题意:给定一个有向带权图,使得每一个点都在一个环上,而且权之和最小。
分析:每个点在一个环上,入度 = 出度 = 1,拆点入点,出点,s到所有入点全部满载的最小费用MCMF;
#include using namespace std;const int maxn = 105*2;const int INF = 0x3f3f3f3f;typedef pair pii;struct Edge{ int from, to, cap, flow, cost;};struct MCMF{ int n, m; vector edges; vector G[maxn]; bool inq[maxn]; // 是否在队列中 int d[maxn]; // Bellman-Ford int p[maxn]; // 上一条弧 int a[maxn]; // 可改进量 void init(int n) { this->n = n; for(int i = 0; i < n; i++) G[i].clear(); edges.clear(); } void AddEdge(int from, int to, int cap, int cost) { edges.push_back((Edge) { from, to, cap, 0, cost }); edges.push_back((Edge) { to, from, 0, 0, -cost }); m = edges.size(); G[from].push_back(m-2); G[to].push_back(m-1); } bool BellmanFord(int s, int t, int &flow, long long& cost) { memset(inq,0,sizeof(inq)); for(int i=0;i
Q; Q.push(s); while(!Q.empty()) { int u = Q.front(); Q.pop(); inq[u] = false; for(int i = 0; i < G[u].size(); i++) { Edge& e = edges[G[u][i]]; if(e.cap > e.flow && d[e.to] > d[u] + e.cost) { d[e.to] = d[u] + e.cost; p[e.to] = G[u][i]; a[e.to] = min(a[u], e.cap - e.flow); if(!inq[e.to]) { Q.push(e.to); inq[e.to] = true; } } } } if(d[t] == INF) return false; //s-t 不连通,失败退出 flow += a[t]; cost += (long long)d[t] * (long long)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]].from; } return true; } pair
Mincost(int s, int t) { long long cost = 0; int flow = 0; while(BellmanFord(s, t, flow, cost)); return pair {flow,cost}; }}sol;int main(){ int n,m; while(scanf("%d%d",&n,&m)!=EOF) { int s = 0,t=2*n+1; sol.init(2*n+2); for(int i=1;i<=n;i++) sol.AddEdge(s,i,1,0); for(int i=n+1;i<=2*n;i++) sol.AddEdge(i,t,1,0); for(int i=0;i