暴力(n^3)
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
#define MAX 105
#define INF 9999999
struct House { int r, c; } house[MAX];
struct Man { int r, c; } man[MAX];
int H, M, n, m;
int A[MAX], B[MAX];
int visA[MAX], visB[MAX];
int match[MAX], slack[MAX], map[MAX][MAX];
bool find_path ( int i )
{
visA[i] = true;
for ( int j = 0; j < H; j++ )
{
if ( !visB[j] && A[i] + B[j] == map[i][j] )
{
visB[j] = true;
if (match[j] == -1 || find_path(match[j]))
{
match[j] = i;
return true;
}
}
else if ( A[i] + B[j] > map[i][j] ) //j屬於B,且不在交錯路徑中
slack[j] = min(slack[j], A[i]+B[j]-map[i][j]);
}
return false;
}
void KM ()
{
int i, j, d;
memset(A,0,sizeof(A));
memset(B,0,sizeof(B));
memset(match,-1,sizeof(match));
for ( i = 0; i < M; i++ )
for ( j = 0; j < H; j++ )
A[i] = max (map[i][j], A[i]);
for ( i = 0; i < M; i++ )
{
for ( j = 0; j < H; j++ )
slack[j] = INF;
while ( 1 )
{
memset(visA,0,sizeof(visA));
memset(visB,0,sizeof(visB));
if ( find_path ( i ) ) break; //從i點出發找到交錯路徑則跳出循環
for ( d = INF, j = 0; j < H; j++ ) //取最小的slack[j]
if (!visB[j] && d > slack[j]) d = slack[j];
for ( j = 0; j < M; j++ ) //集合A中位於交錯路徑上的-d
if ( visA[j] ) A[j] -= d;
for ( j = 0; j < H; j++ ) //集合B中位於交錯路徑上的+d
if ( visB[j] ) B[j] += d;
else slack[j] -= d; //注意修改不在交錯路徑上的slack[j]
}
}
}
int main()
{
char s[MAX];
int i, j, res;
while ( scanf("%d%d",&n,&m) )
{
if ( !m && !n ) break;
H = M = res = 0;
for ( i = 0; i < n; i++ )
{
scanf("%s",s);
for ( j = 0; j < m; j++ )
{
if ( s[j] == 'H' )
house[H].r = i, house[H++].c = j;
else if ( s[j] == 'm' )
man[M].r = i, man[M++].c = j;
}
}
for ( i = 0; i < M; i++ ) //求最小帶權匹配可以將權值改爲負數
for ( j = 0; j < H; j++ )
map[i][j] = -(abs(man[i].r-house[j].r) + abs(man[i].c-house[j].c));
KM();
for ( j = 0; j < H; j++ )
res -= map[match[j]][j];
printf("%d\n",res);
}
return 0;
}
KM算法
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
const int maxn = 105;
const int INF = 1<<29;
int w[maxn][maxn];
int n;
int ly[maxn],lx[maxn];//頂標
bool S[maxn],T[maxn]; //左/右第i個點是否已經標記
int left[maxn]; //匹配爲右邊第i個點的編號
int H, M;
int R,C;
bool match(int i){
S[i]=1;
for(int j=1;j<=n;j++)
if(lx[i]+ly[j]==w[i][j]&&!T[j]){
T[j]=1;
if(!left[j]||match(left[j])){
left[j]=i;
return true;
}
}
return false;
}
void update(){
int a=INF;
for(int i=1;i<=n;i++){
if(S[i])
for(int j=1;j<=n;j++){
if(!T[j])
a=min(a,lx[i]+ly[j]-w[i][j]);
}
}
for(int i=1;i<=n;i++){
if(S[i]) lx[i]-=a;
if(T[i]) ly[i]+=a;
}
}
void KM(){
for(int i=1;i<=n;i++){
left[i]=lx[i]=ly[i]=0;
for(int j=1; j<=n;j++){
lx[i]=max(lx[i],w[i][j]);
}
}
for(int i=1;i<=n;i++){
while(1){
//printf("1");
memset(T,0,sizeof(T));
memset(S,0,sizeof(S));
if(match(i)) break;
else update();
}
}
}
struct House { int r, c; } house[maxn];
struct Man { int r, c; } man[maxn];
int main()
{
char s[maxn];
int i, j;
while ( scanf("%d %d",&R,&C) )
{
if ( !R && !C ) break;
H = M = 1;
for ( i = 1; i <=R; i++ )
{
scanf("%s",s+1);
for ( j = 1; j <=C; j++ )
{
if ( s[j] == 'H' )
house[H].r = i, house[H++].c = j;
else if ( s[j] == 'm' )
man[M].r = i, man[M++].c = j;
}
}
for ( i = 1; i <= M-1; i++ ) //求最小帶權匹配可以將權值改爲負數
for ( j = 1; j <= H-1; j++ )
w[i][j] = -(abs(man[i].r-house[j].r) + abs(man[i].c-house[j].c));
n=H-1;
KM();
int res=0;
for ( j = 1; j <=H-1; j++ )
res -= w[left[j]][j];
printf("%d\n",res);
}
return 0;
}