The time complexity of both push and pop operations on a stack implemented with an array is O(1).a.FALSEb.TRUE

The correct answer is b. TRUE.

Explanation

1. Understanding Stack Operations: A stack is a data structure that follows the Last In, First Out (LIFO) principle. It means that the last element added to the stack is the first one to be removed. The two primary operations for stacks are push (adding an element) and pop (removing the top element).

2. Array Implementation: When stacks are implemented using arrays, both operations can be performed in constant time. This is because:

   • Push Operation: When you push an element onto the stack, you simply place the new element at the index corresponding to the top of the stack. This action requires a fixed number of steps, regardless of the size of the stack, making its complexity O(1).
   • Pop Operation: When popping an element, you retrieve the element at the top of the stack and adjust the index for the top. This also takes a constant amount of time, which is O(1).

3. No Constraints: It is essential to note that this time complexity holds as long as there is enough space in the array (i.e., the stack's current capacity hasn't been exceeded). If the array needs to be resized, then the push operation can take O(n) time due to copying elements to a new array, but typical implementations handle this efficiently through amortization.

Thus, both push and pop operations on a stack implemented with an array indeed have a time complexity of O(1), making the statement TRUE.