As a smart boy, you notice that to win the award, you must buy much more snacks than it seems to be. To convince your friends not to waste money any more, you should find the expected number of snacks one should buy to collect a full suit of cards.
Note there is at most one card in a bag of snacks. And it is possible that there is nothing in the bag.
You will get accepted if the difference between your answer and the standard answer is no more that 10^-4.
1 0.1 2 0.1 0.4
10.000 10.500
题目大意:
还记得小时候吃的干脆面吗,干脆面包里面有一个卡片,我们收集一套卡片需要吃好多的干脆面,现在一套卡片有
解题思路:
因为卡片出现的概率不一样,所以没有办法直接求,那么观察数据范围
其中
解释一下:假设
初始化
代码:
#include <iostream>
#include <string.h>
#include <string>
#include <algorithm>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <map>
using namespace std;
typedef long long LL;
const int MAXN = 1048576+5;
const double PI = acos(-1);
const double eps = 1e-8;
const LL MOD = 1e9+7;
double dp[MAXN], p[22];
int main(){
//freopen("C:/Users/yaonie/Desktop/in.txt", "r", stdin);
//freopen("C:/Users/yaonie/Desktop/out.txt", "w", stdout);
int n;
while(~scanf("%d", &n)){
p[0] = 0;
double t = 1;//包里表示没有卡的概率
for(int i=0; i<n; i++) scanf("%lf",&p[i]), t -= p[i];
int all = (1<<n);
dp[all-1] = 0;
for(int i=all-2; i>=0; i--){
double t1 = 0, t2 = 0;
for(int j=0; j<n; j++){
if(i&(1<<j)) t2 += p[j];
else t1 += p[j]*dp[i|(1<<j)];
}
dp[i] = (t1+1)/(1-t2-t);
}
printf("%.5f\n",dp[0]);
}
return 0;
}