【模板】线性规划 单纯形算法

原题为[UOJ #179]

Code

#include <bits/stdc++.h>
#define fo(i,a,b) for(int i=a;i<=b;++i)
#define fod(i,a,b) for(int i=a;i>=b;--i)
#define N 50
using namespace std;
const double eps=1e-9;
double a[N][N],ans[N];
int n,m,t,id[N],d[N];
int rd(int k)
{
	return rand()%k;
}
void pivot(int l,int e)
{
	swap(id[l+n],id[e]);
	double t=a[l][e];a[l][e]=1;
	fo(i,0,n) a[l][i]/=t;
	fo(i,0,m)
	{
		if(i!=l&&abs(a[i][e])>eps)
		{
			double t=a[i][e];a[i][e]=0;
			fo(j,0,n) a[i][j]-=t*a[l][j];
		}
	}
}
bool prp()
{
	while(1)
	{
		int l=0,e=0;
		d[0]=0;
		fo(i,1,m) if(a[i][0]<-eps) d[++d[0]]=i;
		if(!d[0]) return 1;
		l=d[rd(d[0])+1],d[0]=0;
		fo(i,1,n) if(a[l][i]<-eps) d[++d[0]]=i;
		if(!d[0]) return 0;
		e=d[rd(d[0])+1];
		pivot(l,e);
	}
}
bool solve()
{
	while(1)
	{
		int l=0,e=0;double mi=1e18;
		fo(i,1,n) 
			if(a[0][i]>eps&&(!e||a[0][i]>a[0][e])) e=i;
		if(!e) return 1;
		fo(i,1,m)
		{
			if(a[i][e]>eps&&a[i][0]/a[i][e]<mi) mi=a[i][0]/a[i][e],l=i;
		}
		if(!l) return 0;
		pivot(l,e);
	}
}
int main()
{
	srand(9982443);
	cin>>n>>m>>t;
	fo(i,1,n)
	{
		int x;
		scanf("%d",&x);
		a[0][i]=x;
	}
	fo(i,1,m)
	{
		int x;
		fo(j,1,n) scanf("%d",&x),a[i][j]=x;
		scanf("%d",&x),a[i][0]=x;
	}
	fo(i,1,n+m) id[i]=i;
	if(!prp()) 
	{
		printf("Infeasible
");
		return 0;
	}
	if(!solve()) 
	{
		printf("Unbounded
");
		return 0;
	}	
	printf("%.10lf
",-a[0][0]);
	if(t==1)
	{
		fo(i,1,m) ans[id[i+n]]=a[i][0];
		fo(i,1,n) printf("%.10lf ",ans[i]);
	}
}