POJ 2195
//题目类型：二分匹配-最小权完美匹配
//算法实现：可以采用KM算法或者最小费用最大流实现
//KM算法实现
#include <iostream>
#include <string>
#include <math.h>
//#include <conio.h>
using namespace std;
#define arraysize 105
int maxData = 1000000000;
int w[arraysize][arraysize];
int match[arraysize];
int lx[arraysize],ly[arraysize],slack[arraysize];
bool finalx[arraysize],finaly[arraysize];
int hcount,mcount; //由题目可知，hcount=mcount,所以直接使用KM算法进行最大权完美匹配
typedef struct house
{
int row;
int col;
}house;
typedef struct littleman
{
int row;
int col;
}littleman;
littleman mans[arraysize];
house houses[arraysize];
bool DFS(int p)
{
int i,j,t;
finalx[p] = true;
for(i=1;i<=hcount;++i)
{
if(finaly[i]) continue;
int temp = lx[p]+ly[i]-w[p][i];
if(temp==0)
{
finaly[i] = true;
t = match[i];
match[i] = p;
if(t==0 || DFS(t)) return true;
match[i] = t;
}
else if(slack[i]>temp)
{
slack[i] = temp;
}
}
return false;
}
int KM()
{
int i,j;
memset(ly,0,sizeof(ly));
memset(match,0,sizeof(match));
for(i=1;i<=mcount;++i)
{
lx[i]=-maxData;
for(j=1;j<=hcount;++j)
{
if(lx[i]<w[i][j])
lx[i] = w[i][j];
}
}
for(i=1;i<=mcount;++i)
{
for(j=1;j<=hcount;++j) slack[j] = maxData;
while(1)
{
memset(finalx,0,sizeof(finalx));
memset(finaly,0,sizeof(finaly));
if(DFS(i)) break;
int d = maxData;
for(j=1;j<=hcount;++j)
{
if(!finaly[j] && d>slack[j])
d = slack[j];
}
for(j=1;j<=mcount;++j)
{
if(finalx[j]) lx[j]-= d;
if(finaly[j]) ly[j]+= d;
else slack[j] -= d;
}
}
}
int ans= 0;
for(i=1;i<=mcount;++i)
{
ans -=(lx[i]+ly[i]); //结果加的权值需要取反
}
return ans;
}
int main()
{
//freopen("1.txt","r",stdin);
int i,j;
int n,m;
string tempstr;
while(cin>>n>>m)
{
if(n==0 && m==0)
break;
hcount = 0;
mcount = 0;
for(i=1;i<=n;++i)
{
cin>>tempstr;
for(j=0;j<tempstr.size();++j)
{
if(tempstr[j]=='H')
{
hcount++;
houses[hcount].row = i;
houses[hcount].col = j+1;
}
else if(tempstr[j]=='m')
{
mcount++;
mans[mcount].row = i;
mans[mcount].col = j+1;
}
}
}
for(i=1;i<=mcount;++i)
{
for(j=1;j<=hcount;++j)
{
//KM算法求的是最大权的完美匹配，所以将权值取反,权值是距离
w[i][j] = -(abs(mans[i].row-houses[j].row)+abs(mans[i].col-houses[j].col));
}
}
cout<<KM()<<endl;
}
//getch();
return 0;
}
//使用最小费用最大流实现
//本题的关键在于建图：将小人和房间都作为图中的点，并设置一超级源点和超级终点，小人和房间的容量设置为1，费用设置为距离。源点到小人
//的容量设置为1，费用为0；房间到终点的容量设置为1，费用设置为0
#include <iostream>
#include <string>
//#include <conio.h>
#include <queue>
#include <math.h>
using namespace std;
#define arraysize 205
typedef struct house
{
int row;
int col;
}house;
typedef struct littleman
{
int row;
int col;
}littleman;
house houses[101];
littleman mans[101];
int n,m;
int mcount,hcount;
int maxData = 10000000;
int capacity[arraysize][arraysize];
int kcost[arraysize][arraysize];
bool final[arraysize]; //SPFA算法中标识结点是否在队列中
int d[arraysize];
int flow[arraysize][arraysize];
int pre[arraysize];
int ncount;
void SPFA(int src)
{
queue<int> myqueue;
int i,j;
memset(final,0,sizeof(final));
memset(pre,-1,sizeof(pre));
myqueue.push(src);
for(i=0;i<=ncount;++i) //SPFA算法与Dij不同，SPFA初始化时将除源点以外所有点的最短距离初始化无穷大,ncount为结点总数
{
d[i] = maxData;
}
d[src] = 0; //源点最短距离设置成0
final[src] = true;
while(!myqueue.empty()) //SPFA算法可入队列多次
{
int frontint = myqueue.front();myqueue.pop();
final[frontint] = false;
for(i=0;i<=ncount;++i)
{
if(capacity[frontint][i]>flow[frontint][i] && d[i]>d[frontint]+kcost[frontint][i]) //c[u][v]>f[u][v]说明<u,v>之间流量可以进行增加
{
d[i] = d[frontint]+kcost[frontint][i];
pre[i] = frontint; //修改前驱
if(!final[i])
{
final[i] = true;
myqueue.push(i);
}
}
}
}
}
void minCost(int src,int des)
{
int minAdd = maxData;
int p;
while(1)
{
SPFA(src);
if(pre[des]==-1) //表示已无增广路
break;
minAdd = maxData;
p = des;
while(pre[p]!=-1)
{
minAdd = min(minAdd,(capacity[pre[p]][p]-flow[pre[p]][p])); //求的增广路的可增流量
p = pre[p];
}
p = des;
while(pre[p]!=-1) //沿着最小费用路进行增广
{
flow[pre[p]][p] += minAdd;
flow[p][pre[p]] -= minAdd;
p = pre[p];
}
}
}
int main()
{
//freopen("1.txt","r",stdin);
int i,j;
int src,des;
int flowcost;
string tempstr;
while(cin>>n>>m)
{
if(n==0 && m==0)
break;
flowcost = 0; //最小费用
mcount = 0; //小人的数目
hcount = 0; //房间的数目
memset(kcost,0,sizeof(kcost));
memset(capacity,0,sizeof(capacity));
memset(flow,0,sizeof(flow));
for(i=1;i<=n;++i)
{
cin>>tempstr;
for(j=0;j<tempstr.size();++j)
{
if(tempstr[j]=='H')
{
hcount++;
houses[hcount].row = i;
houses[hcount].col = j+1;
}
else if(tempstr[j]=='m')
{
mcount++;
mans[mcount].row = i;
mans[mcount].col = j+1;
}
}
}
//小人和房间之间构图
for(i=1;i<=mcount;++i)
{
for(j=1;j<=hcount;++j)
{
kcost[i][j+mcount] = abs(mans[i].row-houses[j].row)+abs(mans[i].col-houses[j].col); //费用设置为距离
kcost[j+mcount][i] = -kcost[i][j+mcount];
capacity[i][j+mcount] = 1;
}
}
src = 0;
des = hcount+mcount+1;
ncount = hcount+mcount+2; //结点总数
//源点到小人之间构图
for(i=1;i<=mcount;++i)
{
capacity[src][i] = 1;
}
//房间到终点之间构图
for(j=1;j<=hcount;++j)
{
capacity[j+mcount][des] = 1;
}
minCost(src,des);
for(i=1;i<=mcount;++i)
{
for(j=1;j<=hcount;++j)
{
flowcost += kcost[i][j+mcount]*flow[i][j+mcount]; //最小费用
}
}
cout<<flowcost<<endl;
}
//getch();
return 0;
}
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