Problem:


Score: 400 points

Problem Statement

There is a cave.

The cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.

It is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.

Since it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.

If you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.

Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 2 \times 10^5

1 \leq A_i, B_i \leq N\ (1 \leq i \leq M)

A_i \neq B_i\ (1 \leq i \leq M)

One can travel between any two rooms by traversing passages.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

If there is no way to place signposts satisfying the objective, print No.

Otherwise, print N lines. The first line should contain Yes, and the i-th line (2 \leq i \leq N) should contain the integer representing the room indicated by the signpost in Room i.

Sample Input 1

4 4
1 2
2 3
3 4
4 2

Sample Output 1

Yes
1
2
2

If we place the signposts as described in the sample output, the following happens:

Starting in Room 2, you will reach Room 1 after traversing one passage: (2) \to 1. This is the minimum number of passages possible.

Starting in Room 3, you will reach Room 1 after traversing two passages: (3) \to 2 \to 1. This is the minimum number of passages possible.

Starting in Room 4, you will reach Room 1 after traversing two passages: (4) \to 2 \to 1. This is the minimum number of passages possible.

Thus, the objective is satisfied.

Sample Input 2

6 9
3 4
6 1
2 4
5 3
4 6
1 5
6 2
4 5
5 6

Sample Output 2

Yes
6
5
5
1
1

If there are multiple solutions, any of them will be accepted.



Sample input:
4 4
1 2
2 3
3 4
4 2


Sample output:
Yes
1
2
2

Submission status: Accepted

Solution code:
def resolve():
  N, M = map(int, input().split(" "))
  AB_map = [[] for i in range(N)]
  for m in range(M):
    AB = [int(x) - 1 for x in input().split(" ")]
    AB_map[AB[0]].append(AB[1])
    AB_map[AB[1]].append(AB[0])

  not_finished = set(range(1, N+1))
  rooms = [None] * N
  rooms[0] = 0
  room_depths = [0] * N

  recent_rooms = [0]
  depth = 1
  while len(not_finished) != 0 and depth < N:
    temp_recent = set()
    for r in recent_rooms:
      for target in AB_map[r]:
        if target in not_finished:
          temp_recent.add(target)
          not_finished.remove(target)
          rooms[target] = r
          room_depths[target] = depth
    depth += 1
    recent_rooms = list(temp_recent)

  print("Yes")
  for r in rooms[1:]:
    print(r + 1)

if __name__ == "__main__":
    resolve()

Submission status: Accepted

Solution code:
inp = input()
inp = inp.split()
N = int(inp[0])
M = int(inp[1])
BigM = N+2

E = []
for m in range(M):
    abinp = input()
    abinp = abinp.split()
    a = int(abinp[0])
    b = int(abinp[1])
    E.append([a,b])

# program
Edict = [[] for n in range(N+1)]
for e in E:
    Edict[e[0]].append(e[1])
    Edict[e[1]].append(e[0])

output = [0] + [0] + [BigM]*(N-1)
prev = [0 for n in range(N+1)]
prev_cnt = 0
now = [1]

prev[1] = 1
while len(now) > 0:
    n = now.pop(0)
    prev_cnt += 1
    for next in Edict[n]:
        if prev[next] == 0:
            output[next] = n
            now.append(next)
            prev[next] = 1

if prev_cnt == N:
    print("Yes")
    for n in range(2,N+1):
        print(output[n])
else:
    print("No")

Submission status: Accepted

Solution code:
import queue
N,M = map(int,input().split())
adj = [[]for i in range(N+1)]
parent = [-1] * (N+1) # -1なら未訪問
for m in range(M):
    a,b = map(int,input().split())
    adj[a].append(b)
    adj[b].append(a)
q = queue.Queue() # 自分の部屋番号、親の部屋番号
q.put((1,0)) # 部屋1の親は部屋0と考える
while(not q.empty()):
    x, p = q.get()
    if parent[x] != -1: # 訪問済み
        continue
    parent[x] = p
    for next in adj[x]:
        if parent[next] == -1: # 未訪問なら
            q.put((next,x)) # 探索候補に追加
print ('Yes') # 必ず目標は達成できる
for p in parent[2:]: # 部屋2以降の親（前の部屋）
    print(p)

