---
title: "Merge sort on 85, 76, 46, 92, ..."
subject: "Data Structure and Algorithm"
chapter: 7
key: "semester_4/data_structure_and_algorithm:merge-sort-trace-85-76"
source: https://www.bctengineer.com/q/semester_4/data_structure_and_algorithm/merge-sort-trace-85-76
site: BCT Engineering
---

# Merge sort on 85, 76, 46, 92, ...

Data Structure and Algorithm · Chapter 7: Sorting

- Asked in: 2072 Asoj, 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-85-76
- Whole chapter: https://www.bctengineer.com/md/semester_4/data_structure_and_algorithm/chapter-7

## Question

Trace the steps to sort the following set of data using merge sort: 85, 76, 46, 92, 30, 41 and 12.

## Short answer

Using merge sort, recursively divide 85,76,46,92,30,41,12 into single elements. Merge stepwise: [85]&[76]→76,85; [46]&[92]→46,92; [30]&[41]→30,41; then merge [76,85]&[46,92]→46,76,85,92; merge [30,41]&[12]→12,30,41; final merge yields 12,30,41,46,76,85,92.

## Answer

Merge sort uses divide and conquer: split the list into two halves until each part has one element, then merge the sorted parts pairwise. Here the left half gets the extra element when the size is odd.

#### Dividing
```text
85 76 46 92 30 41 12
  85 76 46 92 | 30 41 12
  85 76 | 46 92 | 30 41 | 12
  85 | 76 | 46 | 92 | 30 | 41 | 12
```

#### Merging
| Step | Merge | Result |
|---|---|---|
| 1 | [85] + [76] | [76, 85] |
| 2 | [46] + [92] | [46, 92] |
| 3 | [30] + [41] | [30, 41] |
| 4 | [76, 85] + [46, 92] | [46, 76, 85, 92] |
| 5 | [30, 41] + [12] | [12, 30, 41] |
| 6 | [46, 76, 85, 92] + [12, 30, 41] | [12, 30, 41, 46, 76, 85, 92] |

**Answer: 12, 30, 41, 46, 76, 85, 92**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does merge sort start?
   A. Picks a pivot
   B. Splits the list into halves until single elements remain
   C. Builds a heap
   D. Distributes by digit
   Answer: B. Divide until each part has one element. (Key point: Divide)

2. What is the result of merging [76, 85] and [46, 92]?
   A. [46, 76, 85, 92]
   B. [76, 85, 46, 92]
   C. [46, 85, 76, 92]
   D. [76, 46, 85, 92]
   Answer: A. Repeatedly take the smaller front element. (Key point: Merging)

3. What is the sorted result of 85, 76, 46, 92, 30, 41, 12?
   A. 12, 30, 41, 46, 76, 85, 92
   B. 12, 30, 41, 76, 46, 85, 92
   C. 92, 85, 76, 46, 41, 30, 12
   D. 30, 41, 12, 46, 76, 85, 92
   Answer: A. All elements in ascending order. (Key point: Final)

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- [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
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