Problem:


Score : 400 points

Problem Statement

Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.

Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

2 \leq N \leq 5000

1 \leq K \leq 10^9

1 \leq P_i \leq N

P_i \neq i

P_1, P_2, \cdots, P_N are all different.

-10^9 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N

Output

Print the maximum possible score at the end of the game.

Sample Input 1

5 2
2 4 5 1 3
3 4 -10 -8 8

Sample Output 1

8

When we start at some square of our choice and make at most two moves, we have the following options:

If we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.

If we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.

If we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.

If we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.

If we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.

The maximum score achieved is 8.

Sample Input 2

2 3
2 1
10 -7

Sample Output 2

13

Sample Input 3

3 3
3 1 2
-1000 -2000 -3000

Sample Output 3

-1000

We have to make at least one move.

Sample Input 4

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719

Sample Output 4

29507023469

The absolute value of the answer may be enormous.



Sample input:
5 2
2 4 5 1 3
3 4 -10 -8 8


Sample output:
8

Submission status: Accepted

Solution code:
n, k = map(int, input().split())
p = list(map(int, input().split()))
c = list(map(int, input().split()))
l = [[] for i in range(n)]
for i in range(n):
    l2 = [i + 1]
    cnt = 0
    while True:
        l2.append(p[l2[-1] - 1])
        cnt += c[l2[-1] - 1]
        l[i].append(cnt)
        if l2[-1] == i + 1:
            break
ans = -float("inf")
for i in range(n):
    le = len(l[i])
    for j in range(min(k, le)):
        cnt = l[i][j]
        if l[i][-1] > 0:
            cnt += (k - j - 1) // le * l[i][-1]
        ans = max(ans, cnt)
print(ans)

Submission status: Accepted

Solution code:

N,K=map(int,input().split())
P=list(map(lambda x:int(x)-1,input().split()))
C=list(map(int,input().split()))

ans=0
check=set()

for i in range(N):
    
    if i in check:
        continue
    
    # create loop
    tmpK=K
    tmpans=0
    loop_check=set()
    tmp_idx=i
    loop=[]
    while tmp_idx not in loop_check:
        loop.append(C[tmp_idx])
        loop_check.add(tmp_idx)
        check.add(tmp_idx)
        tmp_idx=P[tmp_idx]
    
    S=sum(loop)
    L=len(loop)
    if S>=0 and tmpK//L>=2:
        tmpans=S*(tmpK//L-1)
        tmpK=tmpK%L+L
    
    # 部分最大列を検索
    #print('loop',loop)
    loop=[0]+loop*3
    for i in range(len(loop)-1):
        loop[i+1]+=loop[i]
    n=3*L+1
    def init_min(init_min_val):
        #set_val
        for i in range(n):
            seg_min[i+num_min-1]=init_min_val[i]    
        #built
        for i in range(num_min-2,-1,-1) :
            seg_min[i]=min(seg_min[2*i+1],seg_min[2*i+2])
    def query_min(p,q):
        if q<=p:
            return ide_ele_min
        p += num_min-1
        q += num_min-2
        res=ide_ele_min
        while q-p>1:
            if p&1 == 0:
                res = min(res,seg_min[p])
            if q&1 == 1:
                res = min(res,seg_min[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        if p == q:
            res = min(res,seg_min[p])
        else:
            res = min(min(res,seg_min[p]),seg_min[q])
        return res
    #####単位元######
    ide_ele_min = 10**15
    #num_min:n以上の最小の2のべき乗
    num_min =2**(n-1).bit_length()
    seg_min=[ide_ele_min]*2*num_min

    init_min(loop)
    local_max=0
    for i,v in enumerate(loop):
        if i>=1:
            #print('v,min=',v,query_min(max(0,i-tmpK),i),v-query_min( max(0,i-tmpK),i ))
            local_max=max(local_max,v-query_min( max(0,i-tmpK),i ) )
    
    ans=max(ans,local_max+tmpans)

if ans==0:
    print(max(C))
else:
    print(ans)

