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);

Now each number should have the same probability to be picked up, which is 1/n. The easiest solution is to keep picking a number in the array until we get one that equals target.

public class Solution {
    int[] numbers;
    Random random;
    public Solution(int[] nums) {
        this.numbers = Arrays.copyOf(nums, nums.length);
        random = new Random();
    }
    
    public int pick(int target) {
        int index = random.nextInt(numbers.length);
        while (numbers[index] != target) {
            index = random.nextInt(numbers.length);
        }
        return index;
    }
}