Question

Use the operations push, pop, stacktop, and empty to write pseudo-code operations that do each of the following:

1. set i to the second element from the top of the stack; leaving the stack without its top two elements.
2. set i to the second element from the top of the stack; leaving the stack unchanged.
3. Given an integer n, set i to the nth element from the top of the stack; leaving stack without its top n elements.
4. Given an integer n, set i to the nth element from the top of the stack; leaving stack unchanged.
5. Set i to the bottom element of the stack; leaving the stack empty.
6. Set i to the bottom element of the stack; leaving the stack unchanged (Hint: use another, auxiliary stack)
7. Set i to third element from the bottom of the stack.

Answer 1

This answer provides pseudo-code operations using push, pop, stacktop, and empty to perform various operations on a stack.

Step-by-step explanation:

1. To set i to the second element from the top of the stack and remove the top two elements, you can use the pop operation twice and then use the stacktop operation to get the value of i.

2. To set i to the second element from the top of the stack without changing the stack, you can use the stacktop and push operations to temporarily store the top element, then remove and restore the top element of the stack.

3. To set i to the nth element from the top of the stack and remove the top n elements, you can use a loop to perform the pop operation n times and then use the stacktop operation to get the value of i.

4. To set i to the nth element from the top of the stack without changing the stack, you can use a loop to perform the stacktop and push operations n times to temporarily store the top elements, then remove and restore the top elements of the stack.

5. To set i to the bottom element of the stack and empty the stack, you can use a loop with the pop operation until the stack becomes empty.

6. To set i to the bottom element of the stack without changing the stack, you can use an auxiliary stack to store the elements of the original stack and perform the pop operation on the original stack until it becomes empty.

7. To set i to the third element from the bottom of the stack, you can use an auxiliary stack to store the elements of the original stack, perform the pop operation on the original stack twice, and then use the stacktop operation to get the value of i.