Apply Operations to an Array

Apply Operations to an Array

What is this problem about?

The "Apply Operations to an Array interview question" is a two-step array manipulation problem.

1. Modify: Traverse the array. If two adjacent elements are equal, double the first one and set the second one to zero.
2. Shift: After all modifications, move all zeros to the end of the array while maintaining the relative order of the non-zero elements.

Why is this asked in interviews?

Meta and Google use the "Apply Operations to an Array coding problem" as an introductory question to test basic array traversal and the "Two Pointers interview pattern." It evaluates whether a candidate can perform "in-place" modifications efficiently without creating unnecessary copies of the data.

Algorithmic pattern used

This problem follows the Simulation and Two Pointers (Partitioning) pattern.

• Pass 1: A simple linear loop from $0$ to $n-2$ to handle the doubling and zeroing logic.
• Pass 2: Use two pointers (let's call them write_index and current_index). Iterate through the array; whenever you find a non-zero number at current_index, move it to write_index and increment write_index. After the loop, fill the remaining positions from write_index to $n-1$ with zeros.

Example explanation

Input: [1, 2, 2, 1, 1, 0]

1. Pass 1 (Operations):
   • index 1 & 2 are both 2: [1, 4, 0, 1, 1, 0]
   • index 3 & 4 are both 1: [1, 4, 0, 2, 0, 0]
2. Pass 2 (Shift Zeros):
   • Collect non-zeros: 1, 4, 2.
   • Fill rest with 0: [1, 4, 2, 0, 0, 0] Result: [1, 4, 2, 0, 0, 0]

Common mistakes candidates make

• Modifying while shifting: Trying to do both steps in a single pass, which often leads to incorrect doubling (e.g., doubling a number that was already doubled).
• Losing Order: Using a sorting algorithm to move zeros, which ruins the "relative order" requirement.
• Extra Space: Creating a new array to store the result when the problem can be solved in $O(1)$ extra space.

Interview preparation tip

Master the "Move Zeros to End" pattern. It is a sub-problem in many coding challenges. It's essentially a variation of the Dutch National Flag problem or a simple partition.