Using the Stack ADT to Return Every Third Element

How can we return every third element from a stack?

How do we apply the steps provided to the example stack of 1 2 3 4 5 6 7 8 9?

Answer:

To return every third element from a stack, we can follow the steps outlined:

1. Create a temporary stack to store elements that will be skipped.
2. Initialize a count variable to track the number of elements processed.
3. Iterate through the original stack, popping elements and checking the count.
4. Create a result stack to store elements in the desired order.
5. Iterate through the temporary stack to retrieve elements.
6. Output the elements from the result stack in the desired order.

Using the steps provided, let's apply them to the given example stack of 1 2 3 4 5 6 7 8 9:

1. Create a temporary stack and initialize count to 0.
2. Iterate through the original stack:
• Pop 9, increment count to 1.
• Pop 8, increment count to 2.
• Pop 7, increment count to 3. Since count is a multiple of three, push 7 to the temporary stack.
• Pop 6, increment count to 4.
• Pop 5, increment count to 5.
• Pop 4, increment count to 6. Since count is a multiple of three, push 4 to the temporary stack.
• Pop 3, increment count to 7.
• Pop 2, increment count to 8.
• Pop 1, increment count to 9. Since count is a multiple of three, push 1 to the temporary stack.
3. Create a result stack.
4. Iterate through the temporary stack:
• Pop 1 from temporary stack, push to result stack.
• Pop 4 from temporary stack, push to result stack.
• Pop 7 from temporary stack, push to result stack.
5. Iterate through the result stack and output the elements in the desired order: 7, 4, 1.

This process allows us to efficiently return every third element from the stack by using auxiliary data structures and counting elements.