Problem:


Score : 400 points

Problem Statement

There are N pieces of sushi. Each piece has two parameters: "kind of topping" t_i and "deliciousness" d_i.
You are choosing K among these N pieces to eat.
Your "satisfaction" here will be calculated as follows:

The satisfaction is the sum of the "base total deliciousness" and the "variety bonus".

The base total deliciousness is the sum of the deliciousness of the pieces you eat.

The variety bonus is x*x, where x is the number of different kinds of toppings of the pieces you eat.

You want to have as much satisfaction as possible.
Find this maximum satisfaction.

Constraints

1 \leq K \leq N  \leq 10^5

1 \leq t_i \leq N

1 \leq d_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
t_1 d_1
t_2 d_2
.
.
.
t_N d_N

Output

Print the maximum satisfaction that you can obtain.

Sample Input 1

5 3
1 9
1 7
2 6
2 5
3 1

Sample Output 1

26

If you eat Sushi 1,2 and 3:

The base total deliciousness is 9+7+6=22.

The variety bonus is 2*2=4.

Thus, your satisfaction will be 26, which is optimal.

Sample Input 2

7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5

Sample Output 2

25

It is optimal to eat Sushi 1,2,3 and 4.

Sample Input 3

6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000

Sample Output 3

4900000016

Note that the output may not fit into a 32-bit integer type.



Sample input:
5 3
1 9
1 7
2 6
2 5
3 1


Sample output:
26

Submission status: Accepted

Solution code:
import heapq
N,K = map(int,input().split())

L = [[] for _ in range(N)]
All = []
s = set([])
for i in range(N):
  t,d = map(int,input().split())
  t-=1 #0スタートに
  heapq.heappush(L[t], -d) #最大から取り出したいので負にする。
  heapq.heappush(All,[-d,t]) #すべてから大きい順に取り出せるように 
  s.add(t)

#print(L,s)
point = 0
ns = 0 #現在の種類
later = []
now = []
syurui = set([])
while len(now) < K and All:
  temp = heapq.heappop(All)
  if temp[1] not in syurui:
    ns += 1
    point -= temp[0]
    syurui.add(temp[1])
    heapq.heappush(now, -1*temp[0])
  else:
    later.append(temp)
for i in later:
  heapq.heappush(All,i)

point += ns*ns
while len(now) < K:
  temp = heapq.heappop(All)
  point -= temp[0]
  heapq.heappush(now, -1*temp[0])

#print(ns,point)
#print(now,All,All[0][0])
while All and now[0] < -1*All[0][0]:
  temp = heapq.heappop(All)
  dele = heapq.heappop(now)
  #print(temp,dele)
  upoint = point - temp[0] - dele - ns*ns + (ns-1)**2
  #print(upoint,point)
  if upoint >= point:
    point = upoint
    ns -= 1
  else:
    break
    
print(point)
#print(All)
#print(now)

Submission status: Accepted

Solution code:
N,K = map(int,input().split())
A = sorted([list(map(int,input().split())) for _ in range(N)],key=lambda x:x[1],reverse=True)
C = {}
tot1 = 0
for i in range(K):
    t,d = A[i]
    if t not in C:
        C[t] = 0
    C[t] += 1
    tot1 += d
tot2 = len(C)
tot = tot1+tot2**2
cur = K
for i in range(K-1,-1,-1):
    t,d = A[i]
    if C[t]>1:
        tot1 -= d
        C[t] -= 1
        j = cur
        while j<N:
            t1,d1 = A[j]
            if t1 not in C:
                C[t1]=1
                tot1 += d1
                tot2 += 1
                if tot1+tot2**2>tot:
                    tot = tot1+tot2**2
                cur = j+1
                break
            else:
                j += 1
                cur = j
print(tot)

