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: Time Limit Exceeded

Solution code:
import sys
import numpy as np
# from numba import njit

# @njit(cache=True)
def calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			continue
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleIDs[v] = cycleID
					cycleItemCnts[cycleID] = currentCycleItemCnt
					cycleTotalScores[cycleID] = currentCycleTotal
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID


def main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):

	ans = -1e19

	for n in range(N):

		v = n
		currentCycleItemCnt, currentCycleTotal = cycleItemCnts[ cycleIDs[v] ], cycleTotalScores[ cycleIDs[v] ]

		procCnt = 0
		currentCycleSumTmp = 0

		for k in range(min(K,currentCycleItemCnt)):
			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			# numbaにするとこの辺の処理の値が変になってるきがする。。。？
			procCnt = k+1
			# NOTES: C[v]アクセスが異常に重い。。。
			currentCycleSumTmp += C[v]
			# if K < procCnt:
			# 	break

			cycleLoopCnt = 0
			if 0 < currentCycleTotal:
				cycleLoopCnt = int(( K - procCnt ) // currentCycleItemCnt)

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, "procCnt, cycleLoopCnt, currentCycleTotal=", procCnt, cycleLoopCnt, currentCycleTotal)
			ans = max( ans, currentCycleSumTmp + cycleLoopCnt * currentCycleTotal )

			# if P[v] == n:
				# サイクル終了
				# break
			# NOTES: (多分)通常のpythonだとこの取得だけでTLEする模様。。。
			v = P[v]

	print(int(ans))

if sys.argv[-1]=='ONLINE_JUDGE':
	# from numba import njit
	from numba.pycc import CC
	cc=CC('my_module')
	cc.export('calcCycle','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(calcCycle)
	# cc.export('main','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(main)
	# main=njit(main, cache=True)
	cc.compile()
	exit(0)
# from my_module import main,calcCycle
from my_module import calcCycle



if __name__ == "__main__":
	N,K = map(int,input().split())
	P = np.array( input().split(), np.int64 )
	P -= 1
	C = np.array( input().split(), np.int64 )

	# 一度計算したサイクル情報を一応キャッシュしておく。。。
	# あんまり意味なさそう
	cycleIDs = np.full( N, -1, dtype=np.int64 )
	cycleItemCnts = np.full( N, -1, dtype=np.int64 )
	cycleTotalScores = np.full( N, -1, dtype=np.int64 )

	calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)

	# print(cycleItemCnts)


	main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)
	#print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**6)
ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
nn = lambda: list(stdin.readline().split())
ns = lambda: stdin.readline().rstrip()

n,k = na()
p = na()
c = na()

s = set(range(n))

ans = 0
loops = []
while s:
    loop = [0]
    a = s.pop()
    while True:
        loop.append(loop[-1]+c[p[a]-1])
        if p[a]-1 not in s:
            break
        a = p[a]-1
        s.discard(a)
    loops.append(loop[1:])

ans = -1000000000000000
for tmp in loops:
    kk = k
    if k > len(tmp): kk = k%len(tmp)+len(tmp)
    loop = [0]+tmp+[tmp[-1]+u for u in tmp]+[tmp[-1]*2+u for u in tmp]
    x = -1000000000000
    for i in range(1,kk+1):
        for j in range(len(tmp)+1):
            x = max(x,loop[j+i]-loop[j])
    if k > len(tmp) and tmp[-1] > 0:
        x += tmp[-1]*(k//len(tmp)-1)
    ans = max(ans,x)

print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
import numpy as np
# from numba import njit

# @njit(cache=True)
def calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			continue
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleIDs[v] = cycleID
					cycleItemCnts[cycleID] = currentCycleItemCnt
					cycleTotalScores[cycleID] = currentCycleTotal
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID


def main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):

	ans = -1e19

	for n in range(N):

		v = n
		currentCycleItemCnt, currentCycleTotal = cycleItemCnts[ cycleIDs[v] ], cycleTotalScores[ cycleIDs[v] ]

		procCnt = 0
		currentCycleSumTmp = 0

		for _ in range(currentCycleItemCnt):
			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			# numbaにするとこの辺の処理の値が変になってるきがする。。。？
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = int(( K - procCnt ) // currentCycleItemCnt)

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, "procCnt, cycleLoopCnt, currentCycleTotal=", procCnt, cycleLoopCnt, currentCycleTotal)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( int(ans), int(tmp) )

