Build an Array With Stack Operations

Build an Array With Stack Operations

What is this problem about?

The "Build an Array With Stack Operations interview question" asks you to simulate the construction of a target array using a standard stack data structure. You are given a target array and an integer n. You have a stream of numbers from 1 to n in increasing order. For each number in the stream, you can either "Push" it onto the stack or "Push" then immediately "Pop" it. The goal is to return the sequence of operations required to make the stack match the target array.

Why is this asked in interviews?

Google and other top-tier companies use the "Build an Array With Stack Operations coding problem" to evaluate a candidate's ability to implement simple simulations and understand fundamental data structure operations. It tests your logic in handling stream-based data and your ability to map a desired outcome (the target array) to a set of restricted actions (stack operations). It’s a great test of "Stack interview pattern" and "Simulation" skills.

Algorithmic pattern used

This problem follows the Simulation and Greedy patterns.

1. Iterate: You iterate through the numbers from 1 to n.
2. Comparison: You compare the current number from the stream with the current element needed in the target array.
3. Action:
   • If the numbers match, you only need a "Push" operation and move to the next element in the target.
   • If the stream number is smaller than the target element, it means this number is NOT in the target array. You must "Push" then "Pop" it to skip it.
4. Termination: You stop as soon as you have successfully built the entire target array.

Example explanation

Target: [1, 3], $n = 3$

1. Stream number 1: Matches target[0]. Operation: "Push".
2. Stream number 2: Does not match target[1] (which is 3). Operation: "Push", "Pop".
3. Stream number 3: Matches target[1]. Operation: "Push". Final Operations: ["Push", "Push", "Pop", "Push"].

Common mistakes candidates make

• Over-processing: Continuing to iterate up to $n$ even after the target array is fully built.
• Incorrect operation order: Forgetting that skipping a number requires two operations: "Push" followed by "Pop".
• Index out of bounds: Not correctly tracking the pointer for the target array.

Interview preparation tip

When solving simulation problems, dry-run your logic with a small example on paper. Always look for an early exit condition to optimize your "Simulation interview pattern" solutions.