Submission status: Accepted

Solution code:
import heapq
N,K = map(int, input().split())
L = [[] for _ in range(N)]
h = []
for _ in range(N):
    t,d = map(int, input().split())
    L[t-1].append(d)
    heapq.heappush(h, (-d, t-1))

cnt = 0
for l in L:
    if len(l) > 0:
        cnt += 1

used = [0]*N
h1 = []
h2 = []
num = 0
if K <= cnt:
    while len(h2) < K:
        temp = heapq.heappop(h)
        if used[temp[1]] > 0:
            heapq.heappush(h1, temp)
            continue
        used[temp[1]] += 1
        heapq.heappush(h2, (-temp[0], temp[1]))
        num -= temp[0]
else:
    c2 = 0
    while len(h2) < K:
        temp = heapq.heappop(h)
        if used[temp[1]] > 0:
            if c2 < K-cnt:
                c2 += 1
            else:
                heapq.heappush(h1, temp)
                continue
        used[temp[1]] += 1
        heapq.heappush(h2, (-temp[0], temp[1]))
        num -= temp[0]

cnt = min(K, cnt)
ans = num + cnt**2
while len(h1) > 0 and h2[0][0] < -h1[0][0]:
    t1 = heapq.heappop(h1)
    t2 = heapq.heappop(h2)
    used[t2[1]] -= 1
    used[t1[1]] += 1
    if used[t2[1]] == 0:
        cnt -= 1
    if used[t1[1]] == 1:
        cnt += 1
    num += -t1[0]-t2[0]
    ans = max(ans, num+cnt**2)
    heapq.heappush(h2, (-t1[0], t1[1]))

print(ans)

Submission status: Accepted

Solution code:
from collections import Counter

N, K = map(int, input().split())
TD = [tuple(map(int, input().split())) for _ in range(N)]

TD.sort(reverse=True, key=lambda a: a[1])

A = TD[:K]

B = []
V = set()
for t, d in TD:
    if t in V:
        continue
    B.append((t, d))
    V.add(t)

cntT = Counter([t for t, _ in A])
V = set(cntT.keys())
S = sum([d for _, d in A])
B = [(t, d) for t, d in B if not t in V]

C = []
for t, d in A[::-1]:
    if cntT[t] > 1:
        C.append((t, d))
        cntT[t] -= 1

C = C[::-1]
ans = S + len(V)**2
for t, d in B:
    if not C:
        break
    _, less = C.pop()
    S -= less
    S += d
    V.add(t)
    ans = max(ans, S + len(V)**2)
print(ans)

Submission status: Accepted

Solution code:
import sys,queue,math,copy,itertools,bisect,collections,heapq

def main():
    sys.setrecursionlimit(10**7)
    INF = 10**18
    MOD = 10**9 + 7
    LI = lambda : [int(x) for x in sys.stdin.readline().split()]
    NI = lambda : int(sys.stdin.readline())
    SI = lambda : sys.stdin.readline().rstrip()

    N,K = LI()
    V = [LI() for _ in range(N)]
    V.sort(key=lambda x:x[1],reverse=True)
    c = [0] * (N+1)
    s = []
    ans = 0
    cnt = 0
    for t,d in V[:K]:
        ans += d
        if c[t] == 0:
            ans += 1 + 2*cnt
            cnt += 1
        else:
            s.append((t,d))
        c[t] = 1

    tmp = ans
    for t,d in V[K:]:
        if s == []: break
        if c[t] == 0:
            x,y = s.pop()
            tmp += d + cnt * 2 + 1 - y
            c[t] = 1
            cnt += 1
            ans = max(tmp,ans)
    print(ans)





