Sorting

Quick Sort (Lomuto)

Choose the last item as a pivot, partition smaller values to its left, then recurse on the two sides.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this Swift DSA implementation can be compared directly with the other languages.

pivot The final element is moved to the boundary between smaller and larger values.
partition One scan rearranges the current range before the recursive calls.

Visual walkthrough

The pinned first partition uses [4, 1, 5, 2, 3] with pivot 3. The diagrams track the boundary, swaps, and recursive ranges.

Step 1 - Choose the last value as pivot

The pivot is arr[4] = 3, and i starts just before the current range.

Initial partition state for [4, 1, 5, 2, 3].i0i1i2i3i441523j startspivot

Step 2 - Swap small values left

1 and 2 are <= pivot, so they move into the left partition.

After scanning values before the pivot: [1, 2, 5, 4, 3].i0i1i2i3i412543<= 3<= 3> 3> 3pivot

Step 3 - Place pivot, then recurse

Swapping pivot 3 into index 2 gives [1, 2, 3, 4, 5]; recurse on [1, 2] and [4, 5].

Pivot lands at index 2 and splits the remaining work.left rangepivotright range[1, 2]3 at i2[4, 5]quick_sort(0,1)fixedquick_sort(3,4)

Basic Implementation

basic.swift 
func partition(_ arr: inout [Int], _ low: Int, _ high: Int) -> Int {
	let pivot = arr[high]
	var i = low - 1
	for j in low..<high {
		if arr[j] <= pivot {
			i += 1
			arr.swapAt(i, j)
		}
	}
	arr.swapAt(i + 1, high)
	return i + 1
}

func quickSort(_ arr: inout [Int], _ low: Int, _ high: Int) {
	if low < high {
		let pivotIndex = partition(&arr, low, high)
		quickSort(&arr, low, pivotIndex - 1)
		quickSort(&arr, pivotIndex + 1, high)
	}
}

var arr = [4, 1, 5, 2, 3]
quickSort(&arr, 0, arr.count - 1)
print(arr)

Complexity

  • Time: O(n^2) worst, O(n log n) average
  • Space: O(log n) average call stack
  • Stable: no

Implementation notes

  • partition(_ arr: inout [Int], _ low: Int, _ high: Int) -> Int mutates the caller's Swift [Int] through inout; quickSort(&arr, 0, arr.count - 1) passes the same array variable by inout. Swift Array is a value type with copy-on-write storage, and this source mutates it through swapAt without explicitly allocating a replacement array.
  • The pivot is let pivot = arr[high], so each partition uses the current high-bound element as an immutable Int comparison value.
  • var i = low - 1 tracks the last slot on the left side, while for j in low..<high scans only the elements before the pivot.
  • Values satisfying arr[j] <= pivot increment i and call arr.swapAt(i, j); after the scan, arr.swapAt(i + 1, high) places the pivot and returns i + 1.
  • quickSort recurses only when low < high, then calls the left range low...pivotIndