題干：

In Hanoi, there are N beauty-spots (2 <= N <= 200), connected by M one-way streets. The length of each street does not exceed 10000. You are the director of a travel agency, and you want to create some tours around the city which satisfy the following conditions:

• Each of the N beauty-spots belongs to exactly one tour.
• Each tour is a cycle which consists of at least 2 places and visits each place once (except for the place we start from which is visited twice).
• The total length of all the streets we use is minimal.

Input

The first line of input contains the number of testcases t (t <= 15). The first line of each testcase contains the numbers N, M. The next M lines contain three integers U V W which mean that there is one street from U to V of length W.

Output

For each test case you shold output the minimal total length of all tours.

Example

Input: 2 6 9 1 2 5 2 3 5 3 1 10 3 4 12 4 1 8 4 6 11 5 4 7 5 6 9 6 5 4 5 8 1 2 4 2 1 7 1 3 10 3 2 10 3 4 10 4 5 10 5 3 10 5 4 3Output: 42 40Detailed explanation: Test 1:Tour #1: 1 - 2 - 3 - 1 --> Length = 20Tour #2: 6 - 5 - 4 - 6 --> Length = 22Test 2:Tour #1: 1 - 3 - 2 - 1 --> Length = 27Tour #2: 5 - 4 - 5 --> Length = 13

題目大意：

把一張帶權有向圖劃分成一個或多個環，使環的總權值最小。

解題報告：

類似于二分圖的最小路徑覆蓋，拆點。把每個點 u 拆成兩個點 u1 和 u2， 然后每條邊 u->v 改寫成 u1---v2，就得到了一個二分圖最佳匹配的模型。 由于“把一張帶權有向圖劃分成一個或多個環”其實 等價于“每一個點都保留一個入度和一個出度” ，而匹配模型正好能滿足這一點。于是建圖跑模板就可以了、、

AC代碼：

#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #define ll long long using namespace std;const int MAXN = 70000; const int MAXM = 100005; const int INF = 0x3f3f3f3f; struct Edge {int to,next,cap,flow,cost; } edge[MAXM]; int head[MAXN],tol; int pre[MAXN],dis[MAXN]; bool vis[MAXN]; int N; void init(int n) {N = n;tol = 0;memset(head, -1,sizeof(head)); } void addedge(int u,int v,int cap,int cost) {edge[tol].to = v;edge[tol].cap = cap;edge[tol].cost = cost;edge[tol].flow = 0;edge[tol].next = head[u];head[u] = tol++;edge[tol].to = u;edge[tol].cap = 0;edge[tol].cost = -cost;edge[tol].flow = 0;edge[tol].next = head[v];head[v] = tol++; } bool spfa(int s,int t) {queue<int>q;for(int i = 0; i <= N; i++) {dis[i] = INF;vis[i] = false;pre[i] = -1;}dis[s] = 0;vis[s] = true;q.push(s);while(!q.empty()) {int u = q.front();q.pop();vis[u] = false;for(int i = head[u]; i !=-1; i = edge[i].next) {int v = edge[i].to;if(edge[i].cap > edge[i].flow && dis[v] > dis[u] + edge[i].cost ) {dis[v] = dis[u] + edge[i].cost;pre[v] = i;if(!vis[v]) {vis[v] = true;q.push(v);}}}}if(pre[t] ==-1)return false;else return true; } int minCostMaxflow(int s,int t,int &cost) {int flow = 0;cost = 0;while(spfa(s,t)) {int Min = INF;for(int i = pre[t]; i !=-1; i = pre[edge[i^1].to]) {if(Min > edge[i].cap-edge[i].flow)Min = edge[i].cap-edge[i].flow;}for(int i = pre[t]; i !=-1; i = pre[edge[i^1].to]) {edge[i].flow += Min;edge[i^1].flow-= Min;cost += edge[i].cost * Min;}flow += Min;}return flow; } int main() {int n,m;int t;scanf("%d",&t);while(t--) {scanf("%d%d",&n,&m);init(2*n+1);int st=0,ed=2*n+1;for(int i = 1,a,b,w; i<=m; i++) {scanf("%d%d%d",&a,&b,&w);addedge(a,b+n,1,w);}for(int i = 1; i<=n; i++) addedge(st,i,1,0);for(int i = n+1; i<=2*n; i++) addedge(i,ed,1,0);int cost;int ans = minCostMaxflow(st,ed,cost);printf("%d\n",cost);} return 0 ; }

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