			# NOTES: (多分)通常のpythonだとこの取得だけでTLEする模様。。。
			# if P[v] == n:
				# サイクル終了
				# break
			v = P[v]

	print(int(ans))

if sys.argv[-1]=='ONLINE_JUDGE':
	# from numba import njit
	from numba.pycc import CC
	cc=CC('my_module')
	cc.export('calcCycle','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(calcCycle)
	# cc.export('main','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(main)
	# main=njit(main, cache=True)
	cc.compile()
	exit(0)
# from my_module import main,calcCycle
from my_module import calcCycle



if __name__ == "__main__":
	N,K = map(int,input().split())
	P = np.array( input().split(), np.int64 )
	P -= 1
	C = np.array( input().split(), np.int64 )

	# 一度計算したサイクル情報を一応キャッシュしておく。。。
	# あんまり意味なさそう
	cycleIDs = np.full( N, -1, dtype=np.int64 )
	cycleItemCnts = np.full( N, -1, dtype=np.int64 )
	cycleTotalScores = np.full( N, -1, dtype=np.int64 )

	calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)

	# print(cycleItemCnts)


	main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)
	#print(ans)

Submission status: Time Limit Exceeded

Solution code:
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
from heapq import heappop, heappush
from math import sqrt
from fractions import gcd
import random
import string
import copy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7

#############
# Main Code #
#############

class Roop:
    def __init__(self, array):
        self.n = len(array)
        self.array = array
        # ループ検出
        self.roops = []
        # iはどのループのものか
        self.roop_dict = [-1] * self.n
        # ループ内の何番目にあるか
        self.opt_dic = {}
        ignore = [-1] * self.n
        cnt = 0
        for i in range(self.n):
            if ignore[i] >= 0:
                continue
            opt = [i]
            # opt内の何番目にあるか
            self.opt_dic[i] = 0
            c = 1
            # 探索したらフラグを立てる
            ignore[i] = 1
            # i → array[i]
            to = array[i]
            # ループが詰まるまで回す
            while True:
                if ignore[to] >= 0:
                    # 既にループ作成済なら
                    if self.roop_dict[to] >= 0:
                        break
                    # 作成してないならループ作成
                    for j in range(self.opt_dic[to], len(opt)):
                        self.roop_dict[opt[j]] = cnt
                    self.roops.append(opt[self.opt_dic[to]:])
                    # 次のループはcnt + 1番
                    cnt += 1
                    break
                opt.append(to)
                ignore[to] = 1
                self.opt_dic[to] = c
                c += 1
                to = array[to]

    # xがどの番号のループにあるか
    def roop_n(self, x):
        return self.roop_dict[x]

    # xが入っているループは何か
    # ループ内になければFalse
    def inspect(self, x):
        if self.roop_n(x) == -1:
            return False
        return self.roops[self.roop_dict(x)]

    # ループの大きさ
    def roop_len(self, x):
        return len(self.roops[self.roop_n(x)])

    # xからk回移動してどの場所に行けるか
    def move(self, x, k):
        if k == 1:
            return x + 1
        cnt = k
        to = x
        # ループに入る前にどのルートを通ったか
        # スタート地点から既にループに入っていた場合、headは空になる
        head = []
        # ループ脱出後どのルートを通るか
        tail = []
        # 何回ループしたか
        time = -1
        res = 0
        while cnt > 0:
            to = self.array[to]
            cnt -= 1
            # まだループしておらず、踏んだ場所がループ内にある場合
            if time == -1 and self.roop_n(to) >= 0:
                r = self.roops[self.roop_n(to)]
                time = (cnt // len(r))
                cnt -= time * len(r)
            # ループ前なら
            if time == -1:
                head.append(to)
            # ループ後なら
            else:
                tail.append(to)
        # 例: N, K = 6 727202214173249351
        # A = [6, 5, 2, 5, 3, 2]の時
        # 1回目の移動 1 → 6
        # 2回目の移動 6 → ### ここからループが始まる ### → 2
        # ... 242400738057749783回ループ
        # 727202214173249351回目の移動 3 → 2
        # to, head, tail, time = (1, [5], [1], 242400738057749783)
        return to

N, K = getNM()
P = [i - 1 for i in getList()]
C = getList()
# ループ検出
roop = Roop(P)

