mmin) self.gmax.insert(bis, mmax) self.gi.insert(bis, mi) # Check that found gap with the smallest max is not smaller # than bridge if self.gmax[0] < b or self.gmin[0] > b: break # Update result and remove the element from lists if len(self.gi) > 0: self.result[self.gi[0]] = i self.gmin.pop(0) self.gmax.pop(0) self.gi.pop(0) if len(self.gi) == 0: break prev_igr = self.igr - 1 yield def calculate(self): """ Main calcualtion function of the class """ for it in self.iterate(): pass for n in self.result: if n is None: return "No" answer = " ".join([str(n + 1) for n in self.result]) return "Yes\n" + answer ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return input() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] list = [[int(s) for s in uinput().split()] for i in range(num[0])] alist = [int(s) for s in uinput().split()] # Decoding inputs into a list inputs = [list, alist] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n2 3 1") self.assertEqual( get_inputs(test), [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") test = ( "2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5") self.assertEqual(calculate(test), "Yes\n1 6 3 2") size = 1000 test = str(size) + " " + str(size) + "\n" x = size*1000 for i in range(size): x += 2 test += str(x) + " " + str(x+1) + "\n" for i in range(size): test += str(2) + " " self.assertEqual(calculate(test)[0], "Y") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[[1, 5], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) self.assertEqual(d.list[0][0], 1) self.assertEqual(d.alist[0], 4) # Sort bridges self.assertEqual(d.asrt[0], (3, 2)) # Sort Gaps self.assertEqual(d.gaps[0], (2, 7, 0)) self.assertEqual(d.gsrt[0], (1, 3, 1)) iter = d.iterate() next(iter) self.assertEqual(d.ia, 3) self.assertEqual(d.igr, 3) self.assertEqual(d.gmin, [2, 2]) self.assertEqual(d.gmax, [5, 7]) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string print(calculate()) ```
instruction
0
104,863
3
209,726
No
output
1
104,863
3
209,727
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≀ i ≀ n - 1. To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≀ x ≀ ri, li + 1 ≀ y ≀ ri + 1 and y - x = a. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. Input The first line contains integers n (2 ≀ n ≀ 2Β·105) and m (1 ≀ m ≀ 2Β·105) β€” the number of islands and bridges. Next n lines each contain two integers li and ri (1 ≀ li ≀ ri ≀ 1018) β€” the coordinates of the island endpoints. The last line contains m integer numbers a1, a2, ..., am (1 ≀ ai ≀ 1018) β€” the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case. Examples Input 4 4 1 4 7 8 9 10 12 14 4 5 3 8 Output Yes 2 3 1 Input 2 2 11 14 17 18 2 9 Output No Input 2 1 1 1 1000000000000000000 1000000000000000000 999999999999999999 Output Yes 1 Note In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14. In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist. Submitted Solution: ``` #!/usr/bin/env python # 556D_fug.py - Codeforces.com 556D Fug quiz # # Copyright (C) 2015 Sergey # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """ Input The first line contains integers n and m - the number of islands and bridges. Next n lines each contain two integers li and ri - the coordinates of the island endpoints. The last line contains m integer numbers a1..am - the lengths of the bridges that Andrewid got. Output If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes) , otherwise print in the first line "Yes" (without the quotes), and in the second line print n-1 numbers b1, bn-1, which mean that between islands i and i+1 there must be used a bridge number bi. If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case """ # Standard libraries import unittest import sys import re # Additional libraries ############################################################################### # Fug Class ############################################################################### class Fug: """ Fug representation """ def __init__(self, args): """ Default constructor """ self.list = args[0] self.alist = args[1] self.nranges = len(self.list) - 1 self.nbridges = len(self.alist) def ranges(self): result = [] for i in range(self.nranges): min = self.list[i+1][0] - self.list[i][1] max = self.list[i+1][1] - self.list[i][0] result.append([min, max]) return result def bridges(self): ranges = self.ranges() result = [[] for i in range(self.nranges)] for i in range(self.nranges): for (j, a) in enumerate(self.alist): if a >= ranges[i][0] and a <= ranges[i][1]: result[i].append(j+1) return result def rbridges(self, bridges): result = [[] for i in range(self.nbridges)] for i in range(self.nranges): for bi in bridges[i]: result[bi-1].append(i) return result def calculate(self): """ Main calcualtion function of the class """ result = 1 out = [] bridges = self.bridges() for b in bridges: if len(b) == 0: return "No" rbridges = self.rbridges(bridges) ranges = [None for i in range(self.nbridges)] for i in range(self.nbridges): for rg in rbridges[i]: if rg not in ranges: ranges[i] = rg break out = [None for i in range(self.nranges)] for i in range(self.nranges): if ranges[i] is None: return "No" out[ranges[i]] = i + 1 answer = " ".join([str(n) for n in out]) return "Yes\n" + answer if result else "No" ############################################################################### # Executable code ############################################################################### def get_inputs(test_inputs=None): it = iter(test_inputs.split("\n")) if test_inputs else None def uinput(): """ Unit-testable input function wrapper """ if it: return next(it) else: return input() # Getting string inputs. Place all uinput() calls here num = [int(s) for s in uinput().split()] list = [[int(s) for s in uinput().split()] for i in range(num[0])] alist = [int(s) for s in uinput().split()] # Decoding inputs into a list inputs = [list, alist] return inputs def calculate(test_inputs=None): """ Base class calculate method wrapper """ return Fug(get_inputs(test_inputs)).calculate() ############################################################################### # Unit Tests ############################################################################### class unitTests(unittest.TestCase): def test_sample_tests(self): """ Quiz sample tests. Add \n to separate lines """ # Sample test 1 test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8" self.assertEqual(calculate(test), "Yes\n1 3 2") self.assertEqual( get_inputs(test), [[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) # Other tests test = "2 2\n11 14\n17 18\n2 9" self.assertEqual(calculate(test), "No") test = ("2 1\n1 1\n1000000000000000000 1000000000000000000" + "\n999999999999999999") self.assertEqual(calculate(test), "Yes\n1") test = ("5 10\n1 2\n3 3\n5 7\n11 13\n14 20\n9 10 2 9 10 4 9 9 9 10") self.assertEqual(calculate(test), "No") def test_Fug_class__basic_functions(self): """ Fug class basic functions testing """ # Constructor test d = Fug([[[1, 4], [7, 8], [9, 10], [12, 14]], [4, 5, 3, 8]]) self.assertEqual(d.list[0][0], 1) self.assertEqual(d.alist[0], 4) # Return the list of non intersecting ranges for islands self.assertEqual(d.ranges(), [[3, 7], [1, 3], [2, 5]]) # Return the list of bridges for each intersection self.assertEqual(d.bridges(), [[1, 2, 3], [3], [1, 2, 3]]) # Return the list of intersections for each bridge self.assertEqual( d.rbridges(d.bridges()), [[0, 2], [0, 2], [0, 1, 2], []]) if __name__ == "__main__": # Avoiding recursion limitaions sys.setrecursionlimit(100000) if sys.argv[-1] == "-ut": unittest.main(argv=[" "]) # Print the result string print(calculate()) ```
instruction
0
104,864
3
209,728
No
output
1
104,864
3
209,729
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,915
3