Submission status: Accepted

Solution code:
import sys, math
from functools import lru_cache
from collections import defaultdict
sys.setrecursionlimit(500000)
MOD = 10**9+7

def input():
    return sys.stdin.readline()[:-1]

def mi():
    return map(int, input().split())

def ii():
    return int(input())

def i2(n):
    tmp = [list(mi()) for i in range(n)]
    return [list(i) for i in zip(*tmp)]

def main():
    N, K = mi()
    P = list(mi())
    C = list(mi())

    # loopを格納
    loops = []
    # 数えたかどうか
    done = [False]*N
    
    for i in range(N):
        # もう数えているならskip
        if done[i]:
            continue

        now = P[i]-1
        T = 1
        s = C[now]
        lst = [now]

        done[now] = True

        # 戻ってくるまでループ
        while now != i:
            now = P[now]-1
            T += 1
            s += C[now]
            lst.append(now)

            done[now] = True

        loops.append((T, s, lst))

    # print(loops)

    ans = -math.inf

    # 各loopごと
    for loop in loops:
        # loopの周期、総和、構成要素を取得
        T, s, lst = loop

        if s <= 0:
            m = -math.inf
            for v in lst:
                now = v
                ss = 0
                for _ in range(min(K, T)):
                    now = P[now]-1
                    ss += C[now]
                    m = max(m, ss)

            ans = max(ans, m)

        else:
            n = max(K//T-1, 0)
            rest = K-n*T
            m = -math.inf

            for v in lst:
                now = v
                ss = 0
                for _ in range(rest):
                    now = P[now]-1
                    ss += C[now]
                    m = max(m, ss)
            
            ans = max(ans, m+n*s)
    print(ans)



if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
import math
import collections
import bisect
import itertools

# import numpy as np

sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7
# MOD = 998244353

ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))


# ===CODE===

# https://note.nkmk.me/python-union-find/

class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())


def main():
    n, k = ns()
    p = na1()
    c = na()

    uf = UnionFind(n)
    for i, pi in enumerate(p):
        uf.union(i, pi)

    cycledist = [[-INF for _ in range(2)] for __ in range(n)]
    for lis in uf.all_group_members().values():
        tmp = 0
        l = len(lis)
        for idx in lis:
            tmp += c[idx]
            cycledist[idx][1] = l
        for idx in lis:
            cycledist[idx][0] = tmp

    ans = -INF

    for i in range(n):
        flg = k // cycledist[i][1] > 0
        tmp_ans = cycledist[i][0] * ((k // cycledist[i][1]) - 1) if flg else 0

        tmp = 0
        idx = i
        for j in range(cycledist[i][1] * flg + k % cycledist[i][1]):
            tmp += c[p[idx]]
            idx = p[idx]
            ans = max(ans, tmp_ans + tmp)

        tmp = 0
        idx = i
        for j in range(min(k, cycledist[i][1])):
            tmp += c[p[idx]]
            idx = p[idx]
            ans = max(ans, tmp)

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import copy

def cost_val(visit_list, P, C):
    maxval = [-10**10] * (len(P) + 1)
    for start_idx in visit_list:
        cost = 0
        now_id = start_idx
        for i in range(len(visit_list)):
            now_id = P[now_id]
            cost += C[now_id]
            maxval[i + 1] = max(maxval[i + 1], cost)
    return maxval[1:len(visit_list) + 1]

def cycles(P):
    cycle_list = []
    visit_list = [False] * len(P)
    for i in range(len(P)):
        if visit_list[i]:
            continue
        now_id = i
        cycle = []
        for j in range(len(P)):
            if visit_list[now_id]:
                break
            cycle.append(now_id)
            visit_list[now_id] = True
            now_id = P[now_id]
        cycle_list.append(cycle)
    return cycle_list