# 各ループごと調べる
ans = -float('inf')
for r in roop.roops:
    alta = []
    n = len(r)
    # ループに対応するスコアリストを用意
    for i in range(n):
        alta.append(C[r[i]])
    # １回ループすると何点getできるか
    one_roop = sum(alta)
    # ループ内の各点からスタートする
    for i in range(n):
        s = 0
        opt = -float('inf')
        t = max(n, K)
        # t回まで移動できる
        for j in range(1, t + 1):
            s += alta[(i + j) % n]
            if one_roop >= 0:
                opt = max(opt, s + ((K - j) // n) * one_roop)
            else:
                opt = max(opt, s)
        ans = max(ans, opt)
print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
import numpy as np
# from numba import njit

# @njit(cache=True)
def calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			continue
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleIDs[v] = cycleID
					cycleItemCnts[cycleID] = currentCycleItemCnt
					cycleTotalScores[cycleID] = currentCycleTotal
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID


def main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):

	ans = -1e19

	for n in range(N):

		v = n
		currentCycleItemCnt, currentCycleTotal = cycleItemCnts[ cycleIDs[v] ], cycleTotalScores[ cycleIDs[v] ]

		procCnt = 0
		currentCycleSumTmp = 0

		for _ in range(N):
		# while True:
			# NOTES: (多分)通常のpythonだとこのループだけでTLEする模様。。。

			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = int(( K - procCnt ) // currentCycleItemCnt)

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, "procCnt, cycleLoopCnt, currentCycleTotal=", procCnt, cycleLoopCnt, currentCycleTotal)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( int(ans), int(tmp) )

			v = P[v]
			if v == n:
				# サイクル終了
				break

	print(int(ans))

if sys.argv[-1]=='ONLINE_JUDGE':
	# from numba import njit
	from numba.pycc import CC
	cc=CC('my_module')
	cc.export('calcCycle','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(calcCycle)
	# cc.export('main','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(main)
	# main=njit(main, cache=True)
	cc.compile()
	exit(0)
# from my_module import main,calcCycle
from my_module import calcCycle



if __name__ == "__main__":
	N,K = map(int,input().split())
	P = np.array( input().split(), np.int64 )
	P -= 1
	C = np.array( input().split(), np.int64 )

	# 一度計算したサイクル情報を一応キャッシュしておく。。。
	# あんまり意味なさそう
	cycleIDs = np.full( N, -1, dtype=np.int64 )
	cycleItemCnts = np.full( N, -1, dtype=np.int64 )
	cycleTotalScores = np.full( N, -1, dtype=np.int64 )

	calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)

	# print(cycleItemCnts)


	main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)
	#print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
import numpy as np
# from numba import njit

# @njit(cache=True)
def calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			continue
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleIDs[v] = cycleID
					cycleItemCnts[cycleID] = currentCycleItemCnt
					cycleTotalScores[cycleID] = currentCycleTotal
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID


def main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores):

	ans = -1e19

	for n in range(N):

		v = n
		currentCycleItemCnt, currentCycleTotal = cycleItemCnts[ cycleIDs[v] ], cycleTotalScores[ cycleIDs[v] ]

		procCnt = 0
		currentCycleSumTmp = 0

		while True:

			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = int(( K - procCnt ) // currentCycleItemCnt)

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, "procCnt, cycleLoopCnt, currentCycleTotal=", procCnt, cycleLoopCnt, currentCycleTotal)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( int(ans), int(tmp) )

			v = P[v]
			if v == n:
				# サイクル終了
				break

	print(int(ans))

if sys.argv[-1]=='ONLINE_JUDGE':
	# from numba import njit
	from numba.pycc import CC
	cc=CC('my_module')
	cc.export('calcCycle','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(calcCycle)
	# cc.export('main','void(i8,i8,i8[:],i8[:],i8[:],i8[:],i8[:])')(main)
	# main=njit(main, cache=True)
	cc.compile()
	exit(0)
from my_module import calcCycle



if __name__ == "__main__":
	N,K = map(int,input().split())
	P = np.array( input().split(), np.int64 )
	P -= 1
	C = np.array( input().split(), np.int64 )

	cycleIDs = np.full( N, -1, dtype=np.int64 )
	cycleItemCnts = np.full( N, -1, dtype=np.int64 )
	cycleTotalScores = np.full( N, -1, dtype=np.int64 )

	calcCycle(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)

	# print(cycleItemCnts)


	main(N,K,P,C,cycleIDs,cycleItemCnts,cycleTotalScores)
	#print(ans)

