BOJ 2314 Going Home //二分图KM模板变形

落日映苍穹つ 2022-08-10 14:45 83阅读 0赞

# Going Home #

Time Limit: 1000ms

Memory Limit: 65536KB

This problem will be judged on PKU. Original ID: [2195][]  
64-bit integer IO format: %lld Java class name: Main

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Tag it!

On a grid map there are n little men and n houses. In each unit time, every little man can move one unit step, either horizontally, or vertically, to an adjacent point. For each little man, you need to pay a $1 travel fee for every step he moves, until he enters a house. The task is complicated with the restriction that each house can accommodate only one little man.  
  
Your task is to compute the minimum amount of money you need to pay in order to send these n little men into those n different houses. The input is a map of the scenario, a '.' means an empty space, an 'H' represents a house on that point, and am 'm' indicates there is a little man on that point.  
![2195_1.jpg][]  
You can think of each point on the grid map as a quite large square, so it can hold n little men at the same time; also, it is okay if a little man steps on a grid with a house without entering that house.

## Input ##

There are one or more test cases in the input. Each case starts with a line giving two integers N and M, where N is the number of rows of the map, and M is the number of columns. The rest of the input will be N lines describing the map. You may assume both N and M are between 2 and 100, inclusive. There will be the same number of 'H's and 'm's on the map; and there will be at most 100 houses. Input will terminate with 0 0 for N and M.

## Output ##

For each test case, output one line with the single integer, which is the minimum amount, in dollars, you need to pay.

## Sample Input ##

2 2
    .m
    H.
    5 5
    HH..m
    .....
    .....
    .....
    mm..H
    7 8
    ...H....
    ...H....
    ...H....
    mmmHmmmm
    ...H....
    ...H....
    ...H....
    0 0

## Sample Output ##

2
    10
    28

## Source ##

[Pacific Northwest 2004][]

#include <stdio.h>
    #include <string.h>
    #include <math.h>
    
    #define p 205
    #define m 999999999
    
    struct node
    {
    	int x, y;
    }man[p], hoom[p];
    
    int tu[p][p];
    int link[p], slack[p];
    int lx[p], ly[p];
    int visitx[p], visity[p];
    char ch[p][p];
    int x, y, man1, hoom1;
    
    int MAX(int a, int b)
    {
    	if(a>b)
    		return a;
    	return b;
    }
    int MIN(int a, int b)
    {
    	if(a<b)
    		return a;
    	return b;
    }
    
    int dfs(int k)
    {
    	int i, d;
    
    	visitx[k] = 1;
    	for(i=0; i<man1; i++)
    	{
    		if(visity[i])
    			continue;
    		d = lx[k]+ly[i]-tu[k][i];
    
    		if(d==0)
    		{
    			visity[i] = 1;
    			if(link[i]==-1 || dfs(link[i]))
    			{
    				link[i] = k;
    				return 1;
    			}
    		}
    		else
    			slack[i] = MIN(slack[i], d);
    	}
    	return 0;
    }
    int KM()
    {
    	int i, j, ans;
    
    	for(i=0; i<hoom1; i++)
    		link[i] = -1;
    	memset(lx, 0, sizeof(lx));
    	memset(ly, 0, sizeof(ly));
    	for(i=0; i<man1; i++)
    	{
    		for(j=0; j<hoom1; j++)
    			lx[i] = MAX(lx[i], tu[i][j]);
    	}
    	for(i=0; i<man1; i++)
    	{
    		for(j=0; j<man1; j++)
    		{
    			slack[j] = m;
    		}
    		while(1)
    		{
    			memset(visitx, 0, sizeof(visitx));
    			memset(visity, 0, sizeof(visity));
    			if(dfs(i))
    				break;
    			else
    			{
    				int d;
    				d = m;
    				for(j=0; j<man1; j++)
    				{
    					if(!visity[j])
    						d = MIN(d, slack[j]);
    				}
    				for(j=0; j<man1; j++)
    				{
    					if(visitx[j])
    						lx[j] -= d;
    					if(visity[j])
    						ly[j] += d;
    				}
    			}
    		}
    	}
    	ans = 0;
    	for(i=0; i<man1; i++)
    		ans += tu[link[i]][i];
    	return ans;
    }
    int main()
    {
    	int i, j;
    	while(scanf("%d%d", &x, &y)!=-1 && x+y!=0)
    	{
    		for(i=0; i<x; i++)
    		{			
    			scanf("%s", ch[i]);			
    		}
    		man1 = hoom1 = 0;
    		for(i=0; i<x; i++)
    		{
    			for(j=0; j<y; j++)
    			{
    				if(ch[i][j]=='H')
    				{
    					hoom[hoom1].x = i;
    					hoom[hoom1].y = j;
    					hoom1++;
    				}
    				else if(ch[i][j]=='m')
    				{
    					man[man1].x = i;
    					man[man1].y = j;
    					man1++;
    				}
    			}
    		}
    		for(i=0; i<man1; i++)
    		{
    			for(j=0; j<hoom1; j++)
    			{
    				tu[i][j] =-(abs(man[i].x-hoom[j].x) + abs(man[i].y-hoom[j].y));
    			}
    		}
    		printf("%d\n", -KM());
    	}
    	return 0;
    }

[2195]: http://acm.pku.edu.cn/JudgeOnline/problem?id=2195
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[2195_1.jpg]: http://www.bnuoj.com/bnuoj/images/2195_1.jpg
[Pacific Northwest 2004]: http://www.bnuoj.com/bnuoj/problem.php?search=Pacific+Northwest+2004