def main():
    N, K = map(int, input().split())
    P = list(map(lambda x: int(x) - 1, input().split()))
    C = list(map(int, input().split()))
    cycle_list = cycles(P)
    ans = max(C)
    for cycle in cycle_list:
        maxval = cost_val(cycle, P, C)
        if len(cycle) > K:
            ans = max(ans, max(maxval[:K]))
        else:
            if K % len(cycle) == 0:
                ans = max(ans, max(maxval), max(map(lambda x: x + maxval[-1] * (K // len(cycle) - 1), maxval)), maxval[-1] * (K // len(cycle)))
            else:
                ans = max(ans, max(maxval), max(map(lambda x: x + maxval[-1] * (K // len(cycle) - 1), maxval)), maxval[-1] * (K // len(cycle)) + max(maxval[:(K % len(cycle))]))
    return ans

if __name__ == '__main__':
    print(main())

Submission status: Accepted

Solution code:

def resolve():
    INF = 10 ** 18
    N, K = map(int, input().split())
    P = list(map(lambda x: int(x) - 1, input().split()))
    C = list(map(int, input().split()))

    cycles = []
    ans = -INF
    for n in range(N):
        loop, score = 0, 0
        t = n
        for i in range(min(N, K)):
            n = P[n]
            score += C[n]
            ans = max(ans, score)
            if n == t:
                loop = i + 1
                break
        cycles.append((loop, score))

    for n in range(N):
        loop, score = cycles[n]
        if loop > 0 and score > 0:
            r = (K - 1) // loop
            nscore = r * score
            for i in range(K - r * loop):
                n = P[n]
                nscore += C[n]
                ans = max(nscore, ans)
    print(ans)



if __name__ == "__main__":
    resolve()

Submission status: Accepted

Solution code:
from collections import defaultdict
N, K = [int(x) for x in input().split()]
P = [0] + [int(x) for x in input().split()]
C = [0] + [int(x) for x in input().split()]

max_score = max(C[1:])

for init in range(1, N + 1):   # 初めの場所をiとする
    score = defaultdict(int)  # int/bool/list....
    visited = [-1] * (N + 1)
    visited[init] = 0  # 何回移動後に着いたか？
    i = init
    for k in range(1, K + 1):
        prev = i
        i = P[i]    # k回移動後に着くところ

        if visited[i] < 0:  # まだ訪れてなかった
            visited[i] = k
            score[i] = score[prev] + C[i]
            max_score = max(max_score, score[i])
            continue

        loop_score = (score[prev] + C[i]) - score[i]
        loop_len = k - visited[i]

        score[i] = score[prev] + C[i]

        loop_num = (K - k) // loop_len # ループをあと何回回れるか
        loop_rem = (K - k) % loop_len

        if loop_num > 0 and loop_rem == 0:
            loop_num -= 1
            loop_rem = loop_len

        j = i   # ループを開始するノードから
        temp = 0
        rem_max = 0
        for _ in range(loop_rem):
            j = P[j]
            temp += C[j]
            rem_max = max(rem_max, temp)

        max_score = max(max_score, score[i] + loop_num * loop_score + rem_max)
        break

print(max_score)

Submission status: Accepted

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

sys.setrecursionlimit(10**7)
inf=10**20
mod=10**9+7
dd=[(-1,0),(0,1),(1,0),(0,-1)]
ddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
# def LF(): return [float(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return input()

def main():
  N,K=LI()
  P=LI()
  P=[0]+P
  C=LI()
  C=[0]+C

  l=[[0] for _ in range(N)]
  check=[[False]*(N+1) for _ in range(N)]
  roop=[]
  for i in range(N):
    zahyo=i+1
    check[i][zahyo]=True
    f=False
    for j in range(N+1):
      zahyo=P[zahyo]
      if check[i][zahyo] and not f:
        roop.append(j+1)
        f=True
      score=C[zahyo]
      l[i].append(l[i][-1]+score)
  # for i in range(N):
  #   print(l[i])
  # print(roop)

  ans=-inf
  for i in range(N):
    roop_count=roop[i]
    if K<=roop_count:
      ans=max(ans,max(l[i][1:K+1])) # 1巡以内
    else:
      ans=max(ans,max(l[i][1:K+1])) # 1巡以内

