--- title: "Circular queue vs linear queue" subject: "Data Structure and Algorithm" chapter: 2 key: "semester_4/data_structure_and_algorithm:circular-vs-linear-queue" source: https://www.bctengineer.com/q/semester_4/data_structure_and_algorithm/circular-vs-linear-queue site: BCT Engineering --- # Circular queue vs linear queue Data Structure and Algorithm · Chapter 2: The Stack and Queue - Asked in: 2073 Bhadra, 5 marks - Video: [Linear and circular queue difference - Data structures lecture series](https://www.youtube.com/watch?v=-VzzjEBhbEk) — Eezytutorials CSE & Kids channel - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/data_structure_and_algorithm/circular-vs-linear-queue - Whole chapter: https://www.bctengineer.com/md/semester_4/data_structure_and_algorithm/chapter-2 ## Question Explain how a circular queue differs from a linear queue with suitable example. ## Short answer Linear queue does not reuse freed front cells; circular queue wraps rear modulo N. Example: N=5, insert 10,20,30,40,50, delete two, insert 60 — linear overflows despite free space; circular succeeds, rear wraps to 0. ## Answer A **linear queue** uses an array in a straight line: `rear` only moves forward and positions before `front` are never reused. A **circular queue** joins the last position to the first, so indices wrap around with `(index + 1) % N`. | Linear queue | Circular queue | |---|---| | `rear` increases up to N − 1 and stops | `rear` wraps to 0 using `(rear + 1) % N` | | Freed cells at the front are not reused | Freed cells are reused | | Full test: `rear == N - 1` | Full test: `(rear + 1) % N == front` | | Empty test: `front > rear` | Empty test: `front == -1` | | Can report overflow even when cells are free | Overflows only when all cells are used | | Simple to implement | Slightly more complex | | Poor memory use | Better memory use | #### Example (N = 5): insert 10, 20, 30, 40, 50, delete two, insert 60 **Linear queue** | Operation | Array contents (index 0 → N-1) | front | rear | |---|---|---|---| | enqueue(10) | 10 _ _ _ _ | 0 | 0 | | enqueue(20) | 10 20 _ _ _ | 0 | 1 | | enqueue(30) | 10 20 30 _ _ | 0 | 2 | | enqueue(40) | 10 20 30 40 _ | 0 | 3 | | enqueue(50) | 10 20 30 40 50 | 0 | 4 | | dequeue() returns 10 | _ 20 30 40 50 | 1 | 4 | | dequeue() returns 20 | _ _ 30 40 50 | 2 | 4 | | enqueue(60): rear = 4 → Queue overflow | _ _ 30 40 50 | 2 | 4 | Two cells are free, yet `enqueue(60)` fails. **Circular queue** | Operation | Array contents (index 0 → N-1) | front | rear | |---|---|---|---| | enqueue(10) | 10 _ _ _ _ | 0 | 0 | | enqueue(20) | 10 20 _ _ _ | 0 | 1 | | enqueue(30) | 10 20 30 _ _ | 0 | 2 | | enqueue(40) | 10 20 30 40 _ | 0 | 3 | | enqueue(50) | 10 20 30 40 50 | 0 | 4 | | dequeue() returns 10 | _ 20 30 40 50 | 1 | 4 | | dequeue() returns 20 | _ _ 30 40 50 | 2 | 4 | | enqueue(60) | 60 _ 30 40 50 | 2 | 0 | Here `rear` wraps to index 0 and 60 is stored. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The full test for a circular queue is: A. (rear + 1) % N == front B. rear == N - 1 C. front > rear D. front == -1 Answer: A. A linear queue uses rear == N - 1. (Key point: Full test) 2. Why can a linear queue report overflow with free cells? A. Cells before front are never reused as rear stops at N - 1 B. It wraps rear to 0 C. It uses linked nodes D. front is always 0 Answer: A. A circular queue wraps indices and reuses them. (Key point: Reuse of cells) 3. N=5: insert 10-50, delete two, then enqueue(60). Linear queue gives: A. 60 stored at index 0 B. 60 stored at index 2 C. Queue overflow D. front reset to 0 Answer: C. rear = 4 = N - 1, though two cells are free. (Key point: Example) 4. Which empty test belongs to the circular queue? A. front > rear B. rear == 0 C. (rear+1)%N == front D. front == -1 Answer: D. Linear queue uses front > rear. 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