## 528. Random Pick with Weight

You are given an array of positive integers `w` where `w[i]` describes the weight of `i``th` index (0-indexed).

We need to call the function `pickIndex()` which randomly returns an integer in the range `[0, w.length - 1]``pickIndex()` should return the integer proportional to its weight in the `w` array. For example, for `w = [1, 3]`, the probability of picking the index `0` is `1 / (1 + 3) = 0.25` (i.e 25%) while the probability of picking the index `1` is `3 / (1 + 3) = 0.75` (i.e 75%).

More formally, the probability of picking index `i` is `w[i] / sum(w)`.

Example 1:

```Input
["Solution","pickIndex"]
[[[1]],[]]
Output
[null,0]

Explanation
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. Since there is only one single element on the array the only option is to return the first element.
```

Example 2:

```Input
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output
[null,1,1,1,1,0]

Explanation
Solution solution = new Solution([1, 3]);
solution.pickIndex(); // return 1. It's returning the second element (index = 1) that has probability of 3/4.
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 0. It's returning the first element (index = 0) that has probability of 1/4.

Since this is a randomization problem, multiple answers are allowed so the following outputs can be considered correct :
[null,1,1,1,1,0]
[null,1,1,1,1,1]
[null,1,1,1,0,0]
[null,1,1,1,0,1]
[null,1,0,1,0,0]
......
and so on.
```

Constraints:

• `1 <= w.length <= 10000`
• `1 <= w[i] <= 10^5`
• `pickIndex` will be called at most `10000` times.

## Rust Solution

``````use rand::distributions::WeightedIndex;
use rand::prelude::*;

struct Solution {
dist: WeightedIndex<i32>,
}

impl Solution {
fn new(w: Vec<i32>) -> Self {