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.

Note:

1. 1 <= w.length <= 10000
2. 1 <= w[i] <= 10^5
3. pickIndex will be called at most 10000 times.

Example 1:

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

Example 2:

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

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution's constructor has one argument, the array w. pickIndex has no arguments. Arguments are always wrapped with a list, even if there aren't any.

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;
        int idx = random.nextInt(wSums[len-1]) + 1;
        int left = 0, right = len - 1;
        // search position 
        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;
        }
        return left;
    }
}

https://leetcode.com/problems/random-pick-with-weight/discuss/154044/Java-accumulated-freq-sum-and-binary-search