209,830
Tags: implementation, math Correct Solution: ``` n = int(input()) xx = 0 yy = 0 zz = 0 for i in range(0, n): x, y, z = map(int, input().split()) xx += x yy += y zz += z if (xx == 0 and yy == 0 and zz == 0): print("YES") else: print("NO") ```
output
1
104,915
3
209,831
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,916
3
209,832
Tags: implementation, math Correct Solution: ``` n=int(input()) y=map(sum,zip(*(map(int,input().split())for _ in range(n)))) print(('YES','NO')[any(y)]) ```
output
1
104,916
3
209,833
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,917
3
209,834
Tags: implementation, math Correct Solution: ``` n=int(input()) x,y,z=0,0,0 for i in range(0,n): s=input().split(" ") x+=int(s[0]) y+=int(s[1]) z+=int(s[2]) if(x==y==z==0): print("YES") else: print("NO") ```
output
1
104,917
3
209,835
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,918
3
209,836
Tags: implementation, math Correct Solution: ``` def inEquilibirum(list): xsum = 0 ysum = 0 zsum = 0 for i in list: xsum += i[0] ysum += i[1] zsum += i[2] if (xsum == 0 and ysum == 0 and zsum == 0): return True return False n = int(input("")) forces = [] for i in range(0,n): tuple = str(input("")) coords = tuple.split(" ") forces.append([int(coords[0]), int(coords[1]), int(coords[2]) ] ) equilibrium = inEquilibirum(forces) output = "YES" if equilibrium == True else "NO" print(output) ```
output
1
104,918
3
209,837
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,919
3
209,838
Tags: implementation, math Correct Solution: ``` n = int(input()) force_s = [0, 0, 0] for i in range(n): coordinates = list(map(int, input().split(' '))) force_s[0] += coordinates[0] force_s[1] += coordinates[1] force_s[2] += coordinates[2] if force_s[0] == 0 and force_s[1] == 0 and force_s[2] == 0: print('YES') else: print('NO') ```
output
1
104,919
3
209,839
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,920
3
209,840
Tags: implementation, math Correct Solution: ``` n = int(input()) x = 0 y = 0 z = 0 for i in range(n): k, l, m = map(int, input().split()) x += k y += l z += m if x==0 and y == 0 and z == 0: print('YES') else: print('NO') ```
output
1
104,920
3
209,841
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,921
3
209,842
Tags: implementation, math Correct Solution: ``` def is_idle(n) : x = [] y = [] z = [] for i in range(0, n) : a, b, c = map(int,input().strip().split(" ")) x.append(a) y.append(b) z.append(c) if sum(x) == 0 and sum(y) == 0 and sum(z) == 0 : print("YES") else : print("NO") n = int(input()) is_idle(n) ```
output
1
104,921
3
209,843
Provide tags and a correct Python 3 solution for this coding contest problem. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES
instruction
0
104,922
3
209,844
Tags: implementation, math Correct Solution: ``` n = int(input()) mat = [] flag = 0 for i in range(n): mat.append(list(map(int, input().split()))) for i in range(3): s = 0 for j in range(n): s += mat[j][i] if s != 0: flag = 1 break if flag == 0: print('YES') else: print('NO') ```
output
1
104,922
3
209,845
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` count1,count2,count3=0,0,0 for i in [0]*int(input()): a=[int(j) for j in input().split()] count1+=a[0] count2+=a[1] count3+=a[2] if (count1==0 and count2==0 and count3==0): print('YES') else: print('NO') ```
instruction
0
104,923
3
209,846
Yes
output
1
104,923
3
209,847
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` n=int(input()) sumi=0;sumj=0;sumk=0 while n>0: i,j,k=map(int,input().split()) sumi+=i;sumj+=j;sumk+=k n-=1 if sumi==0 and sumj==0 and sumk==0: print("YES") else: print("NO") ```
instruction
0
104,924
3
209,848
Yes
output
1
104,924
3
209,849
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` def resolve(matrix): sum = [0, 0, 0] for element in matrix: sum[0] += element[0] sum[1] += element[1] sum[2] += element[2] if sum[0] == 0 and sum[1] == 0 and sum[2] == 0: return "YES" else: return "NO" quant = int(input()) matrix = [] for i in range(quant): matrix.append([int(i) for i in input().split(" ")]) print(resolve(matrix)) ```
