Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Hello please answer the following question. Was really stuck on this one :(  Thank you so much!

**Implementing Two Stacks in a Single Array**

To implement two stacks using a single array `A[1..n]`, you can use a two-pointer approach to ensure that neither stack overflows unless their combined total of elements is `n`. This setup also ensures that the push and pop operations run in O(1) time.

**Approach:**

1. **Initialization:**
   - Use a single array `A[1..n]`.
   - Initialize two pointers: 
     - `top1` starting at the beginning of the array (index 0).
     - `top2` starting at the end of the array (index n-1).

2. **Push Operation:**
   - **Stack 1 (`Push1`):** Add an element to the position `top1` and then increment `top1`.
   - **Stack 2 (`Push2`):** Add an element to the position `top2` and then decrement `top2`.

3. **Pop Operation:**
   - **Stack 1 (`Pop1`):** Decrement `top1` and then return the element at the new `top1` position.
   - **Stack 2 (`Pop2`):** Increment `top2` and then return the element at the new `top2` position.

4. **Overflow Condition:**
   - If `top1` exceeds `top2`, it means the array is full, and no more elements can be pushed into either stack.

**Examples:**

- **Example 1:**
  1. Push an element onto Stack 1 by placing it at `A[top1]` and increment `top1`.
  2. Push an element onto Stack 2 by placing it at `A[top2]` and decrement `top2`.
  3. If `top1` becomes greater than `top2`, both stacks are full.

- **Example 2:**
  - Start: `top1 = 0`, `top2 = n-1`.
  - Sequence: Push elements `1, 2, 3` onto Stack 1 and `10, 9, 8` onto Stack 2.
  - Final: `top1` could be `3`, `top2` could be `n-4` (assuming indices 3 and n-4 do not cross).

This dual stack implementation using an array
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Transcribed Image Text:**Implementing Two Stacks in a Single Array** To implement two stacks using a single array `A[1..n]`, you can use a two-pointer approach to ensure that neither stack overflows unless their combined total of elements is `n`. This setup also ensures that the push and pop operations run in O(1) time. **Approach:** 1. **Initialization:** - Use a single array `A[1..n]`. - Initialize two pointers: - `top1` starting at the beginning of the array (index 0). - `top2` starting at the end of the array (index n-1). 2. **Push Operation:** - **Stack 1 (`Push1`):** Add an element to the position `top1` and then increment `top1`. - **Stack 2 (`Push2`):** Add an element to the position `top2` and then decrement `top2`. 3. **Pop Operation:** - **Stack 1 (`Pop1`):** Decrement `top1` and then return the element at the new `top1` position. - **Stack 2 (`Pop2`):** Increment `top2` and then return the element at the new `top2` position. 4. **Overflow Condition:** - If `top1` exceeds `top2`, it means the array is full, and no more elements can be pushed into either stack. **Examples:** - **Example 1:** 1. Push an element onto Stack 1 by placing it at `A[top1]` and increment `top1`. 2. Push an element onto Stack 2 by placing it at `A[top2]` and decrement `top2`. 3. If `top1` becomes greater than `top2`, both stacks are full. - **Example 2:** - Start: `top1 = 0`, `top2 = n-1`. - Sequence: Push elements `1, 2, 3` onto Stack 1 and `10, 9, 8` onto Stack 2. - Final: `top1` could be `3`, `top2` could be `n-4` (assuming indices 3 and n-4 do not cross). This dual stack implementation using an array
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