Pick Index - Implementation

Here's the complete solution:

class Solution
    nums := stored array

    function __init__(nums)
        this.nums := nums

    function pick(target)
        result := -1
        count := 0
        for i from 0 to length of nums - 1
            if nums[i] = target then
                count := count + 1
                // Replace with probability 1/count
                if random() < 1/count then
                    result := i
        return result

Time: $O(n)$ per pick (single scan), Space: $O(1)$ additional space (just storing the array). The reservoir sampling ensures each matching index has equal selection probability.