Submission status: Time Limit Exceeded

Solution code:
import sys
import numpy as np

# 公式解説を見てからやった
# 複数サイクルでき、1-K回移動可能
# N < 5000?多分、O(N * 2N)くらいで行けそうに見えるが。。。

def main(N,K,P,C):


	# 一度計算したサイクル情報を一応キャッシュしておく。。。
	# あんまり意味なさそう
	cycleIDs = np.full( N, -1, dtype=np.int64 )
	cycleInfs = []


	# print(P)

	ans = -1e19
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			currentCycleItemCnt, currentCycleTotal = cycleInfs[ cycleIDs[v] ]
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleInfs.append( (currentCycleItemCnt, currentCycleTotal) )
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID

		procCnt = 0
		currentCycleSumTmp = 0

		while True:

			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = int(( K - procCnt ) // currentCycleItemCnt)

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, procCnt)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( int(ans), int(tmp) )

			v = P[v]
			if v == n:
				# サイクル終了
				break

	print(int(ans))


if __name__ == "__main__":
	N,K = map(int,input().split())
	P = np.array( input().split(), np.int64 )
	P -= 1
	C = np.array( input().split(), np.int64 )

	main(N,K,P,C)
	#print(ans)

Submission status: Time Limit Exceeded

Solution code:
import numpy as np

# 公式解説を見てからやった
# 複数サイクルでき、1-K回移動可能
# N < 5000?多分、O(N * 2N)くらいで行けそうに見えるが。。。

if __name__ == "__main__":

	N,K = map(int,input().split())
	P = np.array( input().split(), int )
	P -= 1
	C = np.array( input().split(), int )


	# 一度計算したサイクル情報を一応キャッシュしておく。。。
	# あんまり意味なさそう
	cycleIDs = np.full( N, -1, int )
	cycleInfs = []


	# print(P)

	ans = -1e10
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			currentCycleItemCnt, currentCycleTotal = cycleInfs[ cycleIDs[v] ]
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleInfs.append( (currentCycleItemCnt, currentCycleTotal) )
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID

		procCnt = 0
		currentCycleSumTmp = 0

		while True:

			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = ( K - procCnt ) // currentCycleItemCnt

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, procCnt)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( ans, tmp )

			v = P[v]
			if v == n:
				# サイクル終了
				break

	print(ans)

Submission status: Time Limit Exceeded

Solution code:
# 公式解説を見てからやった
# 複数サイクルでき、1-K回移動可能
# N < 5000?多分、O(N * 2N)くらいで行けそうに見えるが。。。

if __name__ == "__main__":

	N,K = map(int,input().split())
	P = [ int(p)-1 for p in input().split() ]
	C = list(map(int,input().split()))

	# 一度計算したサイクル情報を一応キャッシュしておく。。。
	# あんまり意味なさそう
	cycleIDs = [ -1 for _ in range(N) ]
	cycleInfs = []


	# print(P)

	ans = -1e10
	cycleID = 0

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		if cycleIDs[v] != -1:
			currentCycleItemCnt, currentCycleTotal = cycleInfs[ cycleIDs[v] ]
			# print(currentCycleItemCnt, currentCycleTotal)
		else:
			while True:
				# 全頂点について、属するサイクルを計算する
				currentCycleItemCnt += 1
				currentCycleTotal += C[v]

				v = P[v]
				if v == n:
					# サイクル発見
					cycleInfs.append( (currentCycleItemCnt, currentCycleTotal) )
					cycleID += 1
					break

				# 一応、一度サイクルを計算した頂点については、
				# その頂点の属するサイクルの情報をメモっておく。。。
				cycleIDs[v] = cycleID

		procCnt = 0
		currentCycleSumTmp = 0

		while True:

			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = ( K - procCnt ) // currentCycleItemCnt

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, procCnt)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( ans, tmp )

			v = P[v]
			if v == n:
				# サイクル終了
				break

	print(ans)

Submission status: Time Limit Exceeded

Solution code:
# 公式解説を見てからやった
# 複数サイクルでき、1-K回移動可能
# N < 5000?多分、O(N * 2N)くらいで行けそうに見えるが。。。

if __name__ == "__main__":

	N,K = map(int,input().split())
	P = [ int(p)-1 for p in input().split() ]
	C = list(map(int,input().split()))

