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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.

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.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Use the Java programming langauge if needed

**Implementing a Queue using Two Stacks** To implement a queue using two stacks, you can follow these steps: 1. **Initialize Two Stacks:** - Stack1 (inputStack): Used for enqueue operations. - Stack2 (outputStack): Used for dequeue operations. 2. **Enqueue Operation:** - Push the new element onto inputStack. 3. **Dequeue Operation:** - If outputStack is empty, transfer all elements from inputStack to outputStack by popping each item from inputStack and pushing it onto outputStack. - Pop the element from outputStack. This is the dequeued element. **Running Time Analysis:** - **Enqueue Operation:** - Time Complexity: O(1) - Explanation: Each enqueue operation involves a single push operation on inputStack. - **Dequeue Operation:** - Average Time Complexity: O(1) - Worst-Case Time Complexity: O(n) - Explanation: In the worst case, all elements are transferred from inputStack to outputStack, which takes O(n). However, when averaged over a series of enqueue and dequeue operations, each element is moved at most twice, leading to an amortized O(1) complexity. This approach efficiently uses the LIFO (Last-In-First-Out) nature of stacks to simulate FIFO (First-In-First-Out) queue behavior.
Transcribed Image Text:**Implementing a Queue using Two Stacks** To implement a queue using two stacks, you can follow these steps: 1. **Initialize Two Stacks:** - Stack1 (inputStack): Used for enqueue operations. - Stack2 (outputStack): Used for dequeue operations. 2. **Enqueue Operation:** - Push the new element onto inputStack. 3. **Dequeue Operation:** - If outputStack is empty, transfer all elements from inputStack to outputStack by popping each item from inputStack and pushing it onto outputStack. - Pop the element from outputStack. This is the dequeued element. **Running Time Analysis:** - **Enqueue Operation:** - Time Complexity: O(1) - Explanation: Each enqueue operation involves a single push operation on inputStack. - **Dequeue Operation:** - Average Time Complexity: O(1) - Worst-Case Time Complexity: O(n) - Explanation: In the worst case, all elements are transferred from inputStack to outputStack, which takes O(n). However, when averaged over a series of enqueue and dequeue operations, each element is moved at most twice, leading to an amortized O(1) complexity. This approach efficiently uses the LIFO (Last-In-First-Out) nature of stacks to simulate FIFO (First-In-First-Out) queue behavior.
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