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LIFO Stack With Overflow and Underflow

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Problem

A Plexus platform component needs a predictable in-memory LIFO buffer for processing operational events. Implement a fixed-capacity stack that supports adding and removing integer elements while explicitly detecting overflow and underflow.

Formal Specification

Write process_stack(capacity, operations), where capacity is a positive integer and operations is a list of commands. Each command is either ['push', value], where value is an integer, or ['pop'].

Use a preallocated array and an integer stack pointer. Do not resize the array, use Python's built-in append, or call list.pop.

Return a list containing one result for each operation:

  1. A successful push returns the string "ok".
  2. A push against a full stack returns "overflow" and does not change the stack.
  3. A successful pop returns the removed integer.
  4. A pop against an empty stack returns "underflow" and does not change the stack.

All successful operations must run in O(1) time.

Constraints

  • 1 <= capacity <= 10^5
  • 0 <= operations.length <= 10^5
  • Every pushed value is an integer in [-10^9, 10^9]
  • Each command is validly formatted as ['push', value] or ['pop']
  • The implementation must use O(capacity) storage and O(1) work per operation

Function Signature

def process_stack(capacity, operations):
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