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.

Solution (Python):
import sys, itertools
def input(): return sys.stdin.readline()
def inpl(): return [int(i) for i in input().split()]
N, K = inpl()
Sushi = []
Neta = set()
ans = 0
for _ in range(N):
    t, d = inpl()
    Sushi.append((d, t))
Sushi.sort(reverse = True)
Db = []
Nd = []
for i in range(K):
    d, t = Sushi[i]
    if t not in Neta:
        Neta.add(t)
        ans += d
    else:
        Db.append(d)
neta = len(Neta)
Db = [0] + list(itertools.accumulate(Db))
Db.reverse()
for i in range(N-K):
    d, t = Sushi[K+i]
    if t not in Neta:
        Neta.add(t)
        Nd.append(d)
Nd = [0] + list(itertools.accumulate(Nd))
print(ans + max([(neta + i)**2 + j + k for i, (j, k) in enumerate(zip(Db, Nd))]))

Solution (Python):
import sys, itertools

def inpl(): return [int(i) for i in input().split()]
N, K = inpl()
Sushi = []
Neta = set()
ans = 0
for _ in range(N):
    t, d = inpl()
    Sushi.append((d, t))
Sushi.sort(reverse = True)
Db = []
Nd = []
for i in range(K):
    d, t = Sushi[i]
    if t not in Neta:
        Neta.add(t)
        ans += d
    else:
        Db.append(d)
neta = len(Neta)
Db = [0] + list(itertools.accumulate(Db))
Db.reverse()
for i in range(N-K):
    d, t = Sushi[K+i]
    if t not in Neta:
        Neta.add(t)
        Nd.append(d)
Nd = [0] + list(itertools.accumulate(Nd))
print(ans + max([(neta + i)**2 + j + k for i, (j, k) in enumerate(zip(Db, Nd))]))

Solution (Python):
import sys, itertools
def input(): return sys.stdin.readline()
def inpl(): return [int(i) for i in input().split()]
N, K = inpl()
Sushi = []
Neta = set()
ans = 0
for _ in range(N):
    t, d = inpl()
    Sushi.append((d, t))
Sushi.sort(reverse = True)
Db = []
Nd = []
for i in range(K):
    d, t = Sushi[i]
    if t not in Neta:
        Neta.add(t)
        ans += d
    else:
        Db.append(d)
neta = len(Neta)
Db = [0] + list(itertools.accumulate(Db))
Db.reverse()
for i in range(N-K):
    d, t = Sushi[K+i]
    if t not in Neta:
        Neta.add(t)
        Nd.append(d)
Nd = [0] + list(itertools.accumulate(Nd))
print(ans + max([(neta + i)**2 + j + k for i, (j, k) in enumerate(zip(Db, Nd))]))

Solution (Python):
n,k = map(int,input().split())
a = [list(map(int,input().split())) for i in range(n)]
mita = [0]*n
a.sort(key = lambda x : -x[1])
ireta = [0]*n
tmp=[]
for c in range(n):
  i,j = a[c]
  if mita[i-1] == 0:
    mita[i-1] = 1
    ireta[c] = 1
    tmp.append([i-1,j])
  if len(tmp) >= k:
    break
c = 0
kazu = sum(mita)
while len(tmp) < k:
  if ireta[c]:
    c+=1
    continue
  ireta[c] = 1
  mita[a[c][0]-1] += 1
  tmp.append(a[c])
tmp.sort(key = lambda x: -x[1])
c = 0
kaku = []
flag = 0
for _ in range(n):
  b = tmp.pop()
  if mita[b[0]] >1:
    tmp.append(b)
    break
  while ireta[c]:
    c+=1
    if c >= n:
      flag = 1
      tmp.append(b)
      break
  if flag:
    break
  if kazu*kazu+b[1] < (kazu-1)**2+a[c][1]:
    kaku.append(a[c])
    ireta[c] = 1
    mita[a[c][0]-1] += 1
    kazu -= 1
  else:
    tmp.append(b)
    break
ans = kazu*kazu
for i,j in tmp:
  ans += j
for i,j in kaku:
  ans += j
print(ans)