Submission status: Accepted

Solution code:
n,m=map(int,input().split())
r=[[] for x in range(n)]
for c in range(m):
    a,b=map(int,input().split())
    r[a-1].append(b-1)
    r[b-1].append(a-1)
s=[-1]*n
s[0]=0
u=[0]
k=1
for c in range(10**5):
    v=[]
    for d in u:
        for e in r[d]:
            if s[e]==-1:
                s[e]=d
                k+=1
                v.append(e)
    if k>n-1:
        break
    u=v
print('Yes')
for c in s[1:]:
    print(c+1)

Submission status: Accepted

Solution code:
# Template 1.0
import sys, re
from collections import deque, defaultdict, Counter, OrderedDict
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from heapq import heappush, heappop, heapify, nlargest, nsmallest
def STR(): return list(input())
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def list2d(a, b, c): return [[c] * b for i in range(a)]
def sortListWithIndex(listOfTuples, idx):   return (sorted(listOfTuples, key=lambda x: x[idx]))
def sortDictWithVal(passedDic):
    temp = sorted(passedDic.items(), key=lambda kv: (kv[1], kv[0]))
    toret = {}
    for tup in temp:
        toret[tup[0]] = tup[1]
    return toret
def sortDictWithKey(passedDic):
    return dict(OrderedDict(sorted(passedDic.items())))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

n, m =MAP()
graph = defaultdict(set)
for _ in range(m):
    temp1, temp2 = MAP()

    graph[temp1].add(temp2)
    graph[temp2].add(temp1)

visited = [0]*(n+1)

q = deque()

q.append(1)
visited[1] = -1
while(q):
    popped = q.popleft()

    for child in graph[popped]:
        if(visited[child]==0):
            q.append(child)
            visited[child] = popped
visited = visited[2:]

if(0 in visited):
    print("No")
else:
    print("Yes")
    for el in visited:
        print(el)

Submission status: Accepted

Solution code:
import sys
def input():return sys.stdin.readline()[:-1]
def N(): return int(input())
def NM():return map(int,input().split())
def L():return list(NM())
def LN(n):return [N() for i in range(n)]
def LL(n):return [L() for i in range(n)]
def YesNo(x):print("Yes")if x==True else print("No")
n,m=NM()
edge=[[] for i in range(n+1)]
for i in range(m):
    a,b=map(int,input().split())
    edge[a].append(b)
    edge[b].append(a)
pre=[-1]*(n+1)
from collections import deque
def bfs(s,n):
    d=[-1 for i in range(n+1)]
    d[s]=0
    q=deque([s])
    while q:
        x=q.popleft()
        for i in edge[x]:
            if d[i]==-1:
                d[i]=d[x]+1
                pre[i]=x
                q.append(i)
    return d
bfs(1,n)
if -1 in pre[2:]:
    print("No")
else:
    print("Yes")
    for i in pre[2:]:
        print(i)

Submission status: Accepted

Solution code:
import queue

N, M = map(int, input().split())
graph = [[] for _ in range(N)]
for _ in range(M):
    A, B = map(int, input().split())
    graph[A-1].append(B-1)
    graph[B-1].append(A-1)

up = [-1 for _ in range(N)]
up[0] = 0

q = queue.Queue()
q.put(0)
while not q.empty():
    now = q.get()
    for x in graph[now]:
        if up[x] != -1:
            continue
        up[x] = now
        q.put(x)

print('Yes')
for i in range(1, N):
    print(up[i]+1)

Submission status: Accepted

Solution code:
from collections import deque

N, M = map(int, input().split())
l =[[] for _ in range(N)]

q=deque([0])

TFl=[0]*N
TFl[0]=1
ml=[-1]*N

for i in range(M):
  A,B=map(int,input().split())
  l[B-1].append(A-1)
  l[A-1].append(B-1)

while q:
  p = q.popleft()
  for i in l[p]: #普通に1行ずつ回してるイメージ
    if TFl[i]==1:
      continue
    TFl[i]=1
    ml[i]=p
    q.append(i)

if all([i==1 for i in TFl]):
  print('Yes')
  for i in range(1, N):
    print(ml[i]+1)

else:
  print('No')