      # 2巡目以降（1巡で負になるなら回らない方がいい）
      if l[i][roop_count]>0:
        c=K//roop_count
        _ans1=c*l[i][roop_count]
        k=K%roop_count
        _ans1+=max(l[i][1:k+1]+[0])
        ans=max(ans,_ans1)

        # 可能な巡数まで行かない方がいい場合も
        _ans2=(c-1)*l[i][roop_count]
        _ans2+=max(l[i][:roop_count]+[0])
        ans=max(ans,_ans1,_ans2)

  return ans

# main()
print(main())

Submission status: Accepted

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

N, K = map(int, input().split())
P = list(map(lambda x: int(x) - 1, input().split()))
C = list(map(int, input().split()))
ans = -float('inf')
for s in range(N):
    scores = [0] * (N+1)
    i = P[s]
    v = scores[i] = C[i]
    l = 1
    while i != s:
        i = P[i]
        v += C[i]
        scores[i] = v
        l += 1
    i = P[s]
    c = 1
    ans = max(ans, scores[i], scores[i] + (K - c) // l * v)
    while i != s and c < K:
        i = P[i]
        c += 1
        ans = max(ans, scores[i], scores[i] + (K - c) // l * v)
print(ans)

Submission status: Accepted

Solution code:
n,k = map(int,input().split())
p = list(map(int,input().split()))
for i in range(n):
    p[i] -= 1
c = list(map(int,input().split()))

reach = [False]*n
x = []
for i in range(n):
    if reach[i]:continue
    buf = []
    cur = i
    while not reach[cur]:
        buf.append(c[cur])
        reach[cur] = True
        cur = p[cur]
    x.append(buf)

ans = max(c)
import itertools
for i in x:
    n = k//len(i)
    ind = k%len(i)
    if n>0:
        n -= 1
        ind += len(i)
    else:
        ind = min(k,len(i)*2)
    ii = i+i+i
    r = list(itertools.accumulate(ii))
    a = max(0,r[len(i)-1]*n)
    for j in range(len(i)):
        for z in range(1,ind+1):
            s = r[j+z]-r[j]
            ans = max(ans,a+s)
print(ans)

Submission status: Accepted

Solution code:
n,k = map(int,input().split())
p = list(map(int,input().split()))
for i in range(n):
    p[i] -= 1
c = list(map(int,input().split()))

reach = [False]*n
x = []
for i in range(n):
    if reach[i]:continue
    buf = []
    cur = i
    while not reach[cur]:
        buf.append(c[cur])
        reach[cur] = True
        cur = p[cur]
    x.append(buf)

ans = max(c)
import itertools
for i in x:
    n = k//len(i)
    ind = k%len(i)
    if n>0:
        n -= 1
        ind += len(i)
    else:
        ind = min(k,len(i)*2)
    ii = i+i+i
    r = list(itertools.accumulate(ii))
    a = max(0,r[len(i)-1]*n)
    for j in range(len(i)):
        for z in range(1,ind+1):
            s = r[j+z]-r[j]
            if z<ind+1:ans = max(ans,a+s)
            else:ans = max(ans,s)
print(ans)

