結果

問題 No.922 東北きりきざむたん
ユーザー terasa
提出日時 2022-11-03 23:31:35
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 999 ms / 2,000 ms
コード長 6,562 bytes
コンパイル時間 126 ms
コンパイル使用メモリ 81,888 KB
実行使用メモリ 136,784 KB
最終ジャッジ日時 2024-07-18 05:30:16
合計ジャッジ時間 15,696 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 26
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.ret = [self.e] * self.N

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

    def _dfs1(self, root):
        stack = [(root, -1)]
        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] = self.ret[d]
                    acc = self.merge(acc, self.f(self.ret[d], v, d, c))
                self.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)


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

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

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

        if x == y:
            return False
        if self.par[x] > self.par[y]:
            x, y = y, x

        self.par[x] += self.par[y]
        self.par[y] = x
        return True

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

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

    def roots(self):
        return [i for i in range(self.N) if self.par[i] < 0]


class LCA:
    def __init__(self, N, E):
        self.N = N
        self.E = E
        self.K = N.bit_length()
        self.par = [[-1 for _ in range(N)] for _ in range(self.K)]
        self.depth = [None] * N

    def _dfs(self, root):
        self.depth[root] = 0
        stack = [(root, -1)]
        while stack:
            v, p = stack.pop()
            if not p < 0:
                self.par[0][v] = p
                self.depth[v] = self.depth[p] + 1

            for _, dest in self.E[v]:
                if dest == p:
                    continue
                stack.append((dest, v))

    def calculate(self):
        for k in range(self.K - 1):
            for i in range(self.N):
                if self.par[k][i] < 0:
                    continue
                self.par[k + 1][i] = self.par[k][self.par[k][i]]

    def la(self, v, x):
        for k in range(self.K):
            if x & (1 << k):
                v = self.par[k][v]
        return v

    def lca(self, u, v):
        if self.depth[u] > self.depth[v]:
            u, v = v, u
        d = self.depth[v] - self.depth[u]
        v = self.la(v, d)

        if u == v:
            return u
        for k in range(self.K)[::-1]:
            if self.par[k][u] != self.par[k][v]:
                u = self.par[k][u]
                v = self.par[k][v]
        return self.par[0][v]

    def dist(self, u, v):
        return self.depth[u] + self.depth[v] - 2 * self.depth[self.lca(u, v)]

    def jump(self, u, v, x):
        lca = self.lca(u, v)
        d1 = self.depth[u] - self.depth[lca]
        d2 = self.depth[v] - self.depth[lca]

        if d1 + d2 < x:
            return -1
        if x <= d1:
            return self.la(u, x)
        return self.la(v, d1 + d2 - x)


N, M, Q = readints()
E = [[] for _ in range(N)]
uf = UnionFind(N)
D = N
for _ in range(M):
    u, v = readints()
    u -= 1
    v -= 1
    E[u].append((1, v))
    E[v].append((1, u))
    if uf.unite(u, v) is True:
        D -= 1

query = []
todo = []
cnt = [0] * N
for _ in range(Q):
    a, b = readints()
    a -= 1
    b -= 1
    if uf.same(a, b) is False:
        cnt[a] += 1
        cnt[b] += 1
    else:
        todo.append((a, b))


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


def g(a, v):
    return (a[0], a[1] + cnt[v])


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


gidx = {}
for i, v in enumerate(uf.roots()):
    gidx[v] = i
V = [[] for _ in range(D)]
for i in range(N):
    V[gidx[uf.find(i)]].append(i)

solver = Rerooting(N, E, f, g, merge, (0, 0))
lca = LCA(N, E)
INF = 1 << 30
cost = [INF] * D
for i in range(D):
    solver.calculate(root=V[i][0])
    lca._dfs(V[i][0])
    for v in V[i]:
        cost[i] = min(cost[i], solver.solve(v)[0])
lca.calculate()
ans = sum(cost)
for s, t in todo:
    ans += lca.dist(s, t)
print(ans)
0