UVA 1486 - Transportation
题意:一个有向图上运输k货物,有一些边,每个边一个系数a,经过该边如果有x货物,就要缴纳a
x x的钱,问运输从1到n最小的代价
思路:费用流,这题边的容量c最大只有5,所以可以拆边,一条边拆成c条边,每条容量1,对应相应的代价为a * (i^2 - (i - 1)^2),然后跑一下费用流即可
代码:
#include <cstdio> #include <cstring> #include <vector> #include <queue> #include <algorithm> using namespace std; const int MAXNODE = 105; const int MAXEDGE = 200005; typedef int Type; const Type INF = 0x3f3f3f3f; struct Edge { int u, v; Type cap, flow, cost; Edge() {} Edge(int u, int v, Type cap, Type flow, Type cost) { this->u = u; this->v = v; this->cap = cap; this->flow = flow; this->cost = cost; } }; struct MCFC { int n, m, s, t; Edge edges[MAXEDGE]; int first[MAXNODE]; int next[MAXEDGE]; int inq[MAXNODE]; Type d[MAXNODE]; int p[MAXNODE]; Type a[MAXNODE]; void init(int n) { this->n = n; memset(first, -1, sizeof(first)); m = 0; } void add_Edge(int u, int v, Type cap, Type cost) { edges[m] = Edge(u, v, cap, 0, cost); next[m] = first[u]; first[u] = m++; edges[m] = Edge(v, u, 0, 0, -cost); next[m] = first[v]; first[v] = m++; } bool bellmanford(int s, int t, Type &flow, Type &cost) { for (int i = 0; i < n; i++) d[i] = INF; memset(inq, false, sizeof(inq)); d[s] = 0; inq[s] = true; p[s] = s; a[s] = INF; queue<int> Q; Q.push(s); while (!Q.empty()) { int u = Q.front(); Q.pop(); inq[u] = false; for (int i = first[u]; i != -1; i = next[i]) { Edge& e = edges[i]; if (e.cap > e.flow && d[e.v] > d[u] + e.cost) { d[e.v] = d[u] + e.cost; p[e.v] = i; a[e.v] = min(a[u], e.cap - e.flow); if (!inq[e.v]) {Q.push(e.v); inq[e.v] = true;} } } } if (d[t] == INF) return false; flow += a[t]; cost += d[t] * a[t]; int u = t; while (u != s) { edges[p[u]].flow += a[t]; edges[p[u]^1].flow -= a[t]; u = edges[p[u]].u; } return true; } Type Mincost(int s, int t, Type D) { Type flow = 0, cost = 0; while (bellmanford(s, t, flow, cost)); if (D != flow) return -1; return cost; } } gao; int n, m, k; int main() { while (~scanf("%d%d%d", &n, &m, &k)) { gao.init(n + 1); gao.add_Edge(0, 1, k, 0); int u, v, a, c; while (m--) { scanf("%d%d%d%d", &u, &v, &a, &c); for (int i = 1; i <= c; i++) { gao.add_Edge(u, v, 1, a * (i * i - (i - 1) * (i - 1))); } } printf("%d\n", gao.Mincost(0, n, k)); } return 0; }
时间: 2024-10-07 12:04:47