Submission status: Accepted

Solution code:

def resolve():
    INF = 10 ** 18
    N, K = map(int, input().split())
    P = list(map(lambda x: int(x) - 1, input().split()))
    C = list(map(int, input().split()))

    visited = [0] * N
    cycles = []

    for i in range(N):
        if visited[i]:
            continue
        score = []
        v = i
        visited[v] = True
        score.append(C[v])
        while not visited[P[v]]:
            v = P[v]
            visited[v] = True
            score.append(C[v])
        cycles.append(score)

    ans = -INF
    for cy in cycles:
        length = len(cy)
        c_num = max(0, (K - 1) // length - 1)
        total = max(0, sum(cy) * c_num)
        rest = K - (c_num * length)
        l_cy = cy + cy + cy
        for l in range(length):
            total_rest = 0
            for diff in range(rest):
                total_rest += l_cy[l + diff]
                ans = max(ans, total + total_rest)

    print(ans)


if __name__ == "__main__":
    resolve()

Submission status: Accepted

Solution code:
def max2(x,y):
    return x if x > y else y

N, K = map(int, input().split())
P = list(map(int, input().split()))
C = list(map(int, input().split()))

off = max(C)
m2 = off
for i in range(N):
    tmp = 0
    m1 = off
    l = i
    S = 0
    k = 0
    for j in range(N):
        S += C[l]
        l = P[l] - 1
        if l==i:
            k = j+1
            break
    cnt = K // k - (K % k == 0)
    cnt = max2(0, cnt -2)
    a = K-cnt*k
    l = i
    for j in range(a):
        tmp += C[l]
        m1 = max2(m1, tmp)
        l = P[l] - 1
    if S > 0:
        m1 += cnt*S
    m2 = max2(m1, m2)

print(m2)
"""
2 4
2 1
10 -7
"""

Submission status: Accepted

Solution code:
from collections import defaultdict
N, K = [int(x) for x in input().split()]
P = [0] + [int(x) for x in input().split()]
C = [0] + [int(x) for x in input().split()]

max_score = max(C[1:])

for init in range(1, N + 1):   # 初めの場所をiとする
    score = defaultdict(int)  # int/bool/list....
    visited = [-1] * (N + 1)
    visited[init] = 0  # 何回移動後に着いたか？
    i = init
    for k in range(1, K + 1):
        prev = i
        i = P[i]    # k回移動後に着くところ

        if visited[i] < 0:  # まだ訪れてなかった
            visited[i] = k
            score[i] = score[prev] + C[i]
            max_score = max(max_score, score[i])
            continue

        loop_score = (score[prev] + C[i]) - score[i]
        loop_len = k - visited[i]

        score[i] = score[prev] + C[i]
        # max_score = max(max_score, score[i])

        # if k == K:
        #     break # これ以上移動できない

        start = i   # ループを開始するノード
        loop_num = (K - k) // loop_len # ループをあと何回回れるか
        loop_rem = (K - k) % loop_len

        if loop_num > 0 and loop_rem == 0:
            loop_num -= 1
            loop_rem = loop_len

        jj = start
        temp = 0
        temp_max = 0
        for l in range(loop_rem):
            jj = P[jj]
            temp += C[jj]
            temp_max = max(temp_max, temp)

        loop_max = temp_max + loop_num * loop_score
        max_score = max(max_score, score[start] + loop_max)
        break

print(max_score)

Submission status: Accepted

Solution code:
import os
import sys
from atexit import register
from io import BytesIO
sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
sys.stdout = BytesIO()
register(lambda: os.write(1, sys.stdout.getvalue()))
input = lambda: sys.stdin.readline().rstrip('\r\n')
raw_input = lambda: sys.stdin.readline().rstrip('\r\n')

n,k = [int(x) for x in input().split()]
perm  =  [int(x)-1 for x in input().split()]
cost = [int(x) for x in input().split()]


ans = -10**10
for node in xrange(n):
    visited = [False for _ in xrange(n)]
    curnode = perm[node]
    cost_lst = [0]
    while not visited[curnode]:
        visited[curnode] = True
        cost_lst.append(cost_lst[-1] + cost[curnode])
        curnode = perm[curnode]

    cycles_n = k // (len(cost_lst)-1)
    rem = k % (len(cost_lst)-1)