if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from operator import itemgetter
import heapq
n, k = map(int, input().split())
TD = sorted([list(map(int, input().split())) for _ in range(n)], reverse=True, key=itemgetter(1))
L = [[] for _ in range(n+1)]
P = []
a = 0
cnt = 0
F = [-float("inf")]*(n+1)
for t, d in TD[:k]:
  L[t].append(d)
  if len(L[t]) == 1:
    a += 1
  cnt += d
F[a] = cnt
for i in range(1, n+1):
  while len(L[i]) > 1:
    heapq.heappush(P, L[i].pop())
now = k
for i in range(a, n):
  if len(P) == 0:
    break
  while now < n and L[TD[now][0]]:
    now += 1
  if now == n:
    break
  t, d = TD[now]
  L[t].append(d)
  F[i+1] = F[i] - heapq.heappop(P) + d
ans = 0
for i in range(a, n+1):
  ans = max(ans, F[i] + i*i)
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from operator import itemgetter
import heapq
n, k = map(int, input().split())
TD = sorted([list(map(int, input().split())) for _ in range(n)], reverse=True, key=itemgetter(1))
L = [[] for _ in range(n+1)]
P = []
a = 0
cnt = 0
F = [-float("inf")]*(n+1)
B = 0
for t, d in TD[:k]:
  if B>>t & 1:
    heapq.heappush(P, d)
  else:
    B |= 1 << t
    a += 1
  cnt += d
F[a] = cnt
for i in range(a, n):
  if len(P) == 0:
    break
  while k < n and B>>TD[k][0] & 1:
    k += 1
  if k == n:
    break
  t, d = TD[k]
  B |= 1 << t
  F[i+1] = F[i] - heapq.heappop(P) + d
ans = 0
for i in range(a, n+1):
  ans = max(ans, F[i] + i*i)
print(ans)

Submission status: Accepted

Solution code:
import sys,bisect,string,math,time,functools,random,fractions
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
def Golf():n,*t=map(int,open(0).read().split())
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
#h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
    mp=[boundary]*(w+2);found={}
    for i in range(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def bit_combination(n,base=2):
    rt=[]
    for tb in range(base**n):s=[tb//(base**bt)%base for bt in range(n)];rt+=[s]
    return rt
def gcd(x,y):
    if y==0:return x
    if x%y==0:return y
    while x%y!=0:x,y=y,x%y
    return y
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)
 
YN=['YES','NO'];Yn=['Yes','No']
mo=10**9+7
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb))
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**7)
read=sys.stdin.buffer.read
readline=sys.stdin.buffer.readline
input=lambda: sys.stdin.readline().rstrip()

class Tree:
    def __init__(self,inp_size=None,ls=None,init=True,index=0):
        self.LCA_init_stat=False
        self.ETtable=[]
        if init:
            if ls==None:
                self.stdin(inp_size,index=index)
            else:
                self.size=len(ls)+1
                self.edges,_=GI(self.size,self.size-1,ls,index=index)
        return
 
    def stdin(self,inp_size=None,index=1):
        if inp_size==None:
            self.size=int(input())
        else:
            self.size=inp_size
        self.edges,_=GI(self.size,self.size-1,index=index)
        return
    
    def listin(self,ls,index=0):
        self.size=len(ls)+1
        self.edges,_=GI(self.size,self.size-1,ls,index=index)
        return
 
    def __str__(self):
        return  str(self.edges)
 
    def dfs(self,x,func=lambda prv,nx,dist:prv+dist,root_v=0):
        q=deque()
        q.append(x)
        v=[-1]*self.size
        v[x]=root_v
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==-1:
                    q.append(nb)
                    v[nb]=func(v[c],nb,d)
        return v
 
    def EulerTour(self,x):
        q=deque()
        q.append(x)
        self.depth=[None]*self.size
        self.depth[x]=0
        self.ETtable=[]
        self.ETdepth=[]
        self.ETin=[-1]*self.size
        self.ETout=[-1]*self.size
        cnt=0
        while q:
            c=q.pop()
            if c<0:
                ce=~c
            else:
                ce=c
                for nb,d in self.edges[ce]:
                    if self.depth[nb]==None:
                        q.append(~ce)
                        q.append(nb)
                        self.depth[nb]=self.depth[ce]+1
            self.ETtable.append(ce)
            self.ETdepth.append(self.depth[ce])
            if self.ETin[ce]==-1:
                self.ETin[ce]=cnt
            else:
                self.ETout[ce]=cnt
            cnt+=1
        return
    
    def LCA_init(self,root):
        self.EulerTour(root)
        self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf)
        self.LCA_init_stat=True
        return
    