instruction
0
104,925
3
209,850
Yes
output
1
104,925
3
209,851
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` n= int(input()) a=[] b=[] c=[] for i in range(n): x,y,z=input().split() x,y,z=int(x),int(y),int(z) a.append(x) b.append(y) c.append(z) s1=0 s2=0 s3=0 for i in range(n): s1+=a[i] s2+=b[i] s3+=c[i] if (s1==0 and s2==0 and s3==0): print("YES") else: print("NO") ```
instruction
0
104,926
3
209,852
Yes
output
1
104,926
3
209,853
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` n = int(input()) l = [] for i in range(n): x,y,z = map(int,input().split()) a = [x,y,z] b = sum(a) l.append(b) if (sum(l)==0): print("YES") else: print("NO") ```
instruction
0
104,927
3
209,854
No
output
1
104,927
3
209,855
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` n=int(input()) x=0 y=0 z=0 for i in range (n): a,b,c=map(int,input().split()) x+=a y+=b z+=c if (a==0) and (b==0) and (c==0): print('YES') else: print('NO') ```
instruction
0
104,928
3
209,856
No
output
1
104,928
3
209,857
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` quantity = int(input()) array = [] for i in range(quantity): x = input().split() x = list(map(int, x)) array.append(x) answer = 0 for valores in array: answer += sum(valores) if answer == 0: print('YES') else: print('NO') ```
instruction
0
104,929
3
209,858
No
output
1
104,929
3
209,859
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" β€” thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces. Input The first line contains a positive integer n (1 ≀ n ≀ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≀ xi, yi, zi ≀ 100). Output Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not. Examples Input 3 4 1 7 -2 4 -1 1 -5 -3 Output NO Input 3 3 -1 7 -5 2 -4 2 -1 -3 Output YES Submitted Solution: ``` def Sum_Force(x,y,z): for i in range(len(x)): if int(x[i]) + int(y[i]) + int(z[i]) != 0: print('NO') return print('YES') n = input() x = input() y = input() z = input() x = x.split() y = y.split() z = z.split() Sum_Force(x,y,z) ```
instruction
0
104,930
3
209,860
No
output
1
104,930
3
209,861
Provide a correct Python 3 solution for this coding contest problem. Aizu has an ancient legend of buried treasure. You have finally found the place where the buried treasure is buried. Since we know the depth of the buried treasure and the condition of the strata to be dug, we can reach the buried treasure at the lowest cost with careful planning. So you decided to create a program that reads the condition of the formation and calculates the route to reach the buried treasure depth at the lowest cost. The state of the formation is represented by cells arranged in a two-dimensional grid, and the position of each cell is represented by the coordinates (x, y). Let the upper left be (1,1), and assume that the x coordinate increases as it goes to the right and the y coordinate increases as it goes deeper down. You choose one of the cells with the smallest y-coordinate and start digging from there, then dig into one of the cells with the largest y-coordinate. There are two types of cells in the formation: 1. A cell filled with soil. There is a fixed cost for each cell to dig. 2. Oxygen-filled cell. There is no need to dig, and each cell can be replenished with a fixed amount of oxygen. The oxygen in the cell that has been replenished with oxygen is exhausted and cannot be replenished again. Also, when you reach this cell, you must replenish oxygen. Only left, right, and down cells can be dug from a cell. Once you have dug a cell, you can move it left or right, but you cannot move it up. You must carry an oxygen cylinder with you when excavating. The moment the oxygen cylinder reaches zero, you will not be able to