結果

問題 No.748 yuki国のお財布事情
ユーザー nanae
提出日時 2018-07-27 17:33:46
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 1,013 ms / 2,000 ms
コード長 2,523 bytes
コンパイル時間 81 ms
コンパイル使用メモリ 12,800 KB
実行使用メモリ 44,120 KB
最終ジャッジ日時 2024-07-04 19:11:45
合計ジャッジ時間 9,188 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
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 operator import itemgetter

N = None
M = None
K = None
edges = []
must  = []

def main():
    get_instance()
    check_constraint()
    solve()

def solve():
    ans = sum(edges[i][2] for i in range(M))
    uf = UnionFind(N)

    for i in range(K):
        ai, bi, ci = edges[must[i]-1]
        uf.unite(ai-1, bi-1)
        ans -= ci

    es = sorted(edges, key=itemgetter(2))

    for i in range(M):
        if uf.numcc == 1:
            break

        ai, bi, ci = es[i]

        if not uf.same(ai-1, bi-1):
            uf.unite(ai-1, bi-1)
            ans -= ci

    print(ans)
    

def get_instance():
    global N, M, K, edges, must
    N, M, K = map(int, input().split())
    edges = [tuple(map(int, input().split())) for i in range(M)]
    must = [int(input()) for i in range(K)]


def check_constraint():
    assert 1 <= N <= 10**5, "Out of Range"
    assert 0 <= M <= min(N*(N-1)//2, 10**5), "Out of Range"
    assert 0 <= K <= M, "Out of Range"

    nwes = []

    for i in range(M):
        ai, bi, ci = edges[i]
        assert 1 <= ai < bi <= N, "Out of Range"
        assert 1 <= ci <= 10**9, "Out of Range"
        nwes.append((ai, bi))

    assert len(set(nwes)) == M, "Not Simple"

    for i in range(K):
        assert 1 <= must[i] <= M, "Out of Range"
        if i > 0:
            assert must[i] > must[i-1], "Not Sorted"

    assert is_connected(), "Not Connected"


def is_connected():
    uf = UnionFind(N)

    for i in range(M):
        ai, bi, ci = edges[i]
        uf.unite(ai-1, bi-1)

    return all(uf.same(0, i) for i in range(N))


class UnionFind:
    def __init__(self, N):
        self.p = list(range(N))
        self.rank = [0] * N
        self.size = [1] * N
        self.numcc = N
 
    def find_root(self, x):
        if self.p[x] != x:
            self.p[x] = self.find_root(self.p[x])
 
        return self.p[x]
 
    def same(self, x, y):
        return self.find_root(x) == self.find_root(y)
 
    def unite(self, x, y):
        u = self.find_root(x)
        v = self.find_root(y)
 
        if u == v: return
 
        if self.rank[u] < self.rank[v]:
            self.p[u] = v
            self.size[v] += self.size[u]
            self.size[u] = 0
        else:
            self.p[v] = u
            self.size[u] += self.size[v]
            self.size[v] = 0
 
            if self.rank[u] == self.rank[v]:
                self.rank[u] += 1

        self.numcc -= 1
 
    def get_size(self, x):
        return self.size[self.find_root(x)]


if __name__ == '__main__':
    main()
0