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2. Show (depict an algorithm or describe in words) how to implement a queue using two stacks. Analyze the running time of the basic queue operations.

2. Show (depict an algorithm or describe in words) how to implement a queue using two stacks. Analyze the running time of the basic queue operations.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Hello please assist with the following. Thank you so much! :)

**Queue Implementation Using Two Stacks** To implement a queue using two stacks, we can follow these steps: 1. **Initialize Two Stacks:** - Let’s call them `stack1` and `stack2`. 2. **Enqueue Operation:** - Push the element onto `stack1`. This maintains the order of insertion as elements are added. 3. **Dequeue Operation:** - If `stack2` is empty, pop all elements from `stack1` and push them onto `stack2`. This reverses the order, making the oldest element accessible. - Pop the top element from `stack2`. This effectively dequeues the element that was first inserted. 4. **Time Complexity:** - **Enqueue:** O(1) - Inserting onto `stack1` is a constant time operation. - **Dequeue:** Amortized O(1) - While transferring elements from `stack1` to `stack2` takes O(n), it happens only once for every n dequeue operations, leading to an average time. By leveraging two stacks, we can efficiently simulate a queue with all the necessary operations. This method ensures that enqueue operations remain constant time while maintaining acceptable efficiency during dequeue operations through amortized complexity.
Transcribed Image Text:**Queue Implementation Using Two Stacks** To implement a queue using two stacks, we can follow these steps: 1. **Initialize Two Stacks:** - Let’s call them `stack1` and `stack2`. 2. **Enqueue Operation:** - Push the element onto `stack1`. This maintains the order of insertion as elements are added. 3. **Dequeue Operation:** - If `stack2` is empty, pop all elements from `stack1` and push them onto `stack2`. This reverses the order, making the oldest element accessible. - Pop the top element from `stack2`. This effectively dequeues the element that was first inserted. 4. **Time Complexity:** - **Enqueue:** O(1) - Inserting onto `stack1` is a constant time operation. - **Dequeue:** Amortized O(1) - While transferring elements from `stack1` to `stack2` takes O(n), it happens only once for every n dequeue operations, leading to an average time. By leveraging two stacks, we can efficiently simulate a queue with all the necessary operations. This method ensures that enqueue operations remain constant time while maintaining acceptable efficiency during dequeue operations through amortized complexity.
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