    # print(cost_lst)
    if cycles_n > 0:
        ans = max(ans, max(cost_lst[1:]))
    if cycles_n == 0:
        ans = max(ans, max(cost_lst[1:rem+1]))
    if cycles_n > 0 and cost_lst[-1] > 0:
        if rem != 0:
            opt1 = cycles_n * cost_lst[-1] + max(cost_lst[1:rem+1])
        else:
            opt1 = (cycles_n-1) * cost_lst[-1] + max(cost_lst[1:])
        ans = max(ans, opt1)

print(ans)

Submission status: Accepted

Solution code:
def mss(l,length,k):
    x = - 1000000001
    for i in range(length):
        temp = 0
        for j in range(i,i+k):
            temp += l[j]
            if temp > x:
                x = temp
    return x
  
def mss2(l,length,total,k):
    x = - 1000000001
    if k <= length:
      for i in range(length):
          temp = 0
          for j in range(i,i+k):
              temp += l[j]
              if temp > x:
                  x = temp
      return x
    else:
      for i in range(length):
          temp = 0
          for j in range(i,i+length):
              temp += l[j]
              r = j - i + 1
              if temp + (total * ((k-r) // length)) > x:
                  x = temp + (total * ((k-r) // length))
      return x
      

if __name__ == '__main__':
    N,K = map(int,input().split())
    P = [int(p)-1 for p in input().split()]
    C = [int(c) for c in input().split()]
    #閉路の探索
    L_close = []
    Done = [0] * N
    for i in range(N):
        if Done[i] == 1:
            continue
        score = []
        #start
        Done[i] = 1
        #Next
        p = P[i]
        Done[p] = 1
        score.append(C[p])
        while p != i:
            p = P[p]
            Done[p] = 1
            score.append(C[p])
        L_close.append(score)
    #それぞれの閉路に対して
    ans = - 1000000001
    for l in L_close:
        total = sum(l)
        length = len(l)
        l = l + l
        if total <= 0:
            ans = max(ans,mss(l,length,min(K,length)))
        else:
            ans = max(ans,mss2(l,length,total,K))
    print(ans)

Submission status: Accepted

Solution code:
N,K = map(int,input().split())
P = list(map(int,input().split()))
for i in range(N):
  P[i]-=1
#print(P)
C = list(map(int,input().split()))
Flag = True
for c in C:
  if c >= 0:
    Flag = False
    break
if Flag:
  print(max(C))
  exit()
L = []
for i in range(N):
  #visited = set([])
  Flag = False
  now = i
  temp = []
  while True:
    if Flag and now == i:
      break
    nxt = P[now]
    Flag = True
    temp.append(C[nxt])
    now = nxt
  L.append(temp)
#print(L)
ans = 0
S = []
for X in L:
  start = [0]
  for i in range(len(X)):
    temp = start[-1]+X[i]
    start.append(temp)
  S.append(start)
#print(S)
for X,SS in zip(L,S):
  n = len(X)
  cycle_sum = SS[-1]
  if K <= n:
    kouho = max(SS[:K+1])
  elif cycle_sum < 0:
    kouho = max(SS)
  else:
    amari = K%n
    loop = K//n
    first = 0 #余りよりも後で最大
    second = 0 #余りよりも前で最大
    first = (loop-1)*cycle_sum + max(SS)
    second = loop*cycle_sum + max(SS[:amari+1])
    kouho = max(first,second)
  ans = max(ans,kouho)
print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict
INF = float('inf')
N, K = [int(x) for x in input().split()]
P = [0] + [int(x) for x in input().split()]
C = [0] + [int(x) for x in input().split()]

max_score = -INF
for init in range(1, N + 1):   # 初めの場所をiとする
    score = defaultdict(int)  # int/bool/list....
    visited = [-1] * (N + 1)
    visited[init] = 0  # 何回移動後に着いたか？
    i = init
    # max_init = -INF
    for k in range(1, K + 1):
        prev = i
        i = P[i]    # k回移動後に着くところ

