UVA11383[Golden Tiger Claw] KM算法的应用

题目链接

题意：

给一个n*n的矩阵，每个格子中有正整数w[i][j]，试为每行和每列分别确定一个数字row[i]和col[i]，使得任意格子w[i][j]<=row[i]+col[j]恒成立。先输row，再输出col，再输出全部总和（总和应尽量小）。

解题报告：这道题中w[i][j]<=row[i]+col[j]满足KM算法中顶标的性质，所以可以用KM算法，算法结束时的顶标值就是答案。

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 505;

int w

, n, Lx
, Ly
, slack
, line
;
bool S
, T
;

bool find(int i){
S[i]=1;
for ( int j=1; j<=n; j++ ){
if( !T[j] ){
if( Lx[i]+Ly[j]==w[i][j] ){
T[j]=1;
if( line[j]==-1 || find(line[j]) ){
line[j]=i;
return true;
}
}else slack[j]=min(slack[j],Lx[i]+Ly[j]-w[i][j]);
}
}
return false;
}
#define Inf 0x3f3f3f3f

int KM(){
memset(line, -1, sizeof(line));
memset(Ly,0,sizeof(Ly));
for ( int i=1; i<=n; i++ ){
Lx[i]=-Inf;
for ( int j=1; j<=n; j++ )
if( Lx[i]<w[i][j] ) Lx[i]=w[i][j];
}
for ( int i=1; i<=n; i++ ){
for ( int j=1; j<=n; j++ ) slack[j]=Inf;
while( true ){

memset(S,false,sizeof(S));
memset(T,false,sizeof(T));
if( find(i) ) break;
int d=Inf;
for ( int j=1; j<=n; j++ ) if( !T[j] && d>slack[j]) d=slack[j];
for ( int j=1; j<=n; j++ ){
if( S[j] ) Lx[j]-=d;
}
for ( int j=1; j<=n; j++ ){
if( T[j] ) Ly[j]+=d;
else slack[j]-=d;
}
}
}
for ( int i=1; i<=n; i++ ) printf("%d ", Lx[i] );
printf("\n");
for ( int i=1; i<=n; i++ ) printf("%d ", Ly[i] );
int ans=0;
for ( int i=1; i<=n; i++ )
ans+=Lx[i]+Ly[i];
return ans;
}
int main(){
while( ~scanf("%d", &n ) ){
for ( int i=1; i<=n; i++ )
for ( int j=1; j<=n; j++ )
scanf("%d", &w[i][j] );
printf("\n%d\n", KM() );
}
}