Merge Sort as Divide and Conquer in DSA C - Execution Trace

Concept Flow - Merge Sort as Divide and Conquer

Start with full array

↓

Divide array into two halves

↓

Recursively sort left half

→Recursively sort right half

↓

Merge two sorted halves

↓

Sorted array

↓

Done

Merge Sort splits the array into halves recursively, sorts each half, then merges them back in order.

Execution Sample

DSA C

void mergeSort(int arr[], int left, int right) {
  if (left < right) {
    int mid = left + (right - left) / 2;
    mergeSort(arr, left, mid);
    mergeSort(arr, mid + 1, right);
    merge(arr, left, mid, right);
  }
}

This code recursively divides the array and merges sorted halves.

Execution Table

Step	Operation	Sub-array Indices	Action Detail	Array State
1	Divide	[0..7]	Split into [0..3] and [4..7]	[38, 27, 43, 3, 9, 82, 10, 15]
2	Divide	[0..3]	Split into [0..1] and [2..3]	[38, 27, 43, 3, 9, 82, 10, 15]
3	Divide	[0..1]	Split into [0..0] and [1..1]	[38, 27, 43, 3, 9, 82, 10, 15]
4	Base case	[0..0]	Single element, no action	[38, 27, 43, 3, 9, 82, 10, 15]
5	Base case	[1..1]	Single element, no action	[38, 27, 43, 3, 9, 82, 10, 15]
6	Merge	[0..1]	Merge [38] and [27] into sorted [27, 38]	[27, 38, 43, 3, 9, 82, 10, 15]
7	Divide	[2..3]	Split into [2..2] and [3..3]	[27, 38, 43, 3, 9, 82, 10, 15]
8	Base case	[2..2]	Single element, no action	[27, 38, 43, 3, 9, 82, 10, 15]
9	Base case	[3..3]	Single element, no action	[27, 38, 43, 3, 9, 82, 10, 15]
10	Merge	[2..3]	Merge [43] and [3] into sorted [3, 43]	[27, 38, 3, 43, 9, 82, 10, 15]
11	Merge	[0..3]	Merge [27, 38] and [3, 43] into sorted [3, 27, 38, 43]	[3, 27, 38, 43, 9, 82, 10, 15]
12	Divide	[4..7]	Split into [4..5] and [6..7]	[3, 27, 38, 43, 9, 82, 10, 15]
13	Divide	[4..5]	Split into [4..4] and [5..5]	[3, 27, 38, 43, 9, 82, 10, 15]
14	Base case	[4..4]	Single element, no action	[3, 27, 38, 43, 9, 82, 10, 15]
15	Base case	[5..5]	Single element, no action	[3, 27, 38, 43, 9, 82, 10, 15]
16	Merge	[4..5]	Merge [9] and [82] into sorted [9, 82]	[3, 27, 38, 43, 9, 82, 10, 15]
17	Divide	[6..7]	Split into [6..6] and [7..7]	[3, 27, 38, 43, 9, 82, 10, 15]
18	Base case	[6..6]	Single element, no action	[3, 27, 38, 43, 9, 82, 10, 15]
19	Base case	[7..7]	Single element, no action	[3, 27, 38, 43, 9, 82, 10, 15]
20	Merge	[6..7]	Merge [10] and [15] into sorted [10, 15]	[3, 27, 38, 43, 9, 82, 10, 15]
21	Merge	[4..7]	Merge [9, 82] and [10, 15] into sorted [9, 10, 15, 82]	[3, 27, 38, 43, 9, 10, 15, 82]
22	Merge	[0..7]	Merge [3, 27, 38, 43] and [9, 10, 15, 82] into sorted [3, 9, 10, 15, 27, 38, 43, 82]	[3, 9, 10, 15, 27, 38, 43, 82]
23	Done	Full array	Array fully sorted	[3, 9, 10, 15, 27, 38, 43, 82]

💡 All sub-arrays reduced to single elements and merged back sorted

Variable Tracker

Variable	Start	After Step 6	After Step 10	After Step 11	After Step 16	After Step 20	After Step 21	After Step 22	Final
arr	[38, 27, 43, 3, 9, 82, 10, 15]	[27, 38, 43, 3, 9, 82, 10, 15]	[27, 38, 3, 43, 9, 82, 10, 15]	[3, 27, 38, 43, 9, 82, 10, 15]	[3, 27, 38, 43, 9, 82, 10, 15]	[3, 27, 38, 43, 9, 82, 10, 15]	[3, 27, 38, 43, 9, 10, 15, 82]	[3, 9, 10, 15, 27, 38, 43, 82]	[3, 9, 10, 15, 27, 38, 43, 82]
left	0	0	0	0	4	4	4	0	0
right	7	7	7	7	7	7	7	7	7
mid	3	1	2	3	5	6	7	3	7

Key Moments - 3 Insights

Why do we stop dividing when the sub-array has only one element?

Because a single element is already sorted, so no further division or merging is needed. See steps 4, 5, 8, 9, 14, 15, 18, 19 in the execution_table.

How does merging two sorted halves keep the array sorted?

Merging compares elements from both halves and picks the smaller one each time, building a sorted combined array. See steps 6, 10, 11, 16, 20, 21, 22 for merging details.

Why do we calculate mid as (left + right) / 2?

To split the array roughly in half for balanced division, ensuring efficient sorting. This is shown in variable_tracker where mid changes as sub-arrays change.

Visual Quiz - 3 Questions

Look at the execution_table at step 6, what is the array state after merging?

A [27, 38, 43, 3, 9, 82, 10, 15]

B [38, 27, 43, 3, 9, 82, 10, 15]

C [3, 27, 38, 43, 9, 82, 10, 15]

D [27, 38, 3, 43, 9, 82, 10, 15]

💡 Hint

Check the 'Array State' column in execution_table row with Step 6.

At which step does the full array become completely sorted?

A Step 21

B Step 22

C Step 23

D Step 20

💡 Hint

Look for 'Done' operation and final sorted array in execution_table.

If the initial array had only 4 elements, how would the number of divide steps change?

A It would increase

B It would decrease

C It would stay the same

D It would be zero

💡 Hint

Fewer elements mean fewer splits; check divide steps in execution_table.

Concept Snapshot

Merge Sort divides array into halves recursively
Sorts each half separately
Merges sorted halves into one sorted array
Uses mid = (left + right) / 2 to split
Stops dividing when sub-array size is 1
Merging compares and combines sorted halves

Full Transcript

Merge Sort works by splitting the array into smaller parts until each part has one element. Then it merges these parts back together in sorted order. The code divides the array by calculating the middle index and recursively sorting the left and right halves. When merging, it compares elements from both halves and builds a sorted array. This process continues until the entire array is sorted. The execution table shows each divide and merge step with the array state. Key points include stopping division at single elements and merging sorted halves carefully to maintain order.