UVa 11248 - Frequency Hopping - 最大流 - 最小割

题目描述：lrj厚白书第5章第6节第一道例题

题目分析：建图求最大流，如果最大流大于c，那么直接输出possible；如果最大流小于c，那么就要改变属于最小割边的值。

下面是代码：（水过，有时间在优化吧）

#include <cstdio>#include <cstring>#include <vector>#include <queue>#include <algorithm>using namespace std;const int maxn_v = 110;const int maxn_e = 22000;const int inf = 2100000000 ;struct edge{int from,to,cap,flow;edge() {}edge(int f,int t,int cp,int fl){from = f;to = t;cap = cp;flow = fl;}};vector<edge> E;vector<int> G[maxn_v];vector<int> cut;int n,m,c,s,t;int d[maxn_v];bool vis[maxn_v];int cur[maxn_e];int cmp(edge a,edge b){if(a.from == b.from) return a.to < b.to;else return a.from < b.from;}void add_e(int from,int to,int cap){E.push_back(edge(from,to,cap,0));E.push_back(edge(to,from,0,0));int e = E.size();G[from].push_back(e-2);G[to].push_back(e-1);}void read_graph(){s = 1;t = n;for(int i = 0; i <= n; i++) G[i].clear();E.clear();for(int i = 0; i < m; i++){int from,to,cap;scanf("%d%d%d",&from,&to,&cap);add_e(from,to,cap);}}bool bfs(){memset(vis,0,sizeof(vis));queue<int> q;q.push(s);d[s] = 0;vis[s] = 1;while(!q.empty()){int u = q.front(); q.pop();for(int i = 0; i < G[u].size(); i++){edge& e = E[G[u][i]];int v = e.to;if(!vis[v] && e.cap > e.flow){vis[v] = 1;d[v] = d[u] + 1;q.push(v);}}}return vis[t];}int dfs(int u,int a){if(u == t || a == 0) return a;int flow = 0, f;for(int& i = cur[u]; i < G[u].size(); i++){edge& e = E[G[u][i]];if(d[u] + 1 == d[e.to] && (f = dfs(e.to,min(a,e.cap-e.flow))) > 0){e.flow += f;E[G[u][i]^1].flow -= f;flow += f;a -= f;if(a == 0) break;}}return flow;}int max_flow(){int flow = 0;while(bfs()){memset(cur,0,sizeof(cur));flow += dfs(s,inf);}return flow;}void min_cut(){bfs();cut.clear();for(int i = 0; i < E.size(); i++){edge& e = E[i];if(vis[e.from] && !vis[e.to] && e.cap > 0) cut.push_back(i);}}void reduce(){for(int i = 0; i < E.size(); i++)E[i].cap -= E[i].flow;}void clear(){for(int i = 0; i < E.size(); i++) E[i].flow = 0;}void print(){for(int i = 0; i < E.size(); i++)printf("%d -> %d %d\n",E[i].from,E[i].to,E[i].cap);}int main(){int cas = 0;while(scanf("%d%d%d",&n,&m,&c) && n){read_graph();//print();printf("Case %d: ",++cas);int maxflow = max_flow();if(maxflow >= c || c == 0) printf("possible\n");else{vector<edge> ans;min_cut();reduce();for(int i = 0; i < cut.size(); i++){clear();edge& e = E[cut[i]];e.cap += c;if(maxflow + max_flow() >= c) ans.push_back(E[cut[i]]);e.cap -= c;}if(ans.empty()) printf("not possible\n");else{sort(ans.begin(),ans.end(),cmp);for(int i = 0; i < ans.size(); i++){if(i == 0) printf("possible option:(%d,%d)",ans[i].from,ans[i].to);else printf(",(%d,%d)",ans[i].from,ans[i].to);}printf("\n");}}}return 0;}