Submission status: Accepted

Solution code:
from sys import stdin
from collections import deque
input = stdin.readline


def main():
    n, m = map(int, input().split())

    nexts = [[] for i in range(n)]
    
    for _ in range(m):
        ai, bi = map(int, input().split())
        ai -= 1
        bi -= 1
        nexts[ai].append(bi)
        nexts[bi].append(ai)

    blues = [-1] * n # 1 is in blues
    blues[0] = 0 # 0 is not in blues
    checked = [0] * n

    red_deque = deque([0])

    while len(red_deque) > 0:
        rd = red_deque[0]
        red_deque.popleft()
        if checked[rd] == 0:
            checked[rd] = 1
            for nxt in nexts[rd]:
                if blues[nxt] == -1:
                    blues[nxt] = rd
                    red_deque.append(nxt)

    print("Yes")
    for blue in blues[1:]:
        print(blue + 1)
    

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
from collections import deque

n, m = map(int, input().split())

nodes = {i: set() for i in range(n)}

for _ in range(m):
    a, b = map(int, input().split())
    nodes[a-1].add(b)
    nodes[b-1].add(a)

def bfs(r):
    queue = deque([r])
    ds = [None]*n
    ds[r-1] = 0
    while(queue):
        v = queue.popleft()
        for i in nodes[v-1]:
            if ds[i-1] == None:
                ds[i-1] = ds[v-1] + 1
                queue.append(i)
    return ds

ds = bfs(1)
for i in range(n):
    if i == 0:
        print("Yes")
    else:
        for j in nodes[i]:
            if ds[i]-1 == ds[j-1]:
                print(j)
                break

Submission status: Accepted

Solution code:
from collections import deque
n, m = map(int, input().split())
room_adjacent = [[] for _ in range(n)]
for _ in range(m):
  room1, room2 = map(int, input().split())
  room_adjacent[room1-1].append(room2)
  room_adjacent[room2-1].append(room1)

room_labels = [1]+[0]*(n-1)
old_room = 1
path_queue = deque((old_room, room) for room in room_adjacent[old_room-1])
while path_queue:
  old_room, new_room = path_queue.pop()
  if room_labels[new_room-1] == 0:
    room_labels[new_room-1] = old_room
    for another_room in room_adjacent[new_room-1]:
      path_queue.appendleft((new_room, another_room))
  
if 0 in room_labels:
  print("No")
else:
  print("Yes")
  [print(value) for value in room_labels[1:]]

Submission status: Accepted

Solution code:
# abc168 D
from collections import deque

def bfs(graph, N, start):
    visited = [-1] * N
    visited[start] = 0
    que = deque([start])
    while que:
        node = que.popleft()
        for n in graph[node]:
            if visited[n] == -1:
                visited[n] = node
                que.append(n)
    return visited


## ----main
N, M = list(map(int,input().split()))
graph = [[] for _ in range(N)]

for _ in range(M):
    a,b = list(map(int,input().split()))
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)

visited = bfs(graph,N,0)

if -1 not in visited[1:]:
    print("Yes")
    for v in visited[1:]:
        print(v+1)
else:
    print("No")

Submission status: Accepted

Solution code:
from collections import deque

N, M = map(int, input().split())
AB = [map(int, input().split()) for _ in range(M)]
A, B = [list(i) for i in zip(*AB)]

reach = [[] for i in range(N+1)]
reach[0].append(1)

for i in range(M):
    reach[A[i]].append(B[i])
    reach[B[i]].append(A[i])

d = deque()
visited = [-1]*(N+1)
ans = [-1]*(N+1)

d.appendleft(1)
visited[1] = 0

while d:
    now = d.pop()
    nexts = reach[now]

    for next in nexts:
        if visited[next] == -1:
            visited[next] = visited[now] + 1
            ans[next] = now
            d.appendleft(next)
        elif visited[now]+1 < visited[next]:
            visited[next] = visited[now]
            ans[next] = now

print('Yes')
for v in ans[2:]:
    print(v)