Solution (Python):
N, K = map( int, input().split())
T = [(0,0)]*N
for i in range(N):
    t, d = map( int, input().split())
    T[i] = (d,t)
T.sort( key= None, reverse = True)
C = T[:K]
AC = T[K:]
kiso = 0
s = 0
S = [0]*(N+1)
for i in range(K):
    d, t = T[i]
    kiso += d
    if S[t] == 0:
        S[t] = 1
        s += 1
    else:
        S[t] += 1
ans = kiso + s**2
C.sort()
r = 0

for i in range(K):
    d, t = C[i]
    if S[t] >= 2:
        while r < N-K:
            if S[ AC[r][1]] == 0:
                S[t] -= 1
                S[ AC[r][1]] += 1
                s += 1
                kiso -= d
                kiso += AC[r][0]
                r += 1
                break
            r += 1
    ans = max( ans, kiso + s**2)
print( ans)

Solution (Python):
N, K = [int(_) for _ in input().split()]
TD = [[int(_) for _ in input().split()] for i in range(N)]



xs = sorted(TD, key=lambda x:-x[1])



baset = 0
ts = set([])
ds = []

for t, d in xs[:K]:
    baset += d
    if not t in ts:
        ts.add(t)
    else:
        ds.append(d)

result = baset + len(ts) ** 2
r = result



for t, d in xs[K:]:
    if not ds:
        break
    if not t in ts:
        r += 2 * len(ts) + 1
        r += d - ds.pop()
        ts.add(t)
        result = max(result, r)
        



print(result)

Solution (Python):
N, K = map( int, input().split())
T = [(0,0)]*N
for i in range(N):
    t, d = map( int, input().split())
    T[i] = (d,t)
T.sort( key= None, reverse = True)
C = T[:K]
AC = T[K:]
kiso = 0
s = 0
S = [0]*(N+1)
for i in range(K):
    d, t = T[i]
    kiso += d
    if S[t] == 0:
        S[t] = 1
        s += 1
    else:
        S[t] += 1
ans = kiso + s**2
C.sort()
r = 0

for i in range(K):
    d, t = C[i]
    if S[t] >= 2:
        while r < N-K:
            if S[ AC[r][1]] == 0:
                S[t] -= 1
                S[ AC[r][1]] += 1
                s += 1
                kiso -= d
                kiso += AC[r][0]
                r += 1
                break
            r += 1
    ans = max( ans, kiso + s**2)
print( ans)

Solution (Python):
from collections import defaultdict
N, K = map(int, input().split())
T = defaultdict(list)
for i in range(N):
    t, d = map(int, input().split())
    T[t].append(d)
S = []; U = []
for k, v in T.items():
    v.sort(reverse=1)
    U.append((v[0], k))
    for w in v[1:]:
        S.append((w, k))
S.sort(reverse=1)
U.sort(reverse=1)
D = defaultdict(int)
t = cnt = 0
res = 0
for w, k in S:
    D[k] += 1
    if D[k] == 1:
        t += 1
    cnt += 1
    res += w
ans = 0
can = 1
for v, k in U:
    D[k] += 1
    if D[k] == 1:
        t += 1
    cnt += 1
    res += v
    while cnt > K:
        if not S:
            can = 0
            break
        cnt -= 1
        w, l = S.pop()
        D[l] -= 1
        if D[l] == 0:
            t -= 1
        res -= w
    if not can:
        break
    ans = max(ans, t*t + res)
print(ans)

Solution (Python):
n,k = map(int,input().split())
top = [0]*n
sub = []
for i in range(n):
    t,d = map(int,input().split())
    t -=1
    if top[t]==0:
        top[t]=d
    else:
        if top[t]>=d:
            sub.append(d)
        else:
            sub.append(top[t])
            top[t]=d

top.sort()
top = top[::-1]
res = [0]
for i in range(n):
    if top[i]!=0:
        res.append(res[-1]+top[i])
    else:
        res.append(-1)
sub.sort()
sub = sub[::-1]
w = [0]
for i in range(len(sub)):
    w.append(w[-1]+sub[i])
tmp = 0
for i in range(1,k+1):
    if len(w)-1>=k-i and res[i]!=-1:
        tmp = max(res[i]+w[k-i]+i*i,tmp)

print(tmp)