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:
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 = [-1] * self.n
        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] = cnt
            # i → array[i]
            to = array[i]
            # ループが詰まるまで回す
            while True:
                if ignore[to] >= 0:
                    # 既に探索していたら
                    if ignore[to] < cnt:
                        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] = cnt
                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):
        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, A = getNM()
A -= 1
K = getN()
B = [i - 1 for i in getList()]
roop = Roop(B)
print(roop.move(A, K) + 1)

"""

"""
# ABC167 D - Teleporter
N, K = getNM()
N -= 1
A = [i - 1 for i in getList()]
roop = Roop(A)
print(roop.move(0, K) + 1)
"""


# ABC175 D - Moving Piece
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:
    n = len(r)
    # ループに対応するスコアリストを用意
    alta = []
    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)
    alta += alta
    imos = [0]
    for i in range(len(alta)):
        imos.append(imos[i] + alta[i])

    t = min(n, K)
    for i in range(n):
        # 長さ1からtまでの区間の総和の最大値を探索
        for j in range(1, t + 1):
            if one_roop >= 0:
                opt = (imos[i + j] - imos[i]) + ((K - j) // n) * one_roop
            else:
                opt = imos[i + j] - imos[i]
            ans = max(ans, opt)

print(ans)

Submission status: Accepted

Solution code:
def solve_loop(loop, K):
    S = sum(loop)
    L = len(loop)
    if S < 0:
        acc = 0
        K = min(K, L)
        minL = 1
    elif K//L >= 2:
        acc = S * (K//L - 1)
        K = K - L * (K//L - 1)
        minL = 0
    else:
        acc = 0
        minL = 1

    ans = -10 ** 9 - 1
    for i in range(L):
        #print(loop[i:] + loop[:i], "acc=", acc, "min=", minL, "max=", K)
        tmp = 0
        if minL:
            tmp = loop[i]

        for l in range(minL, K):
            ans = max(tmp, ans)
            tmp += loop[(i+l) % L]
            #print(tmp)
            #print(i, l, tmp)
        ans = max(tmp, ans)

    #print(loop, ans, acc)
    return acc + ans
    if K >= L:
        return max(acc, acc + ans)
    else:
        return ans

def solve():
    N, K = map(int, input().split())
    P = list(map(lambda n: int(n)-1, input().split())) # 0-based index
    C = list(map(int, input().split()))

    flag = [False] * N
    ans = -10**9-1  # worst case is -10**9
    for i in range(N):
        if flag[i]:
            continue
        loop = []
        j = P[i]
        for _ in range(N):
            if flag[j]: # loop end
                break
            flag[j] = True
            loop += [C[j]]
            j = P[j]
        ans = max(ans, solve_loop(loop, K))
    print(ans)

solve()

Submission status: Accepted

Solution code:
'''
4 4
4 1 2 3
-19 4 10 6

4 5
4 1 2 3
-19 4 10 6

4 8
4 1 2 3
-19 4 10 6
'''
n, k = map(int, input().split())
p = list(map(int, input().split()))
p = [i-1 for i in p]
c = list(map(int, input().split()))

minusOnly = True
for i in range(n):
    if c[i] > 0:
        minusOnly = False
        break

if minusOnly:
    print(max(c))
    exit()

ans = 0
used = [False]*n

for st in range(n):
    if not used[st]:
        gr = []
        now = st
        gr.append(st)
        used[st] = True
        while True:
            now = p[now]
            gr.append(now)
            used[now] = True
            if now == st:
                break
        gr.pop()

        cs = [c[i] for i in gr]
        s = sum(cs)
        point = 0
        r = k
        if r > 2*len(gr):
            if s > 0:
                point += s*(k//len(gr)-1)
                r -= len(gr)*(k//len(gr)-1)
            else:
                r = 2*len(gr)
        
        cs = cs + cs + cs
        plus = 0
        for i in range(len(gr)):
            nowSum = 0
            for g in range(r):
                nowSum += cs[i+g]
                plus = max(plus, nowSum)
        
        point += plus
        ans = max(ans, point)

print(ans)

