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]

// Prefix Sum + Binary search

class Solution {
    private:
        vector<int> data;
public:
    Solution(vector<int>& w) {
        data = w;
        for (int i = 1; i < w.size(); i++) {
            data[i] = data[i -1] + w[i];
        }
    }
   
    int pickIndex() {
        int size = data.size();
        int random = rand() % data.back() + 1;
        int st = 0, end = size - 1;
        while (st < end) {
            int mid = st + (end - st) / 2;
            if (data[mid] == random) {
                return mid;
            } else if (data[mid] < random) {
                st = mid + 1;
            } else {
                end = mid;
            }
        }
        return st;
    }
};

/**
 * Your Solution object will be instantiated and called as such:
 * Solution* obj = new Solution(w);
 * int param_1 = obj->pickIndex();
 */