## 1230. Toss Strange Coins

You have some coins. The `i`

-th coin has a probability `prob[i]`

of facing heads when tossed.

Return the probability that the number of coins facing heads equals `target`

if you toss every coin exactly once.

**Example 1:**

Input:prob = [0.4], target = 1Output:0.40000

**Example 2:**

Input:prob = [0.5,0.5,0.5,0.5,0.5], target = 0Output:0.03125

**Constraints:**

`1 <= prob.length <= 1000`

`0 <= prob[i] <= 1`

`0 <= target`

`<= prob.length`

- Answers will be accepted as correct if they are within
`10^-5`

of the correct answer.

## Rust Solution

```
struct Solution;
impl Solution {
fn probability_of_heads(prob: Vec<f64>, target: i32) -> f64 {
let n = prob.len();
let mut dp = vec![vec![0.0; n + 1]; n + 1];
dp[0][0] = 1.0;
for i in 0..n {
for j in 0..=i {
dp[i + 1][j + 1] += dp[i][j] * prob[i];
dp[i + 1][j] += dp[i][j] * (1.0 - prob[i]);
}
}
dp[n][target as usize]
}
}
#[test]
fn test() {
use assert_approx_eq::assert_approx_eq;
let prob = vec![0.4];
let target = 1;
let res = 0.4;
assert_approx_eq!(Solution::probability_of_heads(prob, target), res);
let prob = vec![0.5, 0.5, 0.5, 0.5, 0.5];
let target = 0;
let res = 0.03125;
assert_approx_eq!(Solution::probability_of_heads(prob, target), res);
}
```

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