Submission status: Accepted

Solution code:
N,K = map(int,input().split())
P = list(map(int,input().split()))
C = list(map(int,input().split()))
answer = -float('inf')
for s in range(N):
    S = []
    i = P[s]-1
    S.append(C[i])
    while i!= s:
        i = P[i]-1
        S.append(S[-1]+C[i])
        
    if K<=len(S):
        score = max(S[:K])
    elif S[-1]<=0:
        score = max(S)
    else:
        score1 = S[-1]*(K//len(S))
        amari = K%len(S)
        if amari!=0:
            score1 += max(0,max(S[:amari]))
        score2 = S[-1]*(K//len(S)-1)
        score2 += max(S)
        score = max(score1,score2)
    
    answer = max(answer,score)
print(answer)

Submission status: Accepted

Solution code:
import sys
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()
def resolve():
    n, k = map(int, input().split())
    P = list(map(lambda x : int(x) - 1, input().split()))
    C = list(map(int, input().split()))

    # doubling table
    nexts = [P]
    vals = [C]
    totals = [C]
    for _ in range(60):
        next, val, total = nexts[-1], vals[-1], totals[-1]
        nnext, nval, ntotal = [0] * n, [0] * n, [0] * n
        for i in range(n):
            nnext[i] = next[next[i]]
            nval[i] = val[i] + val[next[i]]
            ntotal[i] = max(total[i], val[i] + total[next[i]])
        nexts.append(nnext)
        vals.append(nval)
        totals.append(ntotal)

    # answer
    ans = -INF
    for now in range(n):
        score = 0
        for d in range(59, -1, -1):
            if k >> d & 1:
                ans = max(ans, score + totals[d][now])
                score += vals[d][now]
                now = nexts[d][now]
    print(ans)
resolve()

Submission status: Accepted

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

P = [None] + P
C = [None] + C

all_max = C[1]
for st in range(1, N + 1):
    p = P[st]
    scores = [C[p]]

    while p != st and len(scores) < K:
        p = P[p]
        scores.append(C[p])

    num_elem = len(scores)
    all_sum = sum(scores)

    q, r = divmod(K, num_elem)

    max_ = scores[0]
    temp = scores[0]

    max_r = scores[0]
    temp_r = scores[0]
    for x in range(1, num_elem):
        if x < r:
            temp_r += scores[x]
            max_r = max(max_r, temp_r)

        temp += scores[x]
        max_ = max(max_, temp)

    temp_max = scores[0]
    if all_sum > 0 and q > 0:
        if r > 0:
            temp_max = max(all_sum * (q - 1) + max_, all_sum * q + max_r)
        else:
            temp_max = all_sum * (q - 1) + max_
    else:
        temp_max = max_

    all_max = max(all_max, temp_max)


print(all_max)

Submission status: Accepted

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
                    if len(opt[self.opt_dic[to]:]) > 0:
                        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):
        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

"""
# ABC167 D - Teleporter
N, K = getNM()
N -= 1
A = [i - 1 for i in getList()]
roop = Roop(A)
print(roop.move(0, K) + 1)
"""

# ABC175 D - Moving Piece
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:
    n = len(r)
    # ループに対応するスコアリストを用意
    alta = []
    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)
    alta += alta
    imos = [0]
    for i in range(len(alta)):
        imos.append(imos[i] + alta[i])

    t = min(n, K)
    for i in range(n):
        # 長さ1からtまでの区間の総和の最大値を探索
        for j in range(1, t + 1):
            if one_roop >= 0:
                opt = (imos[i + j] - imos[i]) + ((K - j) // n) * one_roop
            else:
                opt = imos[i + j] - imos[i]
            ans = max(ans, opt)

print(ans)

Submission status: Accepted

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

score = -10**18
for st in range(n):
    lap_sc = sum_sc = 0
    nx = st
    for lap_cn in range(1, n+1):
        lap_sc += C[nx]
        nx = P[nx]
        if nx == st: break
    lap_sc = max(0, lap_sc)

    for k_cn in range(1, k+1):
        sum_sc += C[nx]
        score = max(score, sum_sc + lap_sc * ((k - k_cn) // lap_cn))
        nx = P[nx]
        if nx == st: break

print(score)

Submission status: Accepted

Solution code:
import sys, math

def calcweight_tree(N_vertices, edges, times, inf):

