RandomPickWithWeight.java

package Leetcode;

/**
 * @author kalpak
 *
 * You are 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 the index 0 is 1 / (1 + 3) = 0.25 (i.e 25%)
 * while the probability of picking the 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.
 *
 *
 * Constraints:
 *
 * 1 <= w.length <= 10000
 * 1 <= w[i] <= 10^5
 * pickIndex will be called at most 10000 times.
 */
public class RandomPickWithWeight {
    int[] cumulativeWeights;
    public RandomPickWithWeight(int[] w) {
        cumulativeWeights = new int[w.length];

        // build up the array
        cumulativeWeights[0] = w[0];
        for(int i = 1; i < w.length; i++)
            cumulativeWeights[i] = cumulativeWeights[i-1] + w[i];
    }

    public int pickIndexLinearSearch() {
        int target = (int)(cumulativeWeights[cumulativeWeights.length - 1] * Math.random());

        for(int i = 0; i < cumulativeWeights.length; i++) {
            if(target < cumulativeWeights[i])
                return i;
        }
        return -1;
    }

    public int pickIndex() {
        int target = (int)(cumulativeWeights[cumulativeWeights.length - 1] * Math.random());
        int result = -1;
        int left = 0;
        int right = cumulativeWeights.length - 1;

        while(left <= right) {
            int mid = left + (right - left)/2;

            if (target < cumulativeWeights[mid]) {
                result = mid;            // we got a candidate. But check if we can do better. So go left
                right = mid - 1;
            } else {
                left = mid + 1;
            }
        }
        return result;
    }

    public static void main(String[] args) {
        RandomPickWithWeight obj = new RandomPickWithWeight(new int[]{1, 3});
        System.out.println(obj.pickIndex());
        System.out.println(obj.pickIndex());
        System.out.println(obj.pickIndex());
        System.out.println(obj.pickIndex());
    }
}