loj2003 「SDOI2017」新生舞会

分数规划+KM 算法

这个KM不好，看算法竞赛进阶指南的

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
int n, aa[105][105], bb[105][105], mat[105];
double a[105][105], exu[105], exv[105], sla[105];
const double eps=1e-8;
bool viu[105], viv[105];
bool dfs(int x){
	viu[x] = true;
	for(int i=1; i<=n; i++){
		if(viv[i])  continue;
		double gap=exu[x]+exv[i]-a[x][i];
		if(fabs(gap)<eps){
			viv[i] = true;
			if(!mat[i] || dfs(mat[i])){
				mat[i] = x;
				return true;
			}
		}
		else    sla[i] = min(sla[i], gap);
	}
	return false;
}
bool chk(double lim){
	memset(exv, 0, sizeof(exv));
	memset(mat, 0, sizeof(mat));
	for(int i=1; i<=n; i++){
		exu[i] = -1e99;
		for(int j=1; j<=n; j++){
			a[i][j] = aa[i][j] - lim * bb[i][j];
			exu[i] = max(exu[i], a[i][j]);
		}
	}
	for(int i=1; i<=n; i++){
		memset(sla, 127, sizeof(sla));
		while(true){
			memset(viu, 0, sizeof(viu));
			memset(viv, 0, sizeof(viv));
			if(dfs(i))  break;
			double tmp=1e99;
			for(int j=1; j<=n; j++)
				if(!viv[j])
					tmp = min(tmp, sla[j]);
			for(int j=1; j<=n; j++){
				if(viu[j])  exu[j] -= tmp;
				if(viv[j])  exv[j] += tmp;
				else    sla[j] -= tmp;
			}
		}
	}
	double tmp=0.0;
	for(int i=1; i<=n; i++)
		tmp += a[mat[i]][i];
	return tmp>-eps;
}
int main(){
	cin>>n;
	for(int i=1; i<=n; i++)
		for(int j=1; j<=n; j++)
			scanf("%d", &aa[i][j]);
	for(int i=1; i<=n; i++)
		for(int j=1; j<=n; j++)
			scanf("%d", &bb[i][j]);
	double l=0.0, r=1000000.0, mid;
	while(fabs(r-l)>eps){
		mid = (l + r) / 2.0;
		if(chk(mid))	l = mid;
		else	r = mid;
	}
	printf("%.6f\n", mid);
	return 0;
}