    """
    edges: [start, dest, cost] -> [cost, start, end]
    """

    distance = 0

    passed = [False] * N_vertices

    travel_max = -inf
    for i in range(N_vertices):
        if(passed[i] == False):
            distance = 0
            left = i
            cost_sum = 0
            costs = []
            min_distance = inf
            while(True):
                dest = edges[left][1]
                cost = edges[dest][0]
                if(passed[dest]==False):
                    #passed[left] = True
                    passed[dest] = True
                    cost_sum += cost
                    costs.append(cost_sum)
                    left = dest
                    if(min_distance > cost):
                        min_distance = cost
                else:
                    period = len(costs)
                    increase_period = cost_sum
                    break
            # 2 period項準備
            remainder = times%period
            cost_minus = [0]
            for j in range(period-1):
                cost_minus.append(costs[j])
            if(increase_period <= 0):
                """
                for j in range(period):
                    costs.append(costs[j]+increase_period)
                maxindex = 0
                maxindex_start = 0
                maxvalue = -inf

                if(remainder==0):
                    remainder += period

                for st in range(period):
                    maxvalue_candidate = max(costs[st:st+period])
                    if(maxvalue_candidate - cost_minus[st] > maxvalue):
                        maxvalue = maxvalue_candidate - cost_minus[st]
                        maxindex = costs[st:st+period].index(maxvalue_candidate) + st
                        maxindex_start = st
                """
                costs_last = []
                # a_0は0なので。そしてこれは最大値を考えるときには数えないので
                remainder2 = remainder % period

                #print("x", costs, increase_period, remainder2)
                """
                for j in range(remainder2, period):
                    costs_last.append(costs[j])
                for j in range(0, remainder2):
                    costs_last.append(costs[j]+increase_period)
                for j in range(period):
                    costs_last.append(costs_last[j]+increase_period)
                """
                for j in range(period):
                    costs_last.append(costs[j])
                for j in range(period):
                    costs_last.append(costs_last[j]+increase_period)
                maxvalue = -inf
                #print(costs_last, cost_minus)
                for j in range(period):
                    maxvalue_candidate = max(costs_last[j:j+period])
                    if(maxvalue_candidate-cost_minus[j] > maxvalue):
                        maxvalue = maxvalue_candidate-cost_minus[j]

                travel_max = max(maxvalue, travel_max)
            else:
                costs_last = []
                # a_0は0なので。そしてこれは最大値を考えるときには数えないので
                remainder2 = remainder % period
                times_period = times//period-1
                add_n = times_period * increase_period
                #print(costs, increase_period, remainder2, times_period, add_n)
                for j in range(remainder2, period):
                    costs_last.append(costs[j]+add_n)
                for j in range(0, remainder2):
                    costs_last.append(costs[j]+add_n+increase_period)
                for j in range(period):
                    costs_last.append(costs_last[j]+increase_period)
                maxvalue = -inf
                #print(costs_last, cost_minus)
                for j in range(period):
                    maxvalue_candidate = max(costs_last[j:j+period])
                    if(maxvalue_candidate-cost_minus[j] > maxvalue):
                        maxvalue = maxvalue_candidate-cost_minus[j]
                travel_max = max(maxvalue, travel_max)






    return travel_max







if(__name__ == "__main__"):
    """
    N = int( input().strip() )
    Length = list( map(int, input().strip().split() ) )

    edges = [ [] for _ in range(N+2) ]
    for i in range(N):
        edges[0].append([0, i]) #[cost, edge]
    for i in range(1, N+1):
        edges[i].append([0, N+1])
    for i in range(N):
        edges[i].append([ CList[i]*(-1), PList[i] ])
    """
    N, K= map(int, input().strip().split() )
    PList = list( map(int, input().strip().split() ) )
    CList = list( map(int, input().strip().split() ) )
    inf = 10**10


    N_vertices = N

    edges3 = []
    costs = []
    for i in range(N):
        edges3.append([ CList[i], PList[i]-1 ])

    weight = calcweight_tree(N_vertices, edges3, K, inf)

    #weight= calcweight_bellman_ford(N_vertices, 0, edges3, K+2, cost, inf)


    print( weight)

