[COCI2006-2007#1] Bond

状压DP

\(dp[i]\)表示当前选人状态为\(i\)且选择了前\(i.count()\)个物品时最大的概率

#include"cstdio"
#include"cstring"
#include"iostream"
#include"algorithm"
using namespace std;

const int MAXN=20;

int n;
double f[MAXN+1][MAXN+1];
double dp[1<<MAXN];

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i){
		for(int j=1;j<=n;++j){
			scanf("%lf",&f[i][j]);
		}
	}dp[0]=100;
	for(int i=0;i<1<<n;++i){
		int nw=i,ct=0;
		while(nw) nw&=nw-1,++ct;
		for(int j=1;j<=n;++j){
			if(i&(1<<j-1)) continue;
			dp[i|(1<<j-1)]=max(dp[i|(1<<j-1)],dp[i]*f[j][ct+1]/100);
		}
	}printf("%.10lf\n",dp[(1<<n)-1]);
	return 0;
}