Submission status: Accepted

Solution code:
# ダイクストラ法で部屋1から各部屋への最短経路を出す
import queue

n, m = list(map(int, input().split()))
edges = [list(map(int, input().split())) for _ in range(m)]

# 隣接行列の作成
edges_dict = {}
for edge in edges:
    a, b = edge

    if a not in edges_dict:
        edges_dict[a] = [b]
    else:
        edges_dict[a].append(b)

    if b not in edges_dict:
        edges_dict[b] = [a]
    else:
        edges_dict[b].append(a)

# i=0は未使用, i>0は部屋iの最短経路がたどる次の部屋 = 道しるべ
prev_list = [None] * (n + 1)
q = queue.Queue()

# 初期化
q.put(1)
prev_list[1] = 1

while not q.empty():
    v = q.get()
    for w in edges_dict[v]:
        if prev_list[w] is None:
            prev_list[w] = v
            q.put(w)

print("Yes")
for v in prev_list[2:]:
    print(v)

Submission status: Accepted

Solution code:
from heapq import heappop, heappush
n,m = map(int,input().split())
G = [[] for _ in range(n)]
for _ in range(m):
    a,b = map(int,input().split())
    a -= 1
    b -= 1
    G[a].append(b)
    G[b].append(a)
dist = [float("inf")]*n
seen = [False]*n
ans = [0]*n
def f(s):
    PQ = [(0,s)]
    dist[s] = 0
    while PQ:
        md,u = heappop(PQ)
        seen[u] = True
        if dist[u] < md: continue
        for v in G[u]:
            if seen[v]: continue
            if dist[v] > md+1:
                dist[v] = md+1
                heappush(PQ,(dist[v],v))
                ans[v] = u+1
f(0)
print("Yes")
for i in range(1,n): print(ans[i])

Submission status: Accepted

Solution code:
from collections import deque

class Node:
    def __init__(self, data):
        self.data = data
        self.children = []

def main():
    N, M = map(int, input().split())
    dic = {}
    for i in range(1, N + 1):
        dic[i] = Node(i)
    for i in range(0, M):
        A, B = map(int, input().split())
        dic[A].children.append(dic[B])
        dic[B].children.append(dic[A])

    answerDic = {}
    q = deque()
    q.append(dic[1])
    while len(q) > 0:
        current = q.popleft()
        for child in current.children:
            if child.data not in answerDic.keys() :
                answerDic[child.data] = current.data
                q.append(child)

    print('Yes')
    for key in range(2, N + 1):
        print(answerDic[key])

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
from queue import Queue

class Node:
    def __init__(self, data):
        self.data = data
        self.children = []

def main():
    N, M = map(int, input().split())
    dic = {}
    for i in range(1, N + 1):
        dic[i] = Node(i)
    for i in range(0, M):
        A, B = map(int, input().split())
        dic[A].children.append(dic[B])
        dic[B].children.append(dic[A])

    answerDic = {}
    q = Queue()
    q.put(dic[1])
    while not q.empty():
        current = q.get()
        for child in current.children:
            if child.data not in answerDic.keys() :
                answerDic[child.data] = current.data
                q.put(child)

    print('Yes')
    for key in range(2, N + 1):
        print(answerDic[key])

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.buffer.readline
    n,m = map(int, input().split())
    adj = [[] for i in range(n)]
    for i in range(m):
        a,b = map(lambda x: int(x)-1, input().split())
        adj[a].append(b)
        adj[b].append(a)
    
    que = [0]
    parent = [-1] * (n)
    while que:
        node = que.pop(0)
        for child in adj[node]:
            if parent[node] == child:
                continue
            if parent[child] == -1:
                que.append(child)
                parent[child] = node
    if -1 in parent[1:]:
        print('No')
    else:
        print('Yes')
    for i in range(1,n):
        print(parent[i]+1)





if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
link = [[] for i in range(N)]
for i in range(M):
    A, B = map(int, input().split())
    link[A-1].append(B-1)
    link[B-1].append(A-1)
visited = [False for i in range(N)]
result = [0] * N
Q = [0]
visited[0] = True
#Qに要素がなくなるまで
while Q:
    #一番上の要素をpop
    v = Q.pop(0)
    for i in link[v]:
        if visited[i] == False:
            visited[i] = True
            result[i] = v
            Q.append(i)
print("Yes")
for i in range(1, N):
    print(result[i] + 1)

