from __future__ import annotations from typing import NamedTuple, Optional, List from heapq import heappush, heappop class MCFGraph: class Edge(NamedTuple): src: int dst: int cap: int flow: int cost: int class _Edge: def __init__(self, dst: int, cap: int, cost: int) -> None: self.dst = dst self.cap = cap self.cost = cost self.rev: Optional[MCFGraph._Edge] = None def __init__(self, n: int) -> None: self._n = n self._g: List[List[MCFGraph._Edge]] = [[] for _ in range(n)] self._edges: List[MCFGraph._Edge] = [] def add_edge(self, src: int, dst: int, cap: int, cost: int) -> int: assert 0 <= src < self._n assert 0 <= dst < self._n assert 0 <= cap m = len(self._edges) e = MCFGraph._Edge(dst, cap, cost) re = MCFGraph._Edge(src, 0, -cost) e.rev = re re.rev = e self._g[src].append(e) self._g[dst].append(re) self._edges.append(e) return m def get_edge(self, i: int) -> Edge: assert 0 <= i < len(self._edges) e = self._edges[i] re = e.rev return MCFGraph.Edge( re.dst, e.dst, e.cap + re.cap, re.cap, e.cost ) def edges(self) -> List[Edge]: return [self.get_edge(i) for i in range(len(self._edges))] def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> (int, int): return self.slope(s, t, flow_limit)[-1] def slope(self, s: int, t: int, flow_limit: Optional[int] = None) -> List[(int, int)]: assert 0 <= s < self._n assert 0 <= t < self._n assert s != t if flow_limit is None: flow_limit = sum(e.cap for e in self._g[s]) dual = [0] * self._n prev: List[Optional[(int, MCFGraph._Edge)]] = [None] * self._n def refine_dual() -> bool: pq = [(0, s)] visited = [False] * self._n dist: List[Optional[int]] = [None] * self._n dist[s] = 0 while pq: (dist_v, v) = heappop(pq) if visited[v]: continue visited[v] = True if v == t: break dual_v = dual[v] for e in self._g[v]: w = e.dst if visited[w] or e.cap == 0: continue reduced_cost = e.cost - dual[w] + dual_v new_dist = dist_v + reduced_cost dist_w = dist[w] if dist_w is None or new_dist < dist_w: dist[w] = new_dist prev[w] = (v, e) heappush(pq, (new_dist, w)) else: return False dist_t = dist[t] for v in range(self._n): if visited[v]: dual[v] -= dist_t - dist[v] return True flow = 0 cost = 0 prev_cost_per_flow: Optional[int] = None result = [(flow, cost)] while flow < flow_limit: if not refine_dual(): break f = flow_limit - flow v = t while prev[v] is not None: (u, e) = prev[v] f = min(f, e.cap) v = u v = t while prev[v] is not None: (u, e) = prev[v] e.cap -= f e.rev.cap += f v = u c = -dual[s] flow += f cost += f * c if c == prev_cost_per_flow: result.pop() result.append((flow, cost)) prev_cost_per_flow = c return result # https://atcoder.jp/contests/practice2/tasks/practice2_e def main() -> None: n, m = map(int, input().split()) s, t = 0, n - 1 graph = MCFGraph(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) if __name__ == '__main__': main()