Quick Sort Algorithm in DSA Javascript - Execution Trace

Concept Flow - Quick Sort Algorithm

Choose pivot element

↓

Partition array around pivot

↓

Left sub-array < pivot

↓

Recursively quick sort left

↓

Combine sorted parts

↓

Done

Quick Sort picks a pivot, splits the array into smaller and bigger parts, sorts each part by repeating the process, then combines them.

Execution Sample

DSA Javascript

function quickSort(arr) {
  if (arr.length <= 1) return arr;
  const pivot = arr[arr.length - 1];
  const left = [];
  const right = [];
  for (let i = 0; i < arr.length - 1; i++) {
    if (arr[i] < pivot) left.push(arr[i]); else right.push(arr[i]);
  }
  return [...quickSort(left), pivot, ...quickSort(right)];
}

This code sorts an array by choosing the last element as pivot, splitting into left and right arrays, sorting them recursively, and combining.

Execution Table

Step	Operation	Array State	Pivot	Left Array	Right Array	Action
1	Start quickSort	[8, 3, 7, 6, 2]	2	[]	[8, 3, 7, 6]	Choose pivot 2
2	Partition	[8, 3, 7, 6, 2]	2	[]	[8, 3, 7, 6]	8 > 2 → right, 3 > 2 → right, 7 > 2 → right, 6 > 2 → right
3	Recurse left	[]	-	[]	[]	Left empty, return []
4	Recurse right	[8, 3, 7, 6]	6	[3]	[8, 7]	Choose pivot 6, partition into left [3], right [8,7]
5	Partition right	[8, 3, 7, 6]	6	[3]	[8, 7]	3 < 6 → left, 8 > 6 → right, 7 > 6 → right
6	Recurse left of right	[3]	3	[]	[]	Single element, return [3]
7	Recurse left of left of right	[]	-	[]	[]	Left empty, return []
8	Recurse right of left of right	[]	-	[]	[]	Right empty, return []
9	Combine left of right	[3]	3	[]	[]	Combine [] + 3 + [] → [3]
10	Recurse right of right	[8, 7]	7	[]	[8]	Choose pivot 7, left empty, right [8]
11	Recurse left of right of right	[]	-	[]	[]	Left empty, return []
12	Recurse right of right of right	[8]	8	[]	[]	Single element, return [8]
13	Combine right of right	[7, 8]	7	[]	[8]	Combine [] + 7 + [8] → [7,8]
14	Combine right	[3, 6, 7, 8]	6	[3]	[7, 8]	Combine [3] + 6 + [7,8] → [3,6,7,8]
15	Combine all	[2, 3, 6, 7, 8]	2	[]	[3, 6, 7, 8]	Combine [] + 2 + [3,6,7,8] → [2,3,6,7,8]
16	End	[2, 3, 6, 7, 8]	-	-	-	Array sorted

💡 Recursion ends when sub-array length is 0 or 1, fully sorted array returned

Variable Tracker

Variable	Start	After Step 2	After Step 4	After Step 6	After Step 9	After Step 13	Final
arr	[8, 3, 7, 6, 2]	[8, 3, 7, 6, 2]	[8, 3, 7, 6]	[3]	[3]	[7, 8]	[2, 3, 6, 7, 8]
pivot	2	2	6	3	3	7	-
left	[]	[]	[3]	[]	[]	[]	-
right	[]	[8, 3, 7, 6]	[8, 7]	[]	[]	[8]	-

Key Moments - 3 Insights

Why do we choose the last element as the pivot?

Choosing the last element as pivot is a simple rule to split the array; see Step 1 and Step 4 in execution_table where pivot is last element.

What happens when the left or right sub-array is empty?

When left or right is empty, recursion returns immediately as in Step 3 and Step 7, preventing infinite loops.

How does the array get combined back after sorting sub-arrays?

After sorting left and right, the arrays are combined with pivot in the middle, shown in Steps 9, 13, and 14.

Visual Quiz - 3 Questions

Look at the execution_table at Step 4, what is the pivot chosen?

A 6

B 2

C 8

D 3

💡 Hint

Check the 'Pivot' column at Step 4 in execution_table

At which step does the left sub-array become empty for the first time?

A Step 6

B Step 7

C Step 3

D Step 11

💡 Hint

Look at 'Left Array' column in execution_table rows for empty array

If the pivot was chosen as the first element instead of last, how would the partition step change?

A Left and right arrays would be swapped

B Pivot would be different, changing partition elements

C No change in partitioning

D Algorithm would fail

💡 Hint

Pivot choice affects which elements go left or right, see Steps 1 and 4

Concept Snapshot

Quick Sort Algorithm:
- Pick a pivot (commonly last element)
- Partition array into left (< pivot) and right (> pivot)
- Recursively sort left and right sub-arrays
- Combine sorted left + pivot + sorted right
- Stops when sub-array size ≤ 1
- Efficient average O(n log n) sorting

Full Transcript

Quick Sort works by choosing a pivot element, usually the last in the array. It then splits the array into two parts: elements less than the pivot go to the left, and elements greater go to the right. Each part is sorted by repeating the same process recursively. When the parts are small enough (empty or one element), they are returned as sorted. Finally, the sorted left part, the pivot, and the sorted right part are combined to form the fully sorted array. This process is efficient and widely used for sorting arrays.