Design a Stack With Increment Operation

Design a Stack With Increment Operation

1. What is this problem about?

The Design a Stack With Increment Operation interview question asks you to implement a custom stack with a twist. Besides standard push and pop, you need an increment(k, val) function that adds val to the bottom k elements of the stack. This Design a Stack With Increment Operation coding problem is interesting because a naive increment takes $O(k)$ time, but it can be optimized to $O(1)$.

2. Why is this asked in interviews?

Companies like Microsoft and Google use this to see if you can find Lazy Propagation optimizations. It evaluates your ability to defer expensive operations (like updating multiple elements) until they are absolutely necessary. It's a great test of whether you can optimize a "Simulation" into an efficient algorithmic pattern.

3. Algorithmic pattern used

This problem uses a Stack with an auxiliary Increment Array.

• stack[]: Standard array to store the elements.
• inc[]: An array where inc[i] stores the increment value to be applied to all elements from index 0 to i.
• push: Standard $O(1)$ push.
• increment(k, val): Instead of looping, just update inc[min(k, current_size) - 1] += val.
• pop:
  1. The actual value is stack[top] + inc[top].
  2. Propagate the increment down: inc[top-1] += inc[top].
  3. Reset inc[top] = 0 and return the value.

4. Example explanation

1. push(1), push(2), push(3). Stack: [1, 2, 3], Inc: [0, 0, 0].
2. increment(2, 100): Add 100 to index 1. Inc: [0, 100, 0].
3. pop(): Return 3 + 0 = 3. Move inc[2] to inc[1] (it was 0). Stack: [1, 2], Inc: [0, 100].
4. pop(): Return 2 + 100 = 102. Move inc[1] to inc[0]. Stack: [1], Inc: [100].
5. pop(): Return 1 + 100 = 101.

5. Common mistakes candidates make

• Naive Implementation: Using a loop for the increment, which makes it $O(N)$ instead of $O(1)$.
• Off-by-one: Forgetting that k might be larger than the current stack size.
• Incorrect Propagation: Failing to carry the increment value down to the next element during a pop, causing subsequent pops to lose the increment.

6. Interview preparation tip

"Lazy update" is a powerful concept used in Segment Trees and specialized data structures. If you can suggest an $O(1)$ way to perform a range update in a stack problem, you demonstrate very high-level algorithmic thinking.