Submission status: Accepted

Solution code:
def resolve():
    def Dijkstra(s, n, edge, inf=float("inf")):
        import heapq
        d = [inf] * n
        used = [False] * n
        d[s] = 0
        used[s] = True
        queue = []
        path = [-9999] * n
        for e in edge[s]:
            heapq.heappush(queue, e + [s])
        while len(queue):
            dist, point, before = heapq.heappop(queue)
            if used[point]:
                continue
            d[point] = dist
            used[point] = True
            path[point] = before
            for nextdist, nextp in edge[point]:
                if not used[nextp]:
                    heapq.heappush(queue, [dist + nextdist, nextp, point])
        return d, path
    n, m = map(int, input().split())
    inf = 10 ** 10
    from collections import defaultdict
    edge = defaultdict(list)
    for _ in range(m):
        x, y = [int(x) - 1 for x in input().split()]
        edge[x].append([1, y])
        edge[y].append([1, x])
    l, p = Dijkstra(0, n, edge, inf)
    if min(p[1:]) < -1:
        print("No")
    else:
        print("Yes")
        for i in p[1:]:
            print(i + 1)


if __name__ == '__main__':
    resolve()

Submission status: Accepted

Solution code:
n,m=map(int,input().split())
r=[[] for x in range(n)]
for c in range(m):
    a,b=map(int,input().split())
    r[a-1].append(b-1)
    r[b-1].append(a-1)
s=[-1]*n
u=[0]
v=[]
k=1
for c in range(10**5):
    for d in u:
        for e in r[d]:
            if s[e]==-1:
                s[e]=d
                k+=1
                v.append(e)
    if k>n-1:
        break
    u=v
print('Yes')
for c in range(n-1):
    print(s[c+1]+1)

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
X = [[] for i in range(N + 1)]
for i in range(M):
  a, b = map(int, input().split())
  X[a] += [b]
  X[b] += [a]
ans = [0] * (N + 1)
ans[1] = 1
from collections import deque
que = deque([1])
while que:
  q = que.popleft()
  for i in X[q]:
    if ans[i] == 0:
      ans[i] = q
      que.append(i)
print('Yes')
print(*ans[2:], sep='\n')

Submission status: Accepted

Solution code:
import queue
INF = float('inf')

def bfs():
    q = queue.Queue()
    [q.put([x, 0]) for x in graph[0]]
    while not q.empty():
        n = q.get()
        nex = n[0]; now = n[1]
        if visited[nex] == INF:
            visited[nex] = now
            [q.put([x, nex]) for x in graph[nex]]
    return

N, M = map(int, input().split())
graph = [[] for _ in range(N)]
for _ in range(M):
    A, B = map(int, input().split())
    graph[A-1].append(B-1)
    graph[B-1].append(A-1)

visited = [INF for _ in range(N)]
bfs()

if INF in visited:
    print('No')
else:
    print('Yes')
    for i in range(1, N):
        print(visited[i]+1)

Submission status: Accepted

Solution code:
from collections import deque

n, m = map(int, input().split())

adj = [[] for _ in range(n)]

for i in range(m):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    adj[a].append(b)
    adj[b].append(a)

q = deque()

dist = [-1] * n
ans = [0] * n
q.append(0)

while len(q) != 0:
    now = q.popleft()
    for to in adj[now]:
        if dist[to] != -1: continue
        dist[to] = dist[now] + 1
        ans[to] = now
        q.append(to)

print("Yes")
for i in range(1, n):
    print(ans[i] + 1)