    def LCA(self,root,x,y):
        if self.LCA_init_stat==False:
            self.LCA_init(root)
        xin,xout=self.ETin[x],self.ETout[x]
        yin,yout=self.ETin[y],self.ETout[y]
        a=min(xin,yin)
        b=max(xout,yout,xin,yin)
        id_of_min_dep_in_et=self.st.query_id(a,b+1)
        return self.ETtable[id_of_min_dep_in_et]
 
class SparseTable: # O(N log N) for init, O(1) for query(l,r)
    def __init__(self,ls,init_func=min,init_idl=float('inf')):
        self.func=init_func
        self.idl=init_idl
        self.size=len(ls)
        self.N0=self.size.bit_length()
        self.table=[ls[:]]
        self.index=[list(range(self.size))]
        self.lg=[0]*(self.size+1)
        
        for i in range(2,self.size+1):
            self.lg[i]=self.lg[i>>1]+1
 
        for i in range(self.N0):
            tmp=[self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) for j in range(self.size)]
            tmp_id=[self.index[i][j] if self.table[i][j]==self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) else self.index[i][min(j+(1<<i),self.size-1)] for j in range(self.size)]
            self.table+=[tmp]
            self.index+=[tmp_id]
    
    # return func of [l,r)
    def query(self,l,r):
        if r>self.size:r=self.size
        #N=(r-l).bit_length()-1
        N=self.lg[r-l]
        return self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))])
    
    # return index of which val[i] = func of v among [l,r)
    def query_id(self,l,r):
        if r>self.size:r=self.size
        #N=(r-l).bit_length()-1
        N=self.lg[r-l]
        a,b=self.index[N][l],self.index[N][max(0,r-(1<<N))]
        if self.table[0][a]==self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))]):
            b=a
        return b
    
    def __str__(self):
        return str(self.table[0])
 
    def print(self):
        for i in self.table:
            print(*i)

show_flg=False
show_flg=True
ans=0


n,k=LI()
s=[]
for _ in range(n):
    t,d=LI()
    s+=[(d,t)]

s.sort(key=lambda x:x[0])
org_s=s[:]

q=[]
init_q=[[]for i in range(n+1)]
ate=[0]*-~n
for i in range(k):
    d,t=s.pop()
    ate[t]=1
    ans+=d
    heappush(init_q[t],(d,t))
for i in range(n):
    while init_q[i] and len(init_q[i])>1:
        d,t=heappop(init_q[i])
        heappush(q,(d,t))
x=sum(ate)
ans+=x*x

tmp=ans
while s and q:
    d,t=s.pop()
    if ate[t]==1:
        continue
    rd,rt=heappop(q)
    tmp-=rd
    tmp+=d
    tmp+=2*x+1

    ans=max(tmp,ans)
    ate[t]=1
    x+=1

print(ans)

Submission status: Accepted

Solution code:
# Python3 (3.4.3)
import sys
input = sys.stdin.readline

# -------------------------------------------------------------
# function
# -------------------------------------------------------------


# -------------------------------------------------------------
# main
# -------------------------------------------------------------
N,K = map(int,input().split())
TD = [tuple(map(int,input().split())) for _ in range(N)]

# 美味しい順にソートしておく
#  t : ネタの種類
#  d : 美味しさ基礎ポイント
TD.sort(key=lambda x:x[1], reverse=True)

# 美味しい順にK個食べた場合の満足ポイント
ans = 0
s = set() # 食べたネタの集合
r = list() # すでに食べたネタ, あとで交換する用
for i in range(K):
    t,d = TD[i]
    ans += d
    if t not in s:
        s.add(t) # 食べたネタの種類の集合
    else:
        r.append(TD[i])
ans += len(s)**2

Ans = ans

# 美味しい順のK+1番目から, ネタの種類が増えるような操作を順番に試していく
for i in range(K,N):
    t0,d0 = TD[i]
    # まだ食べてないネタ and 交換用の寿司があるなら
    if t0 not in s and len(r) > 0:
        # 交換用の寿司の一番美味しさ基礎ポイントが低いものを交換するのが最善
        t1,d1 = r.pop()
        # 満足ポイントの再計算
        ans = ans - d1 + d0 - len(s)**2 + (len(s)+1)**2
        # 食べたネタの集合に追加
        s.add(t0)
        # 満足度が大きくなったか都度確認
        Ans = max(Ans,ans)

print(Ans)

