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)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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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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