Random Pick with Weight

 Random Pick with Weight

Given an array of positive integers w. where w[i] describes the weight of ith index (0-indexed).

We need to call the function pickIndex() which randomly returns an integer in the range [0, w.length - 1]. pickIndex() should return the integer proportional to its weight in the w array. For example, for w = [1, 3], the probability of picking index 0 is 1 / (1 + 3) = 0.25 (i.e 25%) while the probability of picking index 1 is 3 / (1 + 3) = 0.75 (i.e 75%).

More formally, the probability of picking index i is w[i] / sum(w).

 

Example 1:

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

Explanation
Solution solution = new Solution([1]);
solution.pickIndex(); // return 0. Since there is only one single element on the array the only option is to return the first element.

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

Since this is a randomization problem, multiple answers are allowed so 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.

class Solution {

private:

    vector<int> v;

    int s;

public:

    Solution(vector<int>& w) {

        v.push_back(w[0]);

        for(int i=1;i<w.size();++i)

            v.push_back(w[i]+v.back());

        s=w.size();

    }

    

    int pickIndex() {

        int i=(rand()%v[s-1])+1;

        int l=0,r=s-1;

        while(l<r)

        {

            int mid=(r+l)/2;

            if(v[mid]==i)

                return mid;

            else if(v[mid]<i)

                l=mid+1;

            else

                r=mid;

        }

        return l;

    }

};

/**

 * Your Solution object will be instantiated and called as such:

 * Solution* obj = new Solution(w);

 * int param_1 = obj->pickIndex();

 */