move, excavate, or replenish oxygen. The remaining amount is decremented by 1 each time you move the cell. Even if the remaining amount of the oxygen cylinder is 0 and the depth of the buried treasure is reached, it is not considered to have been reached. In addition, oxygen can be replenished in cells that have accumulated oxygen, but the excess capacity is discarded. Create a program that inputs the size of the formation, the excavation cost, the capacity of the oxygen cylinder, the amount of oxygen in the initial state, and the information of the formation, and outputs the minimum cost to reach the deepest cell. However, if the minimum cost exceeds the excavation cost, or if you cannot reach the buried treasure no matter how you dig, please output "NA". <image> Input A sequence of multiple datasets is given as input. The end of the input is indicated by two zero lines. Each dataset is given in the following format. W H f m o c1,1 c2,1 ... cW,1 c1,2 c2,2 ... cW,2 ... c1, H c2, H ... cW, H The horizontal size W of the formation and the vertical size H (3 ≀ W, H ≀ 10) are given in the first line. The second line is the integer f (1 ≀ f ≀ 10000) that represents your excavation cost, the integer m (3 ≀ m ≀ 50) that represents the capacity of the oxygen cylinder, and the integer o that represents the amount of oxygen you have in the initial state. o ≀ m) is given. The following H line is given the geological information ci, j. ci, j represents the cell information for coordinates (i, j) and is given in the following format: If the value is negative, the cell is full of soil and the value represents the cost. If the value is positive, it is a cell filled with oxygen, and the value represents the amount of oxygen. However, there are no more than 50 cells in which oxygen has accumulated. The number of datasets does not exceed 50. Output Print the minimum cost or NA on one line for each dataset. Example Input 3 3 100 10 10 -100 -20 -100 -100 -20 -100 -100 -20 -100 3 3 100 10 10 -100 -20 -100 -100 -20 -20 -100 -60 -20 3 3 100 10 3 -100 -20 -100 -20 -20 -20 -20 -100 -20 3 3 100 3 3 -100 -20 -30 -100 -20 2 -100 -20 -20 4 5 1500 5 4 -10 -380 -250 -250 -90 2 -80 8 -250 -130 -330 -120 -120 -40 -50 -20 -250 -10 -20 -150 0 0 Output 60 80 NA 50 390
instruction
0
105,191
3
210,382
"Correct Solution: ``` import sys sys.setrecursionlimit(1000000) INF = 10 ** 20 def update_state(state, newx): tmp = list(state) tmp[newx] = 1 return tuple(tmp) def get_co(x, y): dc = do = 0 score = mp[y][x] if score < 0: dc = -score else: do = score return dc, do def minimum_cost(x, y, state, ox, goal, dic, w, m): if (x, y, state, ox) in dic: return dic[(x, y, state, ox)] if y == goal: return 0 if ox <= 1: return INF ret = INF if x >= 1: if state[x - 1] == 0: dc, do = get_co(x - 1, y) ret = min(ret, minimum_cost(x - 1, y, update_state(state, x - 1), min(ox + do - 1, m), goal, dic, w, m) + dc) else: ret = min(ret, minimum_cost(x - 1, y, state, ox - 1, goal, dic, w, m)) if x < w - 1: if state[x + 1] == 0: dc, do = get_co(x + 1, y) ret = min(ret, minimum_cost(x + 1, y, update_state(state, x + 1), min(ox + do - 1, m), goal, dic, w, m) + dc) else: ret = min(ret, minimum_cost(x + 1, y, state, ox - 1, goal, dic, w, m)) dc, do = get_co(x, y + 1) ret = min(ret, minimum_cost(x, y + 1, tuple((1 if i == x else 0 for i in range(w))), min(ox + do - 1, m), goal, dic, w, m) + dc) dic[(x, y, state, ox)] = ret return ret while True: w, h = map(int, input().split()) if w == 0: break f, m, o = map(int, input().split()) mp = [list(map(int, input().split())) for _ in range(h)] if o <= 1: print("NA") continue dic = {} ans = INF for i in range(w): dc, do = get_co(i, 0) state = tuple(1 if i == j else 0 for j in range(w)) ans = min(ans, minimum_cost(i, 0, state, min(o + do - 1, m), h - 1, dic, w, m) + dc) if ans > f: print("NA") else: print(ans) ```
output
1
105,191
3
210,383