Submission status: Accepted

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

N, K = map(int, input().split())
td = [tuple(map(int, input().split())) for _ in range(N)]
td.sort(key=lambda t: t[1], reverse=True)
d = defaultdict(list)
now = 0

for ti, di in td[:K]:
    d[ti].append(di)
    now += di

rem = []

for k in d.keys():
    d[k].sort(reverse=True)
    
    for i in range(1, len(d[k])):
        rem.append(d[k][i])

add = []
s = set()

for ti, di in td[K:]:
    if ti not in d and ti not in s:
        add.append(di)
        s.add(ti)

rem.sort()
add.sort(reverse=True)
var = len(list(d.keys()))
ans = now+var**2

for i in range(min(len(rem), len(add))):
    now -= rem[i]
    now += add[i]
    ans = max(ans, now+(var+i+1)**2)

print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict

N, K = map(int, input().split())
TD = [list(map(int, input().split())) for _ in range(N)]

TD.sort(key = lambda x: -x[1])
#print(TD)

tmp = [[] for _ in range(N + 1)]
cnt = defaultdict(int)
out_candidate = []
kiso = 0
kind = 0
for i in range(K):
    t, d = TD[i]
    tmp[t].append(d)
    if cnt[t]:
        out_candidate.append([t, d])
    else:
        kind += 1
    kiso += d
    cnt[t] += 1
out_candidate.sort(key = lambda x: -x[1])
#print(tmp)
#print(cnt)
#print(out_candidate)
#print(kiso, kind)

answer = []
answer.append(kiso + kind ** 2)

in_candidate = []
if K < N:
    for i in range(K, N):
        in_candidate.append(TD[i])
in_candidate.sort(key = lambda x: x[1])
#print(in_candidate)

while out_candidate and in_candidate:
    in_t, in_d = in_candidate.pop()
    if cnt[in_t] == 0:
        cnt[in_t] += 1
        out_t, out_d = out_candidate.pop()
        kiso += in_d - out_d
        kind += 1
        answer.append(kiso + kind ** 2)
        
print(max(answer))

Submission status: Accepted

Solution code:

n, k = list(map(int, input().split()))
sushi = []
for i in range(n):
    sushi.append(list(map(int, input().split())))
point = 0
sushi_kind = set()
duplication = []
sushi.sort(key=lambda x: x[1],reverse = True)
for i in range(k):
    point += sushi[i][1]
    if sushi[i][0] in sushi_kind:
        duplication.append(sushi[i])
    else:
        sushi_kind.add(sushi[i][0])
ans = point + pow(len(sushi_kind),2)
dup_index = len(duplication) - 1
for i in range(k,n):
    if sushi[i][0] in sushi_kind:
        continue
    else:
        if dup_index >= 0:
            point -= duplication[dup_index][1]
            dup_index -= 1
            point += sushi[i][1]
            sushi_kind.add(sushi[i][0])
    ans = max(ans, point + pow(len(sushi_kind),2))
print(ans)

Submission status: Accepted

Solution code:
import sys
def input(): return sys.stdin.readline().strip()


def main():
    N, K = map(int, input().split())
    sushi = []
    neta = set([])
    for _ in range(N):
        t, d = map(int, input().split())
        sushi.append((d, t))
        neta.add(t)
    sushi.sort()
    L = len(neta)

    eat_kind = set([])
    same_kind = []
    point = 0
    for _ in range(K):
        d, t = sushi.pop()
        point += d
        if t not in eat_kind:
            eat_kind.add(t)
        else:
            same_kind.append((d, t))
    l = len(eat_kind)
    point += l ** 2
    #print("l={}, point={}".format(l, point))

    """
    貪欲でおいしいもの順にネタを取った後、新しい種類のネタにどんどんスイッチしていく方針はあっていたのに
    実装がヘビーになりすぎるから考えを間違っているだろうと撤退したのが愚かだった...!
    