Submission status: Accepted

Solution code:
n, m = [int(x) for x in input().split()] # nは頂点の数、mは辺の数
g = [[] for _ in range(n)] # 隣接リスト

for _ in range(m):
    a, b = [int(x) for x in input().split()]
    g[a-1].append(b)
    g[b-1].append(a)

from collections import deque

def bfs(u):
    queue = deque([u])
    d = [None] * n # uからの距離の初期化
    d[u-1] = 0 # 自分との距離は0
    while queue:
        v = queue.popleft()
        for i in g[v-1]:
            if d[i-1] is None:
                d[i-1] = d[v-1] + 1
                queue.append(i)
    return d

d = bfs(1)
for i in range(n):
    if d[i] == 0:
        print('Yes')
    else:
        for j in g[i]:
            if d[i]-1==d[j-1]:
                print(j)
                break

Submission status: Accepted

Solution code:
from collections import deque


N,M=map(int,input().split())
a=[]
min=[0] * (N + 1)
heya=[[] for _ in range(N + 1)]


for i in range(M):
    tmp = list(input().split())
    tmp_i = [int(s) for s in tmp]
    a.append(tmp_i)

heya[0].append(1)
for i in range(M):
    tmp1 = a[i][0]
    tmp2 = a[i][1]
    heya[tmp1].append(tmp2)
    heya[tmp2].append(tmp1)

que = list(heya[0])
prev = []
tmp = []
prevtmp =[]
cnt = 0
prev.append(0)
while cnt < 1000000:
    #print('cnt:'+str(cnt))
    tmp.clear()
    prevtmp.clear()
    if len(que) == 0:
        #print('探索終了')
        break

    for i in range(len(que)):
        chk = que[i]
        #print('chk')
        #print('chk:' + str(chk))

        #初めて探索する場所、または最小探索回数の場合、次の探索先にする
        if min[chk] == 0:
            #print('i')
            #print(i)
            min[chk] = prev[i]
            for j in range(len(heya[chk])):
                #print('add:' + str(heya[chk][j]))
                tmp.append(heya[chk][j])
                prevtmp.append(chk)

    #次の探索先を設定する
    que.clear()
    for i in range(len(tmp)):
        que.append(tmp[i])

    prev.clear()
    for i in range(len(prevtmp)):
        prev.append(prevtmp[i])

    cnt = cnt + 1

#最小探索回数がない＝どこの部屋ともつながっていない
chk = 0
for i in range(1,N+1):
    if min[i] == 0:
        print('No')
        chk = 1
        break

if chk == 0:
    print('Yes')
    for i in range(2,N+1):
        print(min[i])

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
A = [0]*M
B = [0]*M
for i in range(M):
    A[i], B[i] = map(int, input().split())

from collections import deque
def bfs(graph, start_node, depth):
    next_nodes = deque([])
    seen_nodes = set()
    
    next_nodes.append(start_node)
    seen_nodes.add(start_node)
    depth[start_node] = 0
    while next_nodes:
        node = next_nodes.popleft()
#         if node == key:
#             return node
        if node in graph:
            for n in graph[node]:
                if not n in seen_nodes:
                    next_nodes.append(n)
                    seen_nodes.add(n)
                    depth[n] = node
    return

def Main(N, M, A, B):
    g = {}
    for i in range(M):
        if A[i] not in g:
            g[A[i]] = []
        if B[i] not in g:
            g[B[i]] = []
        g[A[i]].append(B[i])
        g[B[i]].append(A[i])
    depth = {}
    bfs(g, 1, depth)
    ans = []
    for i in range(2, N+1):
        ans.append(depth[i])
    return 'Yes', ans
          
                    
yn, out = Main(N, M, A, B)
print(yn)
for e in out:
    print(e)

Submission status: Accepted

Solution code:
n, m = map(int, input().split())

edges = [ [] for _ in range(n) ]

for _ in range(m):
    a, b = map(int, input().split())
    edges[a - 1].append(b - 1)
    edges[b - 1].append(a - 1)

