HDU--1533--Going Home--KM算法

Going Home

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 2514    Accepted Submission(s): 1269

Problem Description

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.

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

 

题解：把每一个m到H的距离保存起来当作一个边。值记录成负的，由于要求最小距离，常规KM计算的是最大值

#include <iostream>
#include <cstring>
#define MAX (1<<30)
#define MIN -MAX
using namespace std;
struct ssss
{
    int x,y;
};
ssss s1[111],s2[111];
int n,m,l1,l2,map[111][111];
int rode[111],r[111];
bool vx[111],vy[111];
int sx[111],sy[111];
int dfs(int x)
{
    vx[x]=1;    //标记增广路左边已訪问的点
    int i,j,k,l;
    for(i=0;i<l2;i++)
    if(!vy[i])
    {
        k=sx[x]+sy[i]-map[x][i];
        if(k==0)
        {
            vy[i]=1;//訪问它再标记已訪问
            if(rode[i]==-1||dfs(rode[i]))   //假设右边的点没有匹配或者有匹配（继续用他的匹配点继续找）
            {
                rode[i]=x;  //记录右边点匹配到的左边点的序号
                return 1;
            }
        }else if(r[i]>k)r[i]=k;     //记录右端点没訪问的边的最小差值。用来导入
    }
    return 0;
}
int Dinic()
{
    int i,j,k,l;
    memset(sy,0,sizeof(sy));    //标记右端点权值
    memset(rode,-1,sizeof(rode));   //右端点匹配点初始化为-1
    for(i=0;i<l1;i++)
    {
        sx[i]=MIN;
        for(j=0;j<l2;j++)
        sx[i]=max(sx[i],map[i][j]); //左端点权值取最大的边的值
    }
    for(i=0;i<l1;i++)
    {
        for(j=0;j<l2;j++)r[j]=MAX;
        while(1)
        {
            memset(vx,0,sizeof(vx));    //訪问标记初始化
            memset(vy,0,sizeof(vy));
            if(dfs(i))break;    //匹配到了就结束
            k=MAX;
            for(j=0;j<l2;j++)
            if(!vy[j])k=min(k,r[j]);    //不然导入差值最小的边（这是保证匹配的总值从最大逐渐减小）
            for(j=0;j<l1;j++)
            if(vx[j])sx[j]-=k;  //左端点权值减小
            for(j=0;j<l2;j++)
            if(vy[j])sy[j]+=k;  //右端点权值曾加
            //这样导入了边之后其它匹配不变x+y=(x-k)+(y+k)
        }
    }
    for(i=k=0;i<l2;i++)
    k+=map[rode[i]][i];
    return -k;
}
int bb(int x)
{
    return x>0?x:-x;
}
int main (void)
{
    int i,j,k,l;
    char c;
    while(cin>>n>>m&&n)
    {
        l1=l2=0;
        for(i=0;i<n;i++)
        for(j=0;j<m;j++)
        {
            cin>>c;
            if(c=='m')
            {
                s1[l1].x=i;
                s1[l1].y=j;
                l1++;
            }
            if(c=='H')
            {
                s2[l2].x=i;
                s2[l2].y=j;
                l2++;
            }
        }
        for(i=0;i<l1;i++)
        for(j=0;j<l2;j++)
        {
            k=bb(s1[i].x-s2[j].x)+bb(s1[i].y-s2[j].y);
            map[i][j]=(k<0?k:-k);
        }
        cout<<Dinic()<<endl;
    }
    return 0;
}