398. Random Pick Index

Given an array of integers with possible duplicates, randomly output the index of a given target number. You can assume that the given target number must exist in the array.

Note:
The array size can be very large. Solution that uses too much extra space will not pass the judge.

Example:

int[] nums = new int[] {1,2,3,3,3};
Solution solution = new Solution(nums);

// pick(3) should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
solution.pick(3);

// pick(1) should return 0. Since in the array only nums[0] is equal to 1.
solution.pick(1);

Reservoir Sampling

public class Solution {
    int[] nums;
    Random r;

    public Solution(int[] nums) {
        this.nums = nums;
        r = new Random();
    }
    
    public int pick(int target) {
        int idx = 0;
        int count = 0;
        for (int i = 0; i < nums.length; i++) {
            if (nums[i] != target) continue;
// for the nth target, the prob of returning is 1/n
// for the (n-1)th target, the prob of returning is (n-1)/n * 1/(n-1) = 1/n
            if (r.nextInt(++count) == 0) {
                idx = i; 
            }
        }
        
        return idx;
        
    }
}