    今は実装力を上げるパートということですね。
    """

    remain = [(d, t) for d, t in sushi if t not in eat_kind]
    remain.sort()
    #print("remain={}".format(remain))
    val = point # 前状態のポイント
    for i in range(l, L): # 前よりポイントが下がったとしてもどんどんネタの入れ替えをしていく！
        val = val - i ** 2 + (i + 1) ** 2
        if not same_kind: break
        pre_d, _ = same_kind.pop()
        val -= pre_d
        if not remain: break
        d, t = remain.pop()
        while t in eat_kind: d, t = remain.pop()
        val += d
        eat_kind.add(t)
        point = max(point, val)
        #print("l={}, point={}".format(i, val))

    print(point)

    



if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
# D - Various Sushi
import sys
from collections import defaultdict
import heapq

readline = sys.stdin.readline

dd = defaultdict(list)
N, K = map(int, readline().split())
for i in range(N):
    t, d = map(int, readline().split())
    heapq.heappush(dd[t], d*-1)

dd = list(dd.values())
dd.sort()

ans = 0
fix = 0
var = []
len_var = 0
sum_var = 0
tmp_max = 0

for i in range(min(K, len(dd))):
    fix += heapq.heappop(dd[i]) * -1
    for _ in range(len(dd[i])):
        tmp = heapq.heappop(dd[i]) * -1
        heapq.heappush(var, tmp)
        len_var += 1
        sum_var += tmp
    while len_var > K-(i+1) and len_var > 0:
        del_var = heapq.heappop(var)
        len_var -= 1
        sum_var -= del_var
    if len_var == K-(i+1):
        ans = max(ans , fix+sum_var + (i+1)**2)

print(ans)

Submission status: Accepted

Solution code:
from heapq import heappush,heappop,heapify

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

# とりあえずネタは無視しておいしさが大きい寿司からk個を選び(hq)、満足ポイントを計算する。
# それに選ばれなかった寿司から、選ばれた寿司のネタにはないネタで、かつ、
# そのネタの中でおいしさが最大のものを選んでおく(rhq)。
# hqのうち、hqのネタ種類数が減らなように選んだおいしさが最小のものと、
# rhqのうちおいしさが最大のものを入れ替えて、満足ポイントを計算する。
# (こうすると、おいしさの合計は減るがネタの種類数は増える。)
# これを繰り返して、最大の満足ポイントを出力する。

td = []
for i in range(n):
  td.append(tuple(map(int,input().split())))
td.sort(key = lambda x:(x[0],-x[1]))

tf = [False for _ in range(n)]
s = []
for t,d in td:
  t -= 1
  if tf[t]:
    s.append((0,d)) #そのネタの中でおいしさ最大でないもの
  else:
    s.append((1,d)) #そのネタの中でおいしさ最大のもの
    tf[t] = True

s.sort(key = lambda x:-x[1])
#print(s)
hq = s[:k]
heapify(hq)

rhq = []
for t,d in s[k:]:
  if t == 1:
    rhq.append(-d)
heapify(rhq)

ans = 0
tsum = 0
dsum = 0
for t,d in hq:
  tsum += t
  dsum += d
ans = dsum+tsum**2

while(True):
  t,d = heappop(hq)
  if t == 1:
    break
  if len(rhq) == 0:
    break
  newd = heappop(rhq)
  dsum += -newd-d
  tsum += 1
  ans = max(dsum+tsum**2,ans)
print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict
import heapq
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)
U = 10 ** 5 + 1

N, K = map(int, input().split())
DT = []
for _ in range(N):
    t, d = map(int, input().split())
    DT.append((d, t))

