結果

問題 No.1301 Strange Graph Shortest Path
コンテスト
ユーザー Kite_kuma
提出日時 2020-10-30 22:26:41
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,743 ms / 3,000 ms
コード長 4,353 bytes
コンパイル時間 440 ms
コンパイル使用メモリ 82,288 KB
実行使用メモリ 279,592 KB
最終ジャッジ日時 2024-09-13 00:27:03
合計ジャッジ時間 45,984 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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 * 2
other AC * 33
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 heapq import heappop, heappush, heapify
import sys
input = sys.stdin.readline
# N, K = map(int, input().split())
# a = [list(map(int, input().split())) for _ in range(N)]


class MinCostFlow():
    def __init__(self, n):
        self.n = n
        self.graph = [[] for _ in range(n)]
        self.pos = []

    def add_edge(self, fr, to, cap, cost):
        m = len(self.pos)
        self.pos.append((fr, len(self.graph[fr])))
        self.graph[fr].append([to, len(self.graph[to]), cap, cost])
        self.graph[to].append([fr, len(self.graph[fr]) - 1, 0, -cost])
        return m

    def get_edge(self, idx):
        to, rev, cap, cost = self.graph[self.pos[idx][0]][self.pos[idx][1]]
        rev_to, rev_rev, rev_cap, rev_cost = self.graph[to][rev]
        return self.pos[idx][0], to, cap + rev_cap, rev_cap, cost

    def edges(self):
        for i in range(len(self.pos)):
            yield self.get_edge(i)

    def dual_ref(self, s, t):
        dist = [2**63 - 1] * self.n
        dist[s] = 0
        vis = [0] * self.n
        self.pv = [-1] * self.n
        self.pe = [-1] * self.n
        queue = []
        heappush(queue, (0, s))
        while queue:
            k, v = heappop(queue)
            if vis[v]:
                continue
            vis[v] = True
            if v == t:
                break
            for i in range(len(self.graph[v])):
                to, rev, cap, cost = self.graph[v][i]
                if vis[to] or cap == 0:
                    continue
                cost += self.dual[v] - self.dual[to]
                if dist[to] - dist[v] > cost:
                    dist[to] = dist[v] + cost
                    self.pv[to] = v
                    self.pe[to] = i
                    heappush(queue, (dist[to], to))
        if not vis[t]:
            return False
        for v in range(self.n):
            if not vis[v]:
                continue
            self.dual[v] -= dist[t] - dist[v]
        return True

    def flow(self, s, t): return self.flow_with_limit(s, t, 2**63 - 1)
    def flow_with_limit(
        self, s, t, limit): return self.slope_with_limit(s, t, limit)[-1]

    def slope(self, s, t): return self.slope_with_limit(s, t, 2**63 - 1)

    def slope_with_limit(self, s, t, limit):
        flow = 0
        cost = 0
        prev_cost = -1
        res = [(flow, cost)]
        self.dual = [0] * self.n
        while flow < limit:
            if not self.dual_ref(s, t):
                break
            c = limit - flow
            v = t
            while v != s:
                c = min(c, self.graph[self.pv[v]][self.pe[v]][2])
                v = self.pv[v]
            v = t
            while v != s:
                to, rev, cap, _ = self.graph[self.pv[v]][self.pe[v]]
                self.graph[self.pv[v]][self.pe[v]][2] -= c
                self.graph[v][rev][2] += c
                v = self.pv[v]
            d = -self.dual[s]
            flow += c
            cost += c * d
            if prev_cost == d:
                res.pop()
            res.append((flow, cost))
            prev_cost = cost
        return res


inf = 10 ** 10
# mcf = MinCostFlow(2 * N + 2)
# mcf.add_edge(2 * N, 2 * N + 1, N * K, inf)
# for i in range(N):
#     mcf.add_edge(2 * N, i, K, 0)
#     mcf.add_edge(N + i, 2 * N + 1, K, 0)
#     for j in range(N):
#         mcf.add_edge(i, N + j, 1, inf - a[i][j])
# print(-mcf.flow_with_limit(2 * N, 2 * N + 1, N * K)[1] + N * K * inf)
# res = [["."] * N for _ in range(N)]
# for f, t, _, flow, _ in mcf.edges():
#     if flow == 0 or max(f, t) >= 2 * N:
#         continue
#     res[f][t - N] = "X"
# for r in res:
#     print("".join(r))


def main() -> None:
    n, m = map(int, input().split())
    s, t = 0, n - 1
    # graph = mcf_graph(n + m)
    graph = MinCostFlow(n + m)

    for i in range(m):
        u, v, c, d = map(int, input().split())
        assert 1 <= u <= n and 1 <= v <= n and c <= d
        u -= 1
        v -= 1
        mid = n + i
        graph.add_edge(u, mid, 2, c)
        graph.add_edge(mid, v, 1, 0)
        graph.add_edge(mid, v, 1, d - c)
        graph.add_edge(v, mid, 2, c)
        graph.add_edge(mid, u, 1, 0)
        graph.add_edge(mid, u, 1, d - c)

    # flow, cost = graph.flow(s, t, 2)
    flow, cost = graph.flow_with_limit(s, t, 2)
    assert flow == 2
    print(cost)


if __name__ == '__main__':
    main()
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