528. Random Pick with Weight

Problem

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 <= 10^4

• 1 <= w[i] <= 10^5

• pickIndex will be called at most 10^4 times.

Solution (Java)

class Solution {
    private int prefix;
    private final Random random;
    private final TreeSet<int[]> treeSet;

    public Solution(int[] w) {
        prefix = 0;
        treeSet = new TreeSet<>(Comparator.comparingInt(a -> a[0]));
        for (int i = 0; i < w.length; i++) {
            prefix += w[i];
            treeSet.add(new int[] {prefix, i});
        }
        random = new Random();
    }

    public int pickIndex() {
        int target = random.nextInt(prefix) + 1;
        return Objects.requireNonNull(treeSet.ceiling(new int[] {target, 1}))[1];
    }
}

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

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).