hdoj--3488--Tour（KM）-优快云博客

本文介绍了一个旅行路线优化问题，目标是最小化包含至少两个城市的环路总距离，并确保每个城市仅被访问一次（除起点终点外）。通过使用匈牙利算法（KM算法），解决了这一复杂的图论问题。

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Tour

Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others)

Total Submission(s): 2549 Accepted Submission(s): 1257

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

2010 ACM-ICPC Multi-University Training Contest（6）——Host by BIT

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#include<cstdio>
#include<cstring>
#include<algorithm>
#define INF 0x3f3f3f3f
using namespace std;
int n,m;
int map[210][210];
int slock[210];
int lx[210],ly[210];
bool visx[210],visy[210];
int nx,ny,match[210];
void getmap()
{
	scanf("%d%d",&n,&m);
	nx=ny=n;
	for(int i=1;i<=nx;i++)
	for(int j=1;j<=ny;j++)
	map[i][j]=-INF;
	int x,y,w;
	for(int i=0;i<m;i++)
	{
		scanf("%d%d%d",&x,&y,&w);
		if(-w>map[x][y])
			map[x][y]=-w;
	}
}
int DFS(int x)
{
	visx[x]=true;
	for(int y=1;y<=ny;y++)
	{
		if(visy[y]) continue;
		int t=lx[x]+ly[y]-map[x][y];
		if(t==0)
		{
			visy[y]=true;
			if(match[y]==-1||DFS(match[y]))
			{
				match[y]=x;
				return 1;
			}
		}
		else if(t<slock[y])
		slock[y]=t;
	}
	return 0;
}
void KM()
{
	memset(match,-1,sizeof(match));
	memset(ly,0,sizeof(ly));
	for(int x=1;x<=nx;x++)
	{
		lx[x]=-INF;
		for(int y=1;y<=ny;y++)
		lx[x]=max(lx[x],map[x][y]);
	}
	for(int x=1;x<=nx;x++)
	{
		for(int y=1;y<=ny;y++)
		slock[y]=INF;
		while(1)
		{
			memset(visx,false,sizeof(visx));
			memset(visy,false,sizeof(visy));
			if(DFS(x)) break;
			int d=INF;
			for(int i=1;i<=ny;i++)
			{
				if(!visy[i]&&slock[i]<d)
					d=slock[i];
			}
			for(int i=1;i<=nx;i++)
			{
				if(visx[i])
				lx[i]-=d;
			}
			for(int i=1;i<=ny;i++)
			{
				if(visy[i])
					ly[i]+=d;
				else
					slock[i]-=d;
			}
		}
	}
	int ans = 0;
	for(int i = 1;i <= ny; i++)
	ans += map[match[i]][i];
	printf("%d\n",-ans); 
}
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		getmap();
		KM();
	}
	return 0;
}

转载于:https://www.cnblogs.com/playboy307/p/5273477.html