912. Random Pick With Weight¶

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912. Random Pick with Weight

Medium

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.

Solution¶

class Solution {
    private int len;
    private double[] probabilities;
    private Random random;
    public Solution(int[] w) {
        this.len = w.length;
        CustomRandom(w);
    }
    public int pickIndex() {
        double rand = random.nextDouble(); 
        int low = 0, high = probabilities.length - 1;
        while (low < high) {
            int mid = low + (high - low) / 2;
            if (rand > probabilities[mid]) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    private void CustomRandom(int[] w) {
        probabilities = new double[w.length];
        random = new Random();
        int totalSum = 0;
        for (int weight : w) totalSum += weight;
        probabilities[0] = (double) w[0] / totalSum;
        for (int i = 1; i < w.length; i++) probabilities[i] = probabilities[i - 1] + (double) w[i] / totalSum;
    }
}
/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(w);
 * int param_1 = obj.pickIndex();
 */

Complexity Analysis¶

• Time Complexity: O(?)
• Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here