	# print(P)

	ans = -1e10

	for n in range(N):

		v = n
		currentCycleItemCnt = 0
		currentCycleTotal = 0

		while True:
			# 全頂点について、属するサイクルを計算する
			currentCycleItemCnt += 1
			currentCycleTotal += C[v]

			v = P[v]
			if v == n:
				# サイクル発見
				break

		procCnt = 0
		currentCycleSumTmp = 0

		while True:

			# 頂点vにコマが置かれた時の最高スコアを計算し、
			# これまでの最高スコアを上回ったら、これまでの最高スコアを更新する
			procCnt += 1
			currentCycleSumTmp += C[v]
			if K < procCnt:
				break

			cycleLoopCnt = 0
			if procCnt < K and 0 < currentCycleTotal:
				cycleLoopCnt = ( K - procCnt ) // currentCycleItemCnt

			# print("v=", v, "currentCycleSumTmp=", currentCycleSumTmp, procCnt)
			tmp = currentCycleSumTmp + cycleLoopCnt * currentCycleTotal
			ans = max( ans, tmp )

			v = P[v]
			if v == n:
				# サイクル終了
				break

	print(ans)

Submission status: Time Limit Exceeded

Solution code:
N, K = map(int, input().split())
P = [0] + list(map(int, input().split()))
C = [0] + list(map(int, input().split()))

answer = -float('inf')
for start_p in range(1, N+1):

    cycle_total_score = 0
    cycle_in_score = -float('inf')
    cycle_count = 0
    next_p = P[start_p]
    while True:
        cycle_total_score += C[next_p]
        cycle_in_score = max(cycle_in_score, cycle_total_score)
        cycle_count += 1

        if next_p == start_p:
            # print('start_p:', start_p, ' cycle_total_score:', cycle_total_score, 'cycle_in_score:', cycle_in_score, 'cycle_count:', cycle_count)
            break
        next_p = P[next_p]
    
    max_score = 0
    if K == cycle_count:
        max_score = cycle_in_score
    else:
        #あふれたK % cycle_count回数分だけスコアを足すためにmaxを探さす
        add_max_count = K % cycle_count
        add_total_score = 0
        add_score = -float('inf')
        add_count = 0
        add_next_p = P[start_p]
        while True:
            add_total_score += C[add_next_p]
            add_score = max(add_score, add_total_score)
            add_count += 1

            if add_count == add_max_count:
                break
            add_next_p = P[add_next_p]

        if K < cycle_count:
            #最大の試行回数がcycle_countよりも小さい場合K % cycle_countまでで一番良いところでbeak
            max_score = add_total_score
        else:
            if cycle_total_score >= 0:
                #1サイクルでプラスの場合はできるだけサイクルを回してK % cycle_countまでで一番良いところでbeak
                max_score = (K // cycle_count) * cycle_total_score + add_total_score
            else:
                #1サイクルでマイナスの場合はサイクルを回さないで、K % cycle_countまでで一番良いところでbreak
                max_score = add_total_score
    # print('max_score', max_score)
    answer = max(answer, max_score)

print(answer)

Submission status: Time Limit Exceeded

Solution code:
#!/usr/bin python3
# -*- coding: utf-8 -*-

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

ret = - 10 ** 18
for s in range(n):
    nxt = p[s]
    S = [c[nxt]]
    while nxt != s:
        nxt = p[nxt]
        S.append(S[-1]+c[nxt])

    if k<=len(S):
        pt = max(S[:k])
    else:
        if S[-1] <= 0:
            pt = max(S)
        else:
            pt = max(S)
            if k%len(S)!=0:
                pt = max(pt, S[-1]+max(S[:k%len(S)]))
            pt += S[-1]*(k//len(S)-1)
    ret = max(ret, pt)
print(ret)

Submission status: Time Limit Exceeded

Solution code:
n, k = map(int, input().split())
P = [*map(lambda x: int(x)-1, input().split())]
C = [*map(int, input().split())]

INF = 10**18
max_score = -INF
for st in range(n):
    lc = 0 # lap count
    lap_sc = 0 # lap score
    nx = st
    while True:
        lc += 1
        lap_sc += C[nx]
        nx = P[nx]
        if nx == st: break

    lap_sc = max(0, lap_sc)
    sum_sc = 0
    kc = 0
    while True:
        kc += 1
        if k < kc: break
        sum_sc += C[nx]
        score = sum_sc + lap_sc * ((k - kc) // lc)
        max_score = max(max_score, score)
        nx = P[nx]
        if nx == st: break

print(max_score)

