Insertion Sort Algorithm in DSA C++ - Execution Trace

Concept Flow - Insertion Sort Algorithm

Start with second element i=1

↓

Compare current element with elements before it

↓

Shift elements greater than current to the right

↓

Insert current element at correct position

↓

Increment i

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i < array length?

No→Sorted array ready

↩Back to Compare

Insertion sort picks each element from the second one, shifts bigger elements to the right, and inserts it in the correct place, repeating until the array is sorted.

Execution Sample

DSA C++

int arr[] = {5, 3, 8, 1, 2};
int n = 5;
for (int i = 1; i < n; i++) {
  int key = arr[i];
  int j = i - 1;
  while (j >= 0 && arr[j] > key) {
    arr[j + 1] = arr[j];
    j--;
  }
  arr[j + 1] = key;
}

Sorts the array by inserting each element into its correct position among the previously sorted elements.

Execution Table

Step	Operation	Array State	Comparison	Shift or Insert	Visual State
1	Pick element at i=1 (3)	[5, 3, 8, 1, 2]	5 > 3	Shift 5 right	[5, 5, 8, 1, 2]
2	Insert key 3 at position j+1=0	[5, 5, 8, 1, 2]	N/A	Insert 3	[3, 5, 8, 1, 2]
3	Pick element at i=2 (8)	[3, 5, 8, 1, 2]	5 > 8? No	No shift	[3, 5, 8, 1, 2]
4	Pick element at i=3 (1)	[3, 5, 8, 1, 2]	8 > 1	Shift 8 right	[3, 5, 8, 8, 2]
5	Compare 5 > 1	[3, 5, 8, 8, 2]	5 > 1	Shift 5 right	[3, 5, 5, 8, 2]
6	Compare 3 > 1	[3, 5, 5, 8, 2]	3 > 1	Shift 3 right	[3, 3, 5, 8, 2]
7	Insert key 1 at position j+1=0	[3, 3, 5, 8, 2]	N/A	Insert 1	[1, 3, 5, 8, 2]
8	Pick element at i=4 (2)	[1, 3, 5, 8, 2]	8 > 2	Shift 8 right	[1, 3, 5, 8, 8]
9	Compare 5 > 2	[1, 3, 5, 8, 8]	5 > 2	Shift 5 right	[1, 3, 5, 5, 8]
10	Compare 3 > 2	[1, 3, 5, 5, 8]	3 > 2	Shift 3 right	[1, 3, 3, 5, 8]
11	Compare 1 > 2? No	[1, 3, 3, 5, 8]	1 > 2? No	No shift	[1, 3, 3, 5, 8]
12	Insert key 2 at position j+1=1	[1, 3, 3, 5, 8]	N/A	Insert 2	[1, 2, 3, 5, 8]
13	i=5 equals array length, sorting done	[1, 2, 3, 5, 8]	N/A	Done	[1, 2, 3, 5, 8]

💡 i reaches array length 5, no more elements to insert, array is sorted

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	After Step 8	After Step 9	After Step 10	After Step 11	After Step 12	Final
i	1	1	1	2	3	3	3	3	4	4	4	4	4	5
key	3	3	3	8	1	1	1	1	2	2	2	2	2	N/A
j	0	-1	-1	1	1	0	-1	-1	2	1	0	0	0	N/A
Array	[5, 3, 8, 1, 2]	[5, 5, 8, 1, 2]	[3, 5, 8, 1, 2]	[3, 5, 8, 1, 2]	[3, 5, 8, 8, 2]	[3, 5, 5, 8, 2]	[3, 3, 5, 8, 2]	[1, 3, 5, 8, 2]	[1, 3, 5, 8, 8]	[1, 3, 5, 5, 8]	[1, 3, 3, 5, 8]	[1, 3, 3, 5, 8]	[1, 2, 3, 5, 8]	[1, 2, 3, 5, 8]

Key Moments - 3 Insights

Why do we shift elements to the right instead of swapping directly?

We shift elements to the right to make space for the key element to be inserted at the correct position. This is shown in steps 1, 4, 5, 6, 8, 9, and 10 where elements are moved right before inserting the key.

Why does the inner loop stop when arr[j] <= key?

The inner loop stops because the correct position for the key is found when the element at j is less than or equal to the key. This is shown in step 11 where 1 > 2 is false, so no more shifting happens.

What happens when the key is already greater than the previous element?

No shifting is needed and the key stays in place. This is shown in step 3 where 5 > 8 is false, so the array remains unchanged.

Visual Quiz - 3 Questions

Look at the execution table, what is the array state after step 7?

A [1, 3, 5, 8, 2]

B [3, 3, 5, 8, 2]

C [3, 5, 8, 1, 2]

D [1, 2, 3, 5, 8]

💡 Hint

Check the 'Array State' column in row with Step 7 in execution_table.

At which step does the condition 'arr[j] > key' become false for the first time?

A Step 6

B Step 11

C Step 3

D Step 9

💡 Hint

Look at the 'Comparison' column in execution_table rows to find where 'arr[j] > key' is false.

If the initial array was already sorted, how would the 'Shift or Insert' column change?

A All shifts would be replaced by inserts

B No shifts would occur, only inserts at the same position

C Shifts would increase because elements are moved more

D The array would be reversed

💡 Hint

Refer to variable_tracker and execution_table to see when shifts happen and when they don't.

Concept Snapshot

Insertion Sort Algorithm:
- Start from second element (index 1)
- Compare with previous elements
- Shift larger elements right
- Insert current element at correct position
- Repeat until array is sorted
- Time: O(n^2), Space: O(1)

Full Transcript

Insertion sort works by taking each element from the second position onward and inserting it into the correct place among the elements before it. We compare the current element (key) with elements to its left. If those elements are bigger, we shift them one position to the right to make space. When we find the right spot, we insert the key. This repeats until the whole array is sorted. The execution table shows each step with array states, comparisons, shifts, and insertions. Variables i, j, and key track the current positions and values. Key moments clarify why shifting is done instead of swapping, when the inner loop stops, and what happens if the array is already sorted. The visual quiz tests understanding of array states and conditions during sorting. Insertion sort is simple but can be slow for large arrays.