INF = 10 ** 6

def dijkstra_travel(edges):
    dists = [ INF  for _ in range(n) ]
    paths = [ None for _ in range(n) ]

    dists[0] = 0
    paths[0] = 0

    next_travel = [ 0 ]

    def travel_adjacent():
        n = next_travel.pop(0)

        adjacent_nodes = list(
            map(
                lambda node: (node, paths[node]),
                edges[n],
            )
        )

        for node, path in adjacent_nodes:
            if path is None or dists[node] > dists[n] + 1:
                dists[node] = dists[n] + 1
                paths[node] = n
                next_travel.append(node)


    while len(next_travel) > 0:
        travel_adjacent()

    return paths[1:]

result = dijkstra_travel(edges)

if all(map(lambda x: x is not None, result)):
    print('Yes')

    for x in result:
        print(x + 1)

else:
    print('No')

Submission status: Accepted

Solution code:
# import numpy as np
# import copy
from collections import defaultdict
import queue


q = queue.Queue()

n, m = map(int, input().split())
graph = defaultdict(list)
for _ in range(m):
    a, b = map(lambda x: int(x), input().split())
    graph[a].append(b)
    graph[b].append(a)


# l = np.array(l)
# lc = copy.deepcopy(l)
li = [-1 for _ in range(n)]
li[0] = 1

def search(x):
#     if sum(l[x]) == 0:
#         q.queue = False
#         return
    
#     ind_lis = np.where(lc[x] == 1)[0]
#     ind_lis = [e for e in ind_lis if li[e] == -1]
#     print(li)
#     print(lc[x])
    for e in graph[x]:
#         print(e)
        if li[e-1] != -1:
            continue
        li[e-1] = x
#         print('q', i+1)
        q.put(e)
x = 1
search(x)
while q.queue:
    search(q.get())

if li[1:].count(-1) == 0:
    print('Yes')
    for e in li[1:]:
        print(e)
else:
    print('No')

Submission status: Accepted

Solution code:
import collections
def main():
    N,M = map(int, input().split())
    A = [0]*M
    B = [0]*M
    road = [[] for i in range(N)]
    for i in range(M):
        A[i],B[i] = map(lambda x:x-1, map(int, input().split()))
        road[A[i]].append(B[i])
        road[B[i]].append(A[i])
    
    # 距離を1から増やしていけば高々O(N)で済む
    # 新しく行ける部屋が無くなったら終わり
    remainroom = [True for i in range(N)]
    sign = [-1]*N
    cur = [0]
    while len(cur)>0:
        # 行ける部屋全てについて
        new = []
        for i in cur:
            for j in road[i]:
                if remainroom[j]:
                    remainroom[j]=False
                    sign[j] = i
                    new.append(j)
        cur = new

    # 出力
    coll = collections.Counter(remainroom)
    if coll.get(True,0)>0:
        print("No")
    else:
        print("Yes")
        for i in range(1,N):
            print(sign[i]+1)

main()

Submission status: Accepted

Solution code:
import pdb

def bfs(graph, start, rooms):
    queue = []
    visited = [False]*rooms
    visited[start] = True
    marking = [0]*rooms
    queue.append(start)
    while queue:
        nodes = queue.pop(0)
        for node in graph[nodes]:
            if not visited[node]:
                visited[node] = True
                queue.append(node)
                marking[node] = nodes + 1
    return marking, visited

if __name__=="__main__":
    N, M = map(int, input().split())
    graph = [[] for i in range(N)]
    for i in range(M):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        graph[a].append(b)
        graph[b].append(a)

    marking, visited = bfs(graph, 0, N)

    if all(visited):
        print("Yes")
        for i in range(1, N):
            print(marking[i])
    else:
        print("No")

Submission status: Accepted

Solution code:
def resolve():
    def Dijkstra(s, n, edge, inf=float("inf")):
        import heapq
        d = [inf] * n
        used = [False] * n
        d[s] = 0
        used[s] = True
        queue = []
        path = [-9999] * n
        for e in edge[s]:
            heapq.heappush(queue, e + [s])
        while len(queue):
            dist, point, before = heapq.heappop(queue)
            if used[point]:
                continue
            d[point] = dist
            used[point] = True
            path[point] = before
            for nextdist, nextp in edge[point]:
                if not used[nextp]:
                    heapq.heappush(queue, [dist + nextdist, nextp, point])
        return d, path
    n, m = map(int, input().split())
    inf = 10 ** 10
    edge = [[] for _ in range(n)]
    for _ in range(m):
        x, y = [int(x) - 1 for x in input().split()]
        edge[x].append([1, y])
        edge[y].append([1, x])
    l, p = Dijkstra(0, n, edge, inf)
    if min(p[1:]) < -1:
        print("No")
    else:
        print("Yes")
        for i in p[1:]:
            print(i + 1)


if __name__ == '__main__':
    resolve()