Submission status: Time Limit Exceeded

Solution code:
## coding: UTF-8

#ループ構造を見つけたらやめるところまで実装
#freshを用意して、Falseになったらやめる実装

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



#log = [1] #訪れた地点を記録するもの
#last  = 1 #最後に訪れた地点を記録するもの（ここから次に行くところを検索する）
fresh = [False] + [True] * N #まだついたことのない場所をTrueにしている
#fresh[1] = False
#turn = ['a'] + [0] * N #なん回目におとづれたか記録する
#status = True



def search_loop(start):
    log = [start] #訪れた地点を記録するもの
    last  = start #最後に訪れた地点を記録するもの（ここから次に行くところを検索する）
    score = [C[start-1]]
    counter = 0
    while True:
        next_spot = P[last - 1]
        counter += 1
        #print(next_spot)
        if(fresh[next_spot]):
            #処理を書く
            log.append(next_spot)
            score.append(C[next_spot-1])
            last = next_spot
            fresh[next_spot] = False
            #turn[next_spot] = counter
        else:
            #log.append(next_spot)
            last = next_spot
            fresh[next_spot] = False
            #最後の人処理をする
            break
    del log[-1]
    del score[-1]
    #print('hit')
    return log, counter-1, sum(score), score
    #last, counter#turn, counter

status = True
list_loop = []
list_elements = []
list_sum = []
list_score = []

while status:
    for i in range(N+1):
        if(fresh[i]):
            #print(search_loop(i))
            a = search_loop(i)
            list_loop.append(a[0])
            list_elements.append(a[1])
            list_sum.append(a[2])
            list_score.append(a[3])
            break
        if(i == N):
            status = False

      
#print('loop', list_loop, 'elements', list_elements, 'sum', list_sum, 'score', list_score)

#print(search_loop(1))

def count_sum(score,elements,start,goal):
    #歩数, 合計値でreturn
    if(start==goal):
        return 0, 0
    elif(goal > start):
        #print(score[start+1:goal+1])
        #ret = sum(score[start+1:goal+1])
        return goal-start, sum(score[start+1:goal+1])
    else:
        l = score + score
        #print(l)
        #print(l[start+1:goal+elements+1])
        return goal+elements-start, sum(l[start+1:goal+elements+1])




#各ループに対して始点終点全探索
def zentansaku(loop, elements, sum, score):
    #ループを入力して、最大値を出力する
    #最終的にはループごとの最大値を出力する
    best = (-1)*(10**10)
    for start in range(elements):
        for goal in range(elements):
            #print(start, goal)
            #print(count_sum(score, elements, start, goal))
            ret = (count_sum(score, elements, start, goal))
            step = ret[0]
            now = ret[1]
            #print('step',step, 'now',now)
            if(step > K):
                #歩きすぎ
                result = (-1)*(10**10)
            else:
                if(sum > 0):
                    #ループの合計値が正の場合、残りは歩けるだけ回る
                    available_looping = (K-step) // elements
                    #print('available_looping', available_looping)
                    result = sum * available_looping + now
                else:
                    if(step > 0):
                        result = now
                    else:
                        result = (-1)*(10**10)
            best = max(result, best)
            #print('result', result, 'best', best)
            #print(score[start:goal])
            #now = sum(score[start:goal])
    return best
            


ans = (-1)*(10**10)
for i in range(len(list_elements)):
    ans = max(ans, zentansaku(list_loop[i], list_elements[i], list_sum[i], list_score[i]))
    #print('ans', ans)
    #print('~~~')

print(ans)

Submission status: Time Limit Exceeded

Solution code:
N,K=map(int,input().split())
P=list(map(int,input().split()))
C=list(map(int,input().split()))
ans=[]
for i in range(N):
    score=[]
    B=[]
    count=1
    nex=P[i]-1
    point=C[nex]
    B.append(C[nex])
    score.append(point)
    while count<=K:
        if nex==i:
            break
        nex=P[nex]-1
        point+=C[nex]
        score.append(point)
        B.append(C[nex])
        count+=1
    if count==K:
        ans.append(max(score))
    else:
        if point<=0:
            ans.append(max(score))
        else:
            a=K//count
            b=K%count
            maxpoint=point*(a-1)
            for j in range(b):
                maxpoint+=B[j]
            c=maxpoint
            for j in range(count):
                if b+j<count:
                    c+=B[b+j]
                else:
                    c+=B[b+j-count]
                maxpoint=max(maxpoint,c)
            ans.append(maxpoint)
print(max(ans))