TourTime Limit: 3000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others)
Problem Description
In the kingdom of Henryy, there are N (2 <= N <= 200) cities, with M (M <= 30000) one-way roads connecting them. You are lucky enough to have a chance to have a tour in the kingdom. The route should be designed as: The route should contain one or more loops.
(A loop is a route like: A->B->……->P->A.) Every city should be just in one route. A loop should have at least two cities. In one route, each city should be visited just once. (The only exception is that the first and the last city should be the same and this city is visited twice.) The total distance the N roads you have chosen should be minimized.
Input
An integer T in the first line indicates the number of the test cases.
In each test case, the first line contains two integers N and M, indicating the number of the cities and the one-way roads. Then M lines followed, each line has three integers U, V and W (0 < W <= 10000), indicating that there is a road from U to V, with the distance of W. It is guaranteed that at least one valid arrangement of the tour is existed. A blank line is followed after each test case.
Output
For each test case, output a line with exactly one integer, which is the minimum total distance.
Sample Input
1
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
Sample Output
42
Source
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题目的意思是是给出一张有向图，要选择几条边使得每个点都落在一个环上，使得所选的边和最小
思路：每个点落在环上，所以每个点的入度出度均为1，这正好符合二分图性质，建立二分图，求最大权匹配，题目要求最小，权值取负数即可
#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
#include <vector>
#include <set>
#include <stack>
#include <map>
#include <climits>
using namespace std; #define LL long long const int MAXN = 505;
const int INF = 0x3f3f3f3f;
int g[MAXN][MAXN];
int lx[MAXN],ly[MAXN]; //顶标
int linky[MAXN];
int visx[MAXN],visy[MAXN];
int slack[MAXN];
int nx,ny;
bool find(int x)
{
visx[x] = true;
for(int y = 0; y < ny; y++)
{
if(visy[y])
continue;
int t = lx[x] + ly[y] - g[x][y];
if(t==0)
{
visy[y] = true;
if(linky[y]==-1 || find(linky[y]))
{
linky[y] = x;
return true; //找到增广轨
}
}
else if(slack[y] > t)
slack[y] = t;
}
return false; //没有找到增广轨（说明顶点x没有对应的匹配，与完备匹配(相等子图的完备匹配)不符）
} int KM() //返回最优匹配的值
{
int i,j;
memset(linky,-1,sizeof(linky));
memset(ly,0,sizeof(ly));
for(i = 0; i < nx; i++)
for(j = 0,lx[i] = -INF; j < ny; j++)
lx[i] = max(lx[i],g[i][j]);
for(int x = 0; x < nx; x++)
{
for(i = 0; i < ny; i++)
slack[i] = INF;
while(true)
{
memset(visx,0,sizeof(visx));
memset(visy,0,sizeof(visy));
if(find(x)) //找到增广轨，退出
break;
int d = INF;
for(i = 0; i < ny; i++) //没找到，对l做调整(这会增加相等子图的边)，重新找
{
if(!visy[i] && d > slack[i])
d = slack[i];
}
for(i = 0; i < nx; i++)
{
if(visx[i])
lx[i] -= d;
}
for(i = 0; i < ny; i++)
{
if(visy[i])
ly[i] += d;
else
slack[i] -= d;
}
}
}
int result = 0;
for(i = 0; i < ny; i++)
if(linky[i]>-1)
result += g[linky[i]][i];
return -result;
} int main()
{
int n,m,u,v,c,T;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
nx=ny=n;
memset(g,-INF,sizeof g);
for(int i=0; i<m; i++)
{
scanf("%d%d%d",&u,&v,&c);
u--,v--;
g[u][v]=max(g[u][v],-c);
}
printf("%d\n",KM());
}
return 0;
}