結果

問題 No.1293 2種類の道路
ユーザー ntuda
提出日時 2025-07-15 22:06:11
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 550 ms / 2,000 ms
コード長 2,821 bytes
コンパイル時間 548 ms
コンパイル使用メモリ 82,144 KB
実行使用メモリ 125,992 KB
最終ジャッジ日時 2025-07-15 22:06:20
合計ジャッジ時間 8,001 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 2
other AC * 22
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 # 

import typing


class DSU:
    '''
    Implement (union by size) + (path halving)

    Reference:
    Zvi Galil and Giuseppe F. Italiano,
    Data structures and algorithms for disjoint set union problems
    '''

    def __init__(self, n: int = 0) -> None:
        self._n = n
        self.parent_or_size = [-1] * n

    def merge(self, a: int, b: int) -> int:
        assert 0 <= a < self._n
        assert 0 <= b < self._n

        x = self.leader(a)
        y = self.leader(b)

        if x == y:
            return x

        if -self.parent_or_size[x] < -self.parent_or_size[y]:
            x, y = y, x

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

        return x

    def same(self, a: int, b: int) -> bool:
        assert 0 <= a < self._n
        assert 0 <= b < self._n

        return self.leader(a) == self.leader(b)

    def leader(self, a: int) -> int:
        assert 0 <= a < self._n

        parent = self.parent_or_size[a]
        while parent >= 0:
            if self.parent_or_size[parent] < 0:
                return parent
            self.parent_or_size[a], a, parent = (
                self.parent_or_size[parent],
                self.parent_or_size[parent],
                self.parent_or_size[self.parent_or_size[parent]]
            )

        return a

    def size(self, a: int) -> int:
        assert 0 <= a < self._n

        return -self.parent_or_size[self.leader(a)]

    def groups(self) -> typing.List[typing.List[int]]:
        leader_buf = [self.leader(i) for i in range(self._n)]

        result: typing.List[typing.List[int]] = [[] for _ in range(self._n)]
        for i in range(self._n):
            result[leader_buf[i]].append(i)

        return list(filter(lambda r: r, result))


N,D,W = map(int,input().split())
dsu1 = DSU(N)
dsu2 = DSU(N)
for _ in range(D):
    a,b = map(int,input().split())
    a -= 1
    b -= 1
    dsu1.merge(a,b)
for _ in range(W):
    c,d = map(int,input().split())
    c -= 1
    d -= 1
    dsu2.merge(c,d)
ans = 0
G1 = dsu1.groups()
G2 = dsu2.groups()
G3 = []
G4 = []
N3 = []
N4 = []

for G in G1:
    n = len(G)
    if n > 1:
        ans += n * (n-1)
        G3.append(set(G))
        N3.append(len(G))
for G in G2:
    n = len(G)
    if n > 1:
        ans += n * (n-1)
        G4.append(set(G))
        N4.append(len(G))

X1 = [-1] * N
X2 = [-1] * N
N1 = len(G3)
N2 = len(G4)
for i,gs in enumerate(G3):
    for g in gs:
        X1[g] = i
for i,gs in enumerate(G4):
    for g in gs:
        X2[g] = i

from collections import defaultdict
E = [defaultdict(int) for _ in range(N1)]

for i in range(N):
    if X1[i] > -1 and X2[i] > -1:
        E[X1[i]][X2[i]] += 1

for i in range(N1):
    for k,v in E[i].items():
        ans -= v * (v - 1)
        ans += (N3[i] - v) * (N4[k] - v)

print(ans)
0