POJ 1459 —— Power Network

来源：互联网发布：生物信息知乎编辑：程序博客网时间：2024/06/08 11:49

原题：http://poj.org/problem?id=1459

题意：一共有n个结点，在这些结点中有 np 个是发电站，有 nc 个是用户，给出m条线路所能运输的电量，以及每个发电站输出的电量、每个用户能接收的电量；

问用户所能接收的最大电量；

思路：因为是多源多汇，所以我们建立一个超级源点 s = n 和一个超级汇点 t = n+1；

建立 s 到发电站的的边，容量就是发电站输出的电量；

建立用户到 t 的边，容量就是用户所能接收的电量；

剩下的 m 条边直接建边即可；

#include<cstdio>#include<cstring>#include<string>#include<queue>#include<vector>#include<algorithm>#define inf 0x3f3f3f3fusing namespace std;const int maxn = 1e5+5;int n, np, nc, m;int num_nodes;struct Edge{int from, to, flow, cap;}edge[maxn*2];vector<int>G[maxn];int edgenum;void add(int u, int v, int c){edge[edgenum].from = u;edge[edgenum].to = v;edge[edgenum].flow = 0;edge[edgenum].cap = c;edgenum++;edge[edgenum].from = v;edge[edgenum].to = u;edge[edgenum].flow = 0;edge[edgenum].cap = 0;edgenum++;G[u].push_back(edgenum-2);G[v].push_back(edgenum-1);}int deep[maxn];bool vis[maxn];void BFS(int s, int t){queue<int>Q;memset(vis, false, sizeof vis);Q.push(t);vis[t] = true;deep[t] = 0;while(!Q.empty()){int now = Q.front();Q.pop();for(int i = 0;i<(int)G[now].size();i++){int v = edge[G[now][i]].to;if(!vis[v]){deep[v] = deep[now] + 1;vis[v] = true;Q.push(v);}}}}int gap[maxn], front[maxn], cur[maxn];int Augment(int s, int t){int minflow = inf;int begin = t;while(begin != s){Edge& e = edge[front[begin]];minflow = min(minflow, e.cap - e.flow);begin = e.from;}begin = t;while(begin != s){edge[front[begin]].flow += minflow;edge[front[begin]^1].flow -= minflow;begin = edge[front[begin]].from;}return minflow;}int Maxflow(int s, int t){int flow = 0;BFS(s, t);memset(gap, 0, sizeof gap);memset(cur, 0, sizeof cur);for(int i = 0;i<num_nodes;i++)gap[deep[i]]++;int begin = s;while(deep[s] < num_nodes){if(begin == t){flow += Augment(s, t);begin = s;}bool flag = false;for(int i = cur[begin];i<(int)G[begin].size();i++){Edge& e = edge[G[begin][i]];if(e.cap > e.flow && deep[begin] == deep[e.to] + 1){front[e.to] = G[begin][i];cur[begin] = i;flag = true;begin = e.to;break;}}if(!flag){int k = num_nodes-1;for(int i = 0;i<(int)G[begin].size();i++){Edge& e = edge[G[begin][i]];if(e.cap > e.flow)k = min(k, deep[e.to]);}if(--gap[deep[begin]] == 0)break;gap[deep[begin] = k+1]++;cur[begin] = 0;if(begin != s){begin = edge[front[begin]].from;}}}return flow;}void init(){for(int i = 0;i<n+2;i++)G[i].clear();edgenum = 0;memset(deep, 0, sizeof deep);}int main(){while(~scanf("%d%d%d%d", &n, &np, &nc, &m)){init();while(m--){int u, v, c;scanf(" (%d,%d)%d", &u, &v, &c);add(u, v, c);}int s = n, t = n+1;while(np--){int v, c;scanf(" (%d)%d", &v, &c);add(s, v, c);}while(nc--){int u, c;scanf(" (%d)%d", &u, &c);add(u, t, c);}num_nodes = n+2;int flow = Maxflow(s, t);printf("%d\n", flow);}return 0;}

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