Keep Multiplying Found Values by Two

Keep Multiplying Found Values by Two

1. What is this problem about?

The Keep Multiplying Found Values by Two interview question is a simulation task. You are given an array of integers and an initial value original. If original exists in the array, you multiply it by 2 and repeat the search. You continue this process until the value is no longer found in the array. Your goal is to return the final value of original.

2. Why is this asked in interviews?

Companies like Goldman Sachs and Meta use this Multiplying Found Values coding problem as a warm-up. it tests basic knowledge of Hash Table interview patterns and sorting. It evaluations whether you can optimize a repeated search from $O(N^2)$ to $O(N)$.

3. Algorithmic pattern used

This problem can be solved using two patterns:

1. Hash Set ($O(N)$): Put all elements into a Set. While original is in the set, original *= 2. This provides $O(1)$ lookup for each step.
2. Sorting ($O(N \log N)$): Sort the array. Iterate once. If you find original, multiply by 2 and continue the scan from your current position.

4. Example explanation

nums = [1, 2, 5, 8], original = 1

1. 1 is in nums. original = 1 * 2 = 2.
2. 2 is in nums. original = 2 * 2 = 4.
3. 4 is not in nums. Result: 4.

5. Common mistakes candidates make

• Nested Loops: Searching the entire array from scratch every time original changes ($O(N \cdot ext{steps})$).
• Early Termination: Stopping after the first match without checking if the doubled value also exists.
• Set creation: Forgetting that re-creating the set inside a loop is inefficient.

6. Interview preparation tip

For "repeated search" problems, a Hash Set is almost always the most efficient tool. It reduces the cost of "is it there?" to constant time, allowing the overall algorithm to focus on the transitions.