Random Pick with Weight

 

You are given a 0-indexed array of positive integers w where w[i] describes the weight of the ith index.

You need to implement the function pickIndex(), which randomly picks an index in the range [0, w.length - 1] (inclusive) and returns it. The probability of picking an index i is w[i] / sum(w).

• For example, if w = [1, 3], the probability of picking index 0 is 1 / (1 + 3) = 0.25 (i.e., 25%), and the probability of picking index 1 is 3 / (1 + 3) = 0.75 (i.e., 75%).

 

Example 1:

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

Explanation
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. The only option is to return 0 since there is only one element in w.

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 is returning the second element (index = 1) that has a probability of 3/4.
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 1
solution.pickIndex(); // return 0. It is returning the first element (index = 0) that has a probability of 1/4.

Since this is a randomization problem, multiple answers are allowed.
All of 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 <= 104
• 1 <= w[i] <= 105
• pickIndex will be called at most 104 times.

 

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

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