poj2516

最小费用最大流初探。过程极为简单：把边作为边权，然后找超级源点和超级汇点之间的最短路，如果有最短路，则对它增广。

http://blog.youkuaiyun.com/lin375691011/article/details/18923267

这是lin的博客，讲得（网络流的概念）比较详细。这个题的细节都在代码中了，就不再叙述了。

#include <iostream>
#include <algorithm>
#include <queue>

using namespace std;

#define M 105
#define inf 1 << 30

int capacity_need[M][M], capacity_have[M][M], construction_cost[M][M][M], n, m, k;
int capacity[M][M];
int flow[M][M];
int weight[M][M];
int shortestdistances[M];
int pre_node[M];
bool visited[M];
/**
 *  insearch for shortest path from SuperSource[0], to SuperSink[n+m+1];
 *
 *  @return whether there are shortest paths
 */
bool spfa() {
	for (int i = 0; i <= n + m + 1; i++) {
		shortestdistances[i] = inf;
		pre_node[i] = -1;
		visited[i] = false;
	}
	shortestdistances[0] = 0;
	visited[0] = true;
	queue <int> q;
	q.push(0);
	while (!q.empty()) {
		int t = q.front();
		q.pop();
		visited[t] = false;
		for (int i = 1; i <= n + m + 1; i++) {
			if (capacity[t][i] > flow[t][i] && shortestdistances[i] > shortestdistances[t] + weight[t][i]) {
				shortestdistances[i] = shortestdistances[t] + weight[t][i];
				pre_node[i] = t;
				if (!visited[i]) {
					q.push(i);
					visited[i] = true;
				}
			}
		}
	}
	if (pre_node[n + m + 1] == -1) {
		return false;
	}
	return true;
}
/**
 *  get maxflow
 */
void getMaxflow() { //if there is the shortest path, find the key edge that controls the flow, then change the flow
	while (spfa()) {
		int maxflow = inf;
		int p = n + m + 1;
		while (pre_node[p] != -1) { //find
			maxflow = min(maxflow, capacity[pre_node[p]][p] - flow[pre_node[p]][p]); // from p'pre to p, the real flow equals to the capacity - flow_now
			p = pre_node[p];
		}
		p = n + m + 1;
		while (pre_node[p] != -1) { //change
			flow[pre_node[p]][p] += maxflow;
			flow[p][pre_node[p]] = -flow[pre_node[p]][p];
			p = pre_node[p];
		}
	}
}

int main() {
	int i, j, d, ans;
	while (cin >> n >> m >> k, n || m || k) {
		ans = 0;
		bool flag = false;
		for (i = 1; i <= n; i++) {
			for (j = 1; j <= k; j++) {
				cin >> capacity_need[i][j];
			}
		}
		for (i = 1; i <= m; i++) {
			for (j = 1; j <= k; j++) {
				cin >> capacity_have[i][j];
			}
		}
		for (i = 1; i <= k; i++) {
			for (j = 1; j <= n; j++) {
				for (d = 1; d <= m; d++) {
					cin >> construction_cost[i][d][j];
				}
			}
		}
		for (i = 1; i <= k; i++) {
			memset(capacity, 0, sizeof(capacity));
			memset(flow, 0, sizeof(flow));
			memset(weight, 0, sizeof(weight));
			for (j = 1; j <= m; j++) {
				capacity[0][j] = capacity_have[j][i]; //SuperSource's capacity should be the capacity current have(dust)
			}
			for (j = 1; j <= n; j++) {
				capacity[m + j][m + n + 1] = capacity_need[j][i]; //SuperSink's capacity should be the capacity current need(store)
			}
			for (j = 1; j <= m; j++) {
				for (d = 1; d <= n; d++) {
					capacity[j][d + m] = capacity_have[j][i]; //Dust to store should be the dust's capacity
				}
			}
			for (j = 1; j <= m; j++) {
				for (d = 1; d <= n; d++) {
					weight[j][d + m] = construction_cost[i][j][d];
					weight[d + m][j] = -construction_cost[i][j][d]; // MINUS FOR REMAINING FLOW NOW
				}
			}
			getMaxflow();
			for (j = 1; j <= n; j++) {
				if (capacity[j + m][n + m + 1] != flow[j + m][n + m + 1]) { // support != requirement
					flag = true;
					break;
				}
			}
			if (flag) {
				break;
			}
			for (j = 1; j <= m; j++) {
				for (d = 1; d <= n; d++) {
					ans += flow[j][d + m] * weight[j][d + m]; //CLEARLY RIGHT
				}
			}
		}
		if (flag) {
			cout << -1 << endl;
		}
		else {
			cout << ans << endl;
		}
	}
}