--- title: "Merge sort on 47, 27, 56, 23, ..." subject: "Data Structure and Algorithm" chapter: 7 key: "semester_4/data_structure_and_algorithm:merge-sort-trace-47-27" source: https://www.bctengineer.com/q/semester_4/data_structure_and_algorithm/merge-sort-trace-47-27 site: BCT Engineering --- # Merge sort on 47, 27, 56, 23, ... Data Structure and Algorithm · Chapter 7: Sorting - Asked in: 2068 Bhadra, 3 marks - Video: [L-3.3: How Merge Sort Works?? Full explanation with example](https://www.youtube.com/watch?v=tn9hxD8gx2M) — Gate Smashers - 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/merge-sort-trace-47-27 - Whole chapter: https://www.bctengineer.com/md/semester_4/data_structure_and_algorithm/chapter-7 ## Question Trace the sorting steps in merge sort for the data: 47, 27, 56, 23, 3, 9, 94, 11. ## Short answer Merge sort recursively divides list into halves then merges sorted halves. The final sorted list is 3, 9, 11, 23, 27, 47, 56, 94. ## Answer Merge sort splits the list in halves down to single elements and then merges sorted halves. #### Dividing ```text 47 27 56 23 3 9 94 11 47 27 56 23 | 3 9 94 11 47 27 | 56 23 | 3 9 | 94 11 47 | 27 | 56 | 23 | 3 | 9 | 94 | 11 ``` #### Merging | Step | Merge | Result | |---|---|---| | 1 | [47] + [27] | [27, 47] | | 2 | [56] + [23] | [23, 56] | | 3 | [3] + [9] | [3, 9] | | 4 | [94] + [11] | [11, 94] | | 5 | [27, 47] + [23, 56] | [23, 27, 47, 56] | | 6 | [3, 9] + [11, 94] | [3, 9, 11, 94] | | 7 | [23, 27, 47, 56] + [3, 9, 11, 94] | [3, 9, 11, 23, 27, 47, 56, 94] | **Answer: 3, 9, 11, 23, 27, 47, 56, 94** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How many single-element lists result from splitting 47, 27, 56, 23, 3, 9, 94, 11? A. 4 B. 8 C. 2 D. 1 Answer: B. The list is split until each element stands alone. (Key point: Split) 2. What is the result of merging [27, 47] and [23, 56]? A. [23, 27, 47, 56] B. [27, 47, 23, 56] C. [23, 56, 27, 47] D. [27, 23, 47, 56] Answer: A. Take the smaller front element each time. (Key point: Merge) 3. What is the final sorted list? A. 3, 9, 11, 23, 27, 47, 56, 94 B. 3, 9, 11, 94, 23, 27, 47, 56 C. 94, 56, 47, 27, 23, 11, 9, 3 D. 3, 11, 9, 23, 27, 47, 56, 94 Answer: A. Merging the two sorted halves gives ascending order. (Key point: Final) ## Related in Data Structure and Algorithm - [Merge sort algorithm and trace](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Amerge-sort-algorithm-trace) — Data Structure and Algorithm, chapter 7 - [Merge and radix sort on 142, 523, ...](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Amerge-radix-trace-142) — Data Structure and Algorithm, chapter 7 - [Merge sort on 85, 76, 46, 92, ...](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Amerge-sort-trace-85-76) — Data Structure and Algorithm, chapter 7 - [Selection sort with trace](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aselection-sort-explain-trace) — Data Structure and Algorithm, chapter 7 - [Radix sort on 25, 57, 48, 37, ...](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aradix-sort-25-57-48) — Data Structure and Algorithm, chapter 7 - [Straight selection sort on 33, 90, 45, ...](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aselection-sort-trace-33-90) — Data Structure and Algorithm, chapter 7 ## Related in other subjects - [De Morgan's theorem and (-47+27) by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademorgan-twos-complement-addition) — Digital Logic, chapter 2 - [Subnet 10.10.10.0/24 for 5, 16, 23, 27](https://www.bctengineer.com/question.md?key=semester_7%2Fcomputer_networks_and_security%3Asubnetting-10-10-10-0) — Computer Networks and Security, chapter 4, asked 2×