結果

問題 No.439 チワワのなる木
ユーザー terasa
提出日時 2022-11-03 21:41:29
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 578 ms / 5,000 ms
コード長 3,620 bytes
コンパイル時間 175 ms
コンパイル使用メモリ 82,100 KB
実行使用メモリ 145,744 KB
最終ジャッジ日時 2024-07-18 04:24:14
合計ジャッジ時間 7,357 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
other AC * 28
権限があれば一括ダウンロードができます

ソースコード

diff # 

from typing import List, Tuple, Callable, TypeVar
from typing import List, Tuple, Optional
import sys
import itertools
import heapq
import bisect
from collections import deque, defaultdict
from functools import lru_cache, cmp_to_key

input = sys.stdin.readline

# for AtCoder Easy test
if __file__ != 'prog.py':
    sys.setrecursionlimit(10 ** 6)


def readints(): return map(int, input().split())
def readlist(): return list(readints())
def readstr(): return input().rstrip()


T = TypeVar('T')


class Rerooting:
    # reference: https://null-mn.hatenablog.com/entry/2020/04/14/124151
    # 適当な頂点vを根とする部分木に対して計算される値dp_vが、vの子c1, c2, ... ckを用いて
    # 下記のように表すことができる
    # dp_v = g(merge(f(dp_c1,c1), f(dp_c2,c2), ..., f(dp_ck,ck)), v)
    def __init__(self, N: int, E: List[Tuple[int, int]],
                 f: Callable[[T, int, int, int], T],
                 g: Callable[[T, int], T],
                 merge: Callable[[T, T], T], e: T):
        self.N = N
        self.E = E
        self.f = f
        self.g = g
        self.merge = merge
        self.e = e

        self.dp = [[self.e for _ in range(len(self.E[v]))] for v in range(self.N)]
        self._calculate()

    def _dfs1(self, root):
        stack = [(root, -1)]
        ret = [self.e] * self.N
        while stack:
            v, p = stack.pop()
            if v < 0:
                v = ~v
                acc = self.e
                for i, (c, d) in enumerate(self.E[v]):
                    if d == p:
                        continue
                    self.dp[v][i] = ret[d]
                    acc = self.merge(acc, self.f(ret[d], v, d, c))
                ret[v] = self.g(acc, v)
                continue

            stack.append((~v, p))
            for i, (c, d) in enumerate(self.E[v]):
                if d == p:
                    continue
                stack.append((d, v))

    def _dfs2(self, root):
        stack = [(root, -1, self.e)]
        while stack:
            v, p, from_par = stack.pop()
            for i, (c, d) in enumerate(self.E[v]):
                if d == p:
                    self.dp[v][i] = from_par
                    break
            ch = len(self.E[v])
            Sr = [self.e] * (ch + 1)
            for i in range(ch, 0, -1):
                c, d = self.E[v][i - 1]
                Sr[i - 1] = self.merge(Sr[i], self.f(self.dp[v][i - 1], v, d, c))
            Sl = self.e
            for i, (c, d) in enumerate(self.E[v]):
                if d != p:
                    val = self.merge(Sl, Sr[i + 1])
                    stack.append((d, v, self.g(val, v)))
                Sl = self.merge(Sl, self.f(self.dp[v][i], v, d, c))

    def _calculate(self, root=0):
        self._dfs1(root)
        self._dfs2(root)

    def solve(self, v):
        ans = self.e
        for i, (c, d) in enumerate(self.E[v]):
            ans = self.merge(ans, self.f(self.dp[v][i], v, d, c))
        return self.g(ans, v)


N = int(input())
S = readstr()
E = [[] for _ in range(N)]
for _ in range(N - 1):
    a, b = readints()
    a -= 1
    b -= 1
    E[a].append((1, b))
    E[b].append((1, a))


def f(a, v, ch, cost):
    return (a[0], a[1], a[0] * a[1])


def g(a, v):
    if S[v] == 'c':
        return (a[0] + 1, a[1], a[2])
    else:
        return (a[0], a[1] + 1, a[2])


def merge(a, b):
    return (a[0] + b[0], a[1] + b[1], a[2] + b[2])


solver = Rerooting(N, E, f, g, merge, (0, 0, 0))
ans = 0
for i in range(N):
    if S[i] != 'w':
        continue
    c, w, d = solver.solve(i)
    ans += c * (w - 1) - d
print(ans)
0