DT.sort(reverse=True)
score = 0
kind = defaultdict(list)
used = [0] * (U + 1)
for d, t in DT[:K]:
    score += d
    used[t] += 1
    kind[t].append(d)

cnt = len(kind)
ans = score + (cnt * cnt)

cand = []  # 交換する可能性のあるやつ, 小さいやつから削除
for key, val in kind.items():
    val.sort(reverse=True)
    while len(val) > 1:
        heapq.heappush(cand, (val.pop(), key))


for d_in, t_in in DT[K:]:
    if not cand:
        break
    if used[t_in]:
        continue

    d_out, t_out = heapq.heappop(cand)
    used[t_in] += 1
    used[t_out] -= 1
    cnt += 1
    score = score - d_out + d_in
    ans = max(ans, score + (cnt * cnt))

print(ans)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(100000000)

def main():
    N,K = map(int,input().split())
    sushi = [tuple(map(int,input().split())) for _ in range(N)]

    sushi.sort(key = lambda x:x[1],reverse = True)
    ans = 0
    dic = {}
    change = []
    for a,b in sushi[:K]:
        if a in dic:
            dic[a].append(b)
            change.append((a,b))
        else:
            dic[a] = [b]
        ans += b

    various = len(dic)
    ans += various ** 2
    ret = ans
    used_type = set(dic.keys())
    suggestion = [p for p in sushi[K:] if p[0] not in used_type]
    for a,b in suggestion:
        if len(change) == 0:
            break
        if a in used_type:
            continue
        dic[change[-1][0]].pop()
        ret -= change[-1][1]
        ret += b + 2*various + 1
        dic[a] = b
        change.pop()
        various += 1
        used_type.add(a)
        ans = max(ans,ret)
    print(ans)
if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
 
 
def main():
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input(): return sys.stdin.readline().rstrip()
    def mi():    return map(int, input().split())
    def lmi():   return list(map(int, input().split()))
    
 
    class MaxPQueue:
        def __init__(self):
            self.h = []
            self.size = 0
 
        def is_empty(self):
            return self.size == 0
        
        def push(self, delicious_dq):
            self.size += 1
            heappush(self.h, list(map(lambda x: -x, delicious_dq)))
        
        def pop(self):
            self.size -= 1
            tmp = heappop(self.h)
            return list(map(lambda x: -x, tmp)) 
 
 
    n, k = mi()
    L = [lmi() for _ in range(n)]
    L.sort(key=lambda x: x[1], reverse=True)
 
    d = dict()
    for neta, delcious in L:
        if neta in d:
            d[neta].append(delcious)
        else:
            d[neta] = [delcious]
 
    group_num = dict()
    group_size = 0
    ans = 0
    for neta, delcious in L[:k]:
        ans += delcious
        if neta in group_num:
            group_num[neta] += 1
        else:
            group_num[neta] = 1
            group_size += 1
    ans += group_size ** 2
    
    pq_new = MaxPQueue()
    for neta in d.keys():
        if neta not in group_num:
            pq_new.push(d[neta])
    
    # print(L)
    # print(ans)
    # print(group_num)
    prev = ans
    for ind in range(k-1, -1, -1):
        neta, delicious = L[ind]
        if group_num[neta] > 1 and not pq_new.is_empty():
            diff = pq_new.pop()[0] + (2 * group_size + 1) - delicious
            ans = max(ans, prev + diff)
            prev += diff
            group_size += 1
            group_num[neta] -= 1
            # print(f"prev {prev}")            
    print(ans)
 
 
 
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

N, K = map(int, input().split())
nums = []
for i in range(N):
    t, d = map(int, input().split())
    nums.append((d, t))
nums.sort(reverse=True)
se = set()
doubled = []
rest = []
points = 0
for i, n in enumerate(nums):
    if i < K:
        if not n[1] in se:
            se.add(n[1])
        else:
            doubled.append(n)
        points += n[0]
    else:
        rest.append(n)
ans = points + pow(len(se), 2)
idx = len(doubled)-1
for d, t in rest:
    if idx < 0: break
    if t in se: continue
    points -= doubled[idx][0]
    idx -= 1
    points += d
    se.add(t)
    ans = max(ans, points+pow(len(se), 2))
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

