期望分数

金牌导航 期望-4

题目大意

告诉你一个01串中每个位置是1的概率，对于连续的x个1，贡献为$x^3$，问你期望贡献是多少

输入样例

3 
0.5 
0.5 
0.5

输入样例

6.0

数据范围

$1⩽N⩽10^5$

解题思路

把$(x+1{)}^3$拆成$x^3+3x^2+3\times x+1$
然后递推得到各项即可

代码

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define N 100010
using namespace std;
int n;
double x, f[N], a[N], b[N];
int main()
{scanf("%d", &n);for (int i = 1; i <= n; ++i){scanf("%lf", &x);f[i] = f[i - 1] + (3 * a[i - 1] + 3 * b[i - 1] + 1) * x;a[i] = (a[i - 1] + 2 * b[i - 1] + 1) * x;//x^2b[i] = (b[i - 1] + 1) * x;//x}printf("%.1lf", f[n]);return 0;
}