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 23:04:27
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,924 ms / 3,000 ms
コード長 4,241 bytes
コンパイル時間 409 ms
コンパイル使用メモリ 82,292 KB
実行使用メモリ 300,372 KB
最終ジャッジ日時 2024-09-13 00:33:21
合計ジャッジ時間 52,369 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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 * 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 # 

import sys
import heapq

import heapq


class mcf_graph:

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

    def add_edge(self, from_, to, cap, cost):
        assert 0 <= from_ < self.n
        assert 0 <= to < self.n
        m = len(self.pos)
        self.pos.append((from_, len(self.g[from_])))
        self.g[from_].append(self.__class__._edge(
            to, len(self.g[to]), cap, cost))
        self.g[to].append(self.__class__._edge(
            from_, len(self.g[from_]) - 1, 0, -cost))
        return m

    class edge:
        def __init__(self, from_, to, cap, flow, cost):
            self.from_ = from_
            self.to = to
            self.cap = cap
            self.flow = flow
            self.cost = cost

    def get_edge(self, i):
        _e = self.g[self.pos[i][0]][self.pos[i][1]]
        _re = self.g[_e.to][_e.rev]
        return self.__class__.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap, _e.cost)

    def edges(self):
        ret = []
        for i in range(len(self.pos)):
            _e = self.g[self.pos[i][0]][self.pos[i][1]]
            _re = self.g[_e.to][_e.rev]
            ret.append(self.__class__.edge(
                self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap, _e.cost))
        return ret

    def slope(self, s, t, flow_limit=float('inf')):
        # assert 0 <= s < self.n
        # assert 0 <= t < self.n
        # assert s != t

        dual = [0] * self.n
        dist = [float('inf')] * self.n
        pv = [-1] * self.n
        pe = [-1] * self.n

        def _dual_ref():
            nonlocal dual, dist, pv, pe
            dist = [float('inf')] * self.n
            pv = [-1] * self.n
            pe = [-1] * self.n

            que = [(0, s)]
            dist[s] = 0
            while que:
                dist_v, v = heapq.heappop(que)
                if dist[v] < dist_v:
                    continue
                if v == t:
                    break
                for i in range(len(self.g[v])):
                    e = self.g[v][i]
                    if e.cap == 0:
                        continue
                    cost = e.cost - dual[e.to] + dual[v]
                    if dist[e.to] > dist[v] + cost:
                        dist[e.to] = dist[v] + cost
                        pv[e.to] = v
                        pe[e.to] = i
                        heapq.heappush(que, (dist[e.to], e.to))
            if dist[t] == float('inf'):
                return False

            for v in range(self.n):
                if dist[v] == float('inf'):
                    continue
                dual[v] -= dist[t] - dist[v]

            return True

        flow = 0
        cost = 0
        prev_cost = -1
        result = [(flow, cost)]
        while flow < flow_limit:
            if not _dual_ref():
                break
            c = flow_limit - flow
            v = t
            while v != s:
                c = min(c, self.g[pv[v]][pe[v]].cap)
                v = pv[v]
            v = t
            while v != s:
                e = self.g[pv[v]][pe[v]]
                e.cap -= c
                self.g[v][e.rev].cap += c
                v = pv[v]
            d = -dual[s]
            flow += c
            cost += c * d
            if prev_cost == d:
                result.pop()
            result.append((flow, cost))
            prev_cost = cost
        return result

    def flow(self, s, t, flow_limit=float('inf')):
        return self.slope(s, t, flow_limit)[-1]

    class _edge:
        def __init__(self, to, rev, cap, cost):
            self.to = to
            self.rev = rev
            self.cap = cap
            self.cost = cost


BIG = 10 ** 9

input = sys.stdin.readline


n, m = map(int, input().split())
s, t = 0, n - 1
graph = mcf_graph(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)
assert flow == 2
print(cost)
0