        if visited[i] < 0:  # まだ訪れてなかった
            visited[i] = k
            score[i] = score[prev] + C[i]
            # max_init = max(max_init, score[i])
            max_score = max(max_score, score[i])
            continue

        loop_score = (score[prev] + C[i]) - score[i]
        loop_len = k - visited[i]

        score[i] = score[prev] + C[i]
        # max_init = max(max_init, score[i])
        max_score = max(max_score, score[i])

        if k == K:
            break # これ以上移動できない

        start = i   # ループを開始するノード
        loop_num = (K - k) // loop_len # ループをあと何回回れるか
        loop_rem = (K - k) % loop_len

        if loop_rem == 0:
            loop_num -= 1
            loop_rem = loop_len

        jj = start
        temp = 0
        temp_max = 0
        for l in range(loop_rem):
            jj = P[jj]
            temp += C[jj]
            temp_max = max(temp_max, temp)

        loop_max = temp_max + loop_num * loop_score
        # max_init = max(max_init, score[start] + loop_max)
        max_score = max(max_score, score[start] + loop_max)
        break

    # max_score = max(max_score, max_init)

if max_score == -INF:
    max_score = max(C[1:])

print(max_score)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
# sys.setrecursionlimit(100000)


def main():
    n, k = [int(i) for i in input().strip().split()]
    p = [int(i) for i in input().strip().split()]
    c = [int(i) for i in input().strip().split()]
    ans = -10**9
    for i in range(n):
        scores = [0]
        seen = set([i])
        now = i
        loop = False
        for _ in range(k):
            now = p[now] - 1
            scores.append(c[now])
            if now in seen:
                loop = True
                break
            seen.add(now)
        for i in range(len(scores) - 1):
            scores[i + 1] += scores[i]
        tmp = max(scores[1:])
        ans = max(ans, tmp)
        if (not loop) or scores[-1] <= 0:
            continue
        tmp = scores[-1] * (k // (len(scores) - 1))
        rem = k % (len(scores) - 1)
        tmp += max(scores[:rem + 1])
        ans = max(ans, tmp)
        tmp = scores[-1] * (k // (len(scores) - 1) - 1)
        tmp += max(scores)
        ans = max(ans, tmp)
    print(ans)

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
N, K = map(int,input().split())
P = list(map(int,input().split()))
C = list(map(int,input().split()))
ans = -float("inf")
for i in range(N):
    hoge = []
    p = i
    s = 0
    for j in range(K):
        p = P[p]-1
        s += C[p]
        hoge.append(s)
        ans = max(ans,s)
        if p == i:
            S1 = s*((K-1)//len(hoge))
            S1 += max(hoge[0:(K-1)%len(hoge)+1])
            S2 = ans
            if (K-1) // len(hoge) > 1:
                S2 = s*((K-1)//len(hoge)-1)
                S2 += max(hoge)
            ans = max(ans,S1,S2)
            break
print(ans)

Submission status: Accepted

Solution code:

max2 = lambda x,y: x if x > y else y
min2 = lambda x,y: x if x < y else y

N,K = map(int,input().split())

P = tuple(map(lambda x: int(x)-1,input().split()))
C = tuple(map(int,input().split()))

acc = [0]*N
visited = [-1]*N
last = [0]*N

res = -10**9

for p in range(N):
    c = 0
    v = p
    for j in range(min2(N+1,K)):
        if visited[v] == p:
            break
        visited[v] = p
        acc[v] = c
        last[v] = j
        c += C[v]
        v = P[v]
        res = max2(c,res)
    else:
        continue

    i = last[v]

    delta = c - acc[v]
    remaining = K - i
    cycle = j-i
    if delta > 0 and remaining >= cycle:
        cnt = remaining//cycle - 1
        c = acc[v]+cnt*delta
        remaining -= cnt*cycle
        for _ in range(remaining):
            c += C[v]
            res = max2(res, c)
            v = P[v]

print(res)

