Ultraviolet A 1486-transportation (network stream + edge splitting)

Ultraviolet A 1486-transportation

Question Link

A directed graph carries K goods, with some sides, each side having a coefficient A. If there is X goods on the side, you have to pay the money of a X, minimum transportation cost from 1 to n

Idea: The cost flow. The maximum capacity of this question side is only 5. Therefore, you can split the edge, one side into a C side, and each line has a capacity of 1, the corresponding cost is a * (I ^ 2-(I-1) ^ 2), and then you can run the billing flow.

Code:

#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;}

Ultraviolet A 1486-transportation (network stream + edge splitting)