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 {
public:
    Solution(vector<int>& w) {
        srand(time(NULL));
        accu_w = w;
        for (int i = 1; i < accu_w.size(); ++i) {
            accu_w[i] += accu_w[i - 1];
        }
    }
    
    int pickIndex() {
        int random_idx = rand() % accu_w.back();
        int left = 0, right = accu_w.size();
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (accu_w[mid] <= random_idx) left = mid + 1;
            else right = mid;
        }
        return left;
    }
private:
    vector<int> accu_w;
};