Submission status: Accepted

Solution code:
N,K=map(int,input().split())
P=list(map(int,input().split()))
C=list(map(int,input().split()))

for i in range(N):
    P[i]-=1

ans=-float('inf')

for start in range(N):
    loop_len=1
    pos=P[start]
    score=C[pos]
    scores=[score]

    while pos!=start:
        loop_len+=1
        pos=P[pos]
        score+=C[pos]
        scores.append(score)
    
    loops=(K-1)//loop_len

    if score>0:
        cand=score*loops + max(scores[:(K-loop_len*loops)])
    else:
        cand=max(scores[:min(K,loop_len)])
    ans=max(ans,cand)
print(ans)

Submission status: Accepted

Solution code:
N,K = map(int,input().split())
P = list(map(lambda x: int(x) - 1, input().split()))
C = list(map(int,input().split()))

ans = max(C)
for i in range(N):
    s = i
    l = [C[i]]
    while True:
        s = P[s]
        if s == i:
            break
        l.append(C[s])
        

    if sum(l) > 0:
        if K>=len(l):
            c = (K//len(l)-1)*sum(l)
            n = K%len(l)+len(l)
        else:
            c = 0
            n = K
        ans = max(ans,c)
        s = i
        for j in range(n):
            c += C[s]
            s = P[s]
            ans = max(ans,c)

    n = min(N,K)
    s = i
    c = 0
    for j in range(n):
        c += C[s]
        s = P[s]
        ans = max(ans,c)
            
print(ans)

Submission status: Accepted

Solution code:
ma = lambda :map(int,input().split())
lma = lambda :list(map(int,input().split()))
tma = lambda :tuple(map(int,input().split()))
ni = lambda:int(input())
yn = lambda fl:print("Yes") if fl else print("No")
import collections
import math
import itertools
import heapq as hq
n,k = ma()
Pt = lma()
P = [p-1 for p in Pt]
C = lma()
class unionfind():
    def __init__(self,n):
        self.par = list(range(n))
        self.size = [1]*n
        self.rank = [0]*n

    def root(self,x):
        if self.par[x] == x:
            return x
        else:
            self.par[x] = self.root(self.par[x])
            return self.par[x]

    def same(self,x,y):
        return self.root(x) == self.root(y)

    def unite(self,x,y):
        x = self.root(x)
        y = self.root(y)
        if x==y:return
        else:
            if self.rank[x] < self.rank[y]:
                 x,y = y,x
            if self.rank[x] == self.rank[y]:
                self.rank[x]+=1
            self.par[y] = x
            self.size[x] +=self.size[y]
    def get_size(self,x):
        x = self.root(x)
        return self.size[x]
uf = unionfind(n)
for i in range(n):
    uf.unite(i,P[i])

def score(x):#xからスタートしたスコア
    l = uf.get_size(x)
    p,r = divmod(k,l)
    tmp = [0 for i in range(l)]#一回の累積gain
    gain_cycle = 0
    tval = 0
    for i in range(l):
        nex = P[x]
        gain_cycle +=C[nex]
        tval+=C[nex]
        tmp[i] = tval
        x = nex

    ### below::return part
    ret = -10**10
    tval = 0
    if p==0:
        for i in range(r):
            ret = max(ret,tmp[i])

    elif gain_cycle>=0:
        for i in range(l):
            if i<=r-1:
                tval=tmp[i] + gain_cycle*p
            else:
                tval=tmp[i] + gain_cycle*(p-1)
            ret = max(ret,tval)
    else:
        for i in range(l):
            ret = max(tmp[i],ret)

    return ret

        #print(ret,"ret")

ans = -10**15
for i in range(n):
    ans = max(ans,score(i))
print(ans)