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys
from collections import deque


input = sys.stdin.readline
def IS(cb): return cb(input().strip())
def IL(cb): return [cb(s) for s in input().strip().split()]
def IR(cb, rows): return [IS(cb) for _ in range(rows)]
def ILL(cb, rows): return [IL(cb) for _ in range(rows)]


def solve():
    N, M = IL(int)
    AB = ILL(int, M)
    graph = [[] for _ in range(N)]
    for a, b in AB:
        graph[a - 1].append(b - 1)
        graph[b - 1].append(a - 1)
    que = deque()
    que.append(0)
    visited = [False] * N
    visited[0] = True
    route = [0] * N
    while len(que):
        current = que.popleft()
        for next in graph[current]:
            if not visited[next]:
                visited[next] = True
                que.append(next)
                route[next] = current + 1

    print('Yes')
    for i in route[1:]:
        print(i)


solve()

Submission status: Accepted

Solution code:
N, M = map(int, input().split())
link = [[] for i in range(N)]
for i in range(M):
    A, B = map(int, input().split())
    link[A-1].append(B-1)
    link[B-1].append(A-1)
visited = [False for i in range(N)]
result = [0] * N
Q = [0]
visited[0] = True
#Qに要素がなくなるまで
while Q:
    #一番上の要素をpop
    v = Q.pop(0)
    for i in link[v]:
        if visited[i] == False:
            visited[i] = True
            result[i] = v
            Q.append(i)
print("Yes")
for i in range(1, N):
    print(result[i] + 1)

Submission status: Accepted

Solution code:
import collections
n,m = list(map(int,input().split()))

di = collections.defaultdict(list)
for i in range(m):
    a,b = list(map(int,input().split()))
    di[a-1].append(b-1)
    di[b-1].append(a-1)

ans=[-1]*n
ans[0]=0
que = [0]
#print(di)

while que:
    v = que.pop(0)
    for i in di[v]:
        if ans[i]!=-1:continue
        ans[i]=v
        que.append(i)
    #print(que)

print("Yes")
for i in ans[1:]:
    print(i+1)

Submission status: Accepted

Solution code:
from collections import deque
n, m = map(int, input().split())
l = [[] for i in range(n)]
for i in range(m):
    a, b = map(int, input().split())
    l[a - 1].append(b - 1)
    l[b - 1].append(a - 1)
que = deque([0])
visited = [False] * n
visited[0] = True
prev = [0] * n
while que:
    p = que.popleft()
    for i in l[p]:
        if visited[i]:
            continue
        visited[i] = True
        prev[i] = p
        que.append(i)
print("Yes")
for i in prev[1:]:
    print(i + 1)

Submission status: Accepted

Solution code:
from heapq import heappush, heappop

INF = 10**15

def dijkstra(s, edges):
    n = len(edges)
    que = []
    d = [INF] * n
    prev = [-1] * n
    d[s] = 0
    heappush(que, (0, s))

    while len(que) > 0:
        (c, v) = heappop(que)
        if d[v] < c:
            continue
        for (cc, w) in edges[v]:
            if d[w] > d[v] + cc:
                d[w] = d[v] + cc
                prev[w] = v
                heappush(que, (d[w], w))

    return d, prev

n, m = map(int, input().split())
edges = [[] for i in range(n)]
for i in range(m):
    ui, vi = map(int, input().split())
    ui, vi = vi-1, ui-1
    edges[ui].append((1, vi))
    edges[vi].append((1, ui))

d, prev = dijkstra(0, edges)
print('Yes')
for i in range(1, n):
    print(prev[i]+1)