Submission status: Accepted

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

score = -10**18
for st in range(n):
    lap_sc = sum_sc = 0
    nx = st
    for lap_cn in range(1, max(n, k)+1):
        lap_sc += C[nx]
        nx = P[nx]
        if nx == st: break
    lap_sc = max(0, lap_sc)

    for k_cn in range(1, k+1):
        sum_sc += C[nx]
        score = max(score, sum_sc + lap_sc * ((k - k_cn) // lap_cn))
        nx = P[nx]
        if nx == st: break

print(score)

Submission status: Accepted

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

score = -10**18
for st in range(n):
    lap_cn = lap_sc = sum_sc = 0
    nx = st
    while True:
        lap_cn += 1
        lap_sc += C[nx]
        nx = P[nx]
        if nx == st: break
    lap_sc = max(0, lap_sc)

    for k_cn in range(1, k+1):
        sum_sc += C[nx]
        score = max(score, sum_sc + lap_sc * ((k - k_cn) // lap_cn))
        nx = P[nx]
        if nx == st: break

print(score)

Submission status: Accepted

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

score = -10**18
for st in range(n):
    lap_cn = 0
    lap_sc = 0
    nx = st
    while True:
        lap_cn += 1
        lap_sc += C[nx]
        nx = P[nx]
        if nx == st: break
    lap_sc = max(0, lap_sc)

    sum_sc = 0
    for k_cn in range(k):
        sum_sc += C[nx]
        score = max(score, sum_sc + lap_sc * ((k - (k_cn + 1)) // lap_cn))
        nx = P[nx]
        if nx == st: break

print(score)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

INF=10**20
def main():
    N,K=mi()
    P=list(mi())
    C=list(mi())

    ans = -INF
    for i in range(N):
        start = i + 1 
        stack = [start]
        score_his = [0]
        scores = 0
        depth = 1
        seen = {}
        while stack:
            if depth > K: break
            current = stack.pop()
            
            if current in seen:
                loop_start_depth = seen[current]
                loop_end_depth = depth - 1 
                loop_scores = score_his[-1] - score_his[loop_start_depth-1]
                loop_len = loop_end_depth - loop_start_depth + 1
                if loop_scores < 0: break

                # print(start,score_his)
                # print(loop_start_depth,loop_end_depth,loop_scores,loop_len)
                
                rest_count = K - depth + 1
                available_loop_count = rest_count // loop_len
                res1 = (available_loop_count-1) * loop_scores + scores

                # print("a",rest_count,available_loop_count,res1)
                
                res2 = res1
                rest_loop_len = rest_count % loop_len + loop_len

                # print("b",rest_loop_len)
                ress = [res1,res2]
                for j in range(rest_loop_len):
                    score = C[P[current-1]-1]
                    res2 += score
                    ress.append(res2)
                    current = P[current-1]

                # print("ress",ress)
                score_his.append(max(ress))

                break

            
            score = C[P[current-1]-1]
            scores += score
            score_his.append(scores)

            seen[current] = depth
            stack.append(P[current-1])

            depth += 1
        
        ans = max(ans,max(score_his[1:]))
    
    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()))

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

ans = -10 ** 18
for si in range(N):
    x = si
    c = []
    tot = 0
    while True:
        x = P[x]
        c.append(C[x])
        tot += C[x]
        if x == si:
            break

    s = 0
    for k in range(len(c)):
        if k + 1 > K:
            break
        s += c[k]
        ss = s
        if tot > 0:
            ss += tot * int((K - (k + 1)) // len(c))
        ans = max(ss, ans)

print(ans)

Submission status: Accepted

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

# 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。。。

# @njit(cache=False)
def main(N,K,P,C,ans):


	# 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)

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



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 )

	ans = -1e9	# NOTES: 2020/08/17 numba関数内でこれをやっていたら、データによってはWAになってしまっていた。詳細は、いまだに不明。
	main(N,K,P,C,ans)
	#print(ans)

Submission status: Accepted

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

# 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。。。

# @njit(cache=False)
def main(N,K,P,C,ans):


	# 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)

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



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 )

	ans = -1e18	# NOTES: 2020/08/17 numba関数内でこれをやっていたら、データによってはWAになってしまっていた。詳細は、いまだに不明。
	main(N,K,P,C,ans)
	#print(ans)