比较简单，每个键分两种情况计算期望。

然而要注意的是，期望是线性运算，期望的平方不是平方的期望 。

```cpp

include

include

include

include

include

include

include

using namespace std;

define scnaf scanf

const int maxn = 100000 + 10;
int n; double a[maxn], dp[maxn], ex[maxn], cnt[maxn];

int main(int argc, char const argv[])
{
scanf("%d", &n);
for(int i = 1; i <= n; ++i) scanf("%lf", a + i);
for(int i = 1; i <= n; ++i) {
ex[i] = a[i] (ex[i - 1] + 2 * cnt[i - 1] + 1);
dp[i] = dp[i - 1] + a[i] * (3 * ex[i - 1] + 3 * cnt[i - 1] + 1);
cnt[i] = a[i] * (cnt[i - 1] + 1);
}
printf("%.1lf\n", dp[n]);

return 0;
}

[BZOJ4318] OSU!

原文：https://www.cnblogs.com/nanjoqin/p/10427502.html