528. 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%).
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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.

Solution

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class Solution {
    Random random = new Random();
    int[] prefix;
    int sum = 0;
    public Solution(int[] w) {
        this.prefix = new int[w.length];
        for (int i = 0; i < prefix.length; i++) {
            sum += w[i];
            prefix[i] = sum;
        }
    }
    
    public int pickIndex() {
        double val = Math.random() * prefix[prefix.length - 1];
        int lo = 0;
        int hi = prefix.length;

        while (lo < hi) { 
            int mid = lo + (hi - lo) / 2;
            if (val > prefix[mid]) {
                lo = mid + 1;
            } else {
                hi = mid;
            }
        }
        return lo;
    }
}

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

Solution 2021-11-18 Double Array

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class Solution {
    double[] prob;
    public Solution(int[] w) {
        int sum = 0;
        for (int i = 0; i < w.length; i++) {
            sum += w[i];
        }
        int preSum = 0;
        prob = new double[w.length];
        for (int i = 0; i < w.length; i++) {
             preSum += w[i];
             prob[i] += (double) preSum / sum;
        }
    }
    public int pickIndex() {
        double val = Math.random();
        int index = Arrays.binarySearch(prob, val);
        if (index < 0) {
            index = -(index + 1);
        }
        return index;
    }
}

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

Solution 2022-01-24, Integer Array

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class Solution {
    Random RANDOM = new Random();
    int[] p;
    public Solution(int[] w) {
        p = new int[w.length];
        int sum = 0;
        for (int i = 0; i < w.length; i++) {
            sum += w[i];
            p[i] = sum;
        }
        System.out.println(Arrays.toString(p));
    }
    
    public int pickIndex() {
        int value = RANDOM.nextInt(p[p.length - 1]) + 1;
        int index = Arrays.binarySearch(p, value);
        return index >= 0 ? index : -(index + 1);
    }
}

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