528. Random Pick with Weight

Given an array w of positive integers, where w[i] describes the weight of index i, write a function pickIndex which randomly picks an index in proportion to its weight.

class Solution {
    Random random;
    int[] wSums;

    public Solution(int[] w) {
        this.random = new Random();
        for (int i = 1; i < w.length; ++i) {
            w[i] += w[i - 1];
        }
        this.wSums = w;
    }

    public int pickIndex() {
        int len = wSums.length;
// if w is 2,3, then there are 5 slots. If we randomly select a value between 1 and 5. If the value is less than or equal to 2, then, it belong to the first item, otherwise, it belongs to the second item.
        int idx = random.nextInt(wSums[len - 1]) + 1;
        int left = 0, right = len - 1;
        // in essence, we need to find out the min value which is greater than or equal to the target.
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (wSums[mid] == idx) {
                return mid;
            } else if (wSums[mid] < idx) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        return left;
    }
}