N, K = map(int, input().split())
nums = []
for i in range(N):
    t, d = map(int, input().split())
    nums.append((d, t))
nums.sort(reverse=True)
se = set()
a1 = []
a2 = []
rest = []
for i, n in enumerate(nums):
    if i < K:
        if not n[1] in se:
            se.add(n[1])
            a1.append(n)
        else:
            a2.append(n)
    else:
        rest.append(n)
points = 0
for (d, t) in a1: points += d
for (d, t) in a2: points += d
ans = points + pow(len(se), 2)
a2.sort()
idx2 = 0
for i, (d, t) in enumerate(rest):
    if t in se: continue
    if len(a2) <= idx2: break
    points -= a2[idx2][0]
    idx2 += 1
    points += d
    se.add(t)
    ans = max(ans, points+pow(len(se), 2))
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

N, K = map(int, input().split())
nums = [[] for i in range(N)]
for i in range(N):
    t, d = map(int, input().split())
    t -= 1
    nums[t].append(d)
maxs = []
rest = []
for i in range(N):
    if len(nums[i]) == 0: continue
    nums[i].sort(reverse=True)
    maxs.append(nums[i][0])
    for n in nums[i][1:]:
        rest.append(n)
maxs.sort(reverse=True)
rest.sort(reverse=True)
if len(maxs) > K:
    maxs = maxs[:K]
other = []
idx = 0
while len(maxs)+len(other) < K:
    other.append(rest[idx])
    idx += 1
rest = rest[idx:]

types = len(maxs)
for i,r in enumerate(rest):
    diff = types*types - pow(types-1, 2)
    if diff < r-maxs[len(maxs)-1-i]:
        maxs[len(maxs)-1-i] = r
        types -= 1
    else:
        break
ans = types*types
for num in maxs:
    ans += num
for num in other:
    ans += num
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

N, K = map(int, input().split())
nums = [[] for i in range(N)]
for i in range(N):
    t, d = map(int, input().split())
    t -= 1
    nums[t].append(d)
maxs = []
rest = []
for i in range(N):
    nums[i].sort(reverse=True)
    if len(nums[i]) > 0:
        maxs.append(nums[i][0])
        for n in nums[i][1:]:
            rest.append(n)
        #rest = rest + nums[i][1:]
maxs.sort(reverse=True)
if len(maxs) > K:
    maxs = maxs[:K]
    for n in maxs[K:]:
        rest.append(n)
    #rest = rest + maxs[K:]
rest.sort(reverse=True)
other = []
idx = 0
while len(maxs)+len(other) < K:
    other.append(rest[idx])
    idx += 1
rest = rest[idx:]

types = len(maxs)
#print(maxs)
#print(rest)
for i,r in enumerate(rest):
    diff = types*types - pow(types-1, 2)
    if diff < r-maxs[len(maxs)-1-i]:
        maxs[len(maxs)-1-i] = r
        types -= 1
    else:
        break
ans = types*types
for num in maxs:
    ans += num
for num in other:
    ans += num
print(ans)

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
nums = [[] for i in range(N)]
for i in range(N):
    t, d = map(int, input().split())
    t -= 1
    nums[t].append(d)
maxs = []
rest = []
for i in range(N):
    nums[i].sort(reverse=True)
    if len(nums[i]) > 0:
        maxs.append(nums[i][0])
        for n in nums[i][1:]:
            rest.append(n)
        #rest = rest + nums[i][1:]
maxs.sort(reverse=True)
if len(maxs) > K:
    maxs = maxs[:K]
    for n in maxs[K:]:
        rest.append(n)
    #rest = rest + maxs[K:]
rest.sort(reverse=True)
other = []
idx = 0
while len(maxs)+len(other) < K:
    other.append(rest[idx])
    idx += 1
rest = rest[idx:]

types = len(maxs)
#print(maxs)
#print(rest)
for i,r in enumerate(rest):
    diff = types*types - pow(types-1, 2)
    if diff < r-maxs[len(maxs)-1-i]:
        maxs[len(maxs)-1-i] = r
        types -= 1
    else:
        break
ans = types*types
for num in maxs:
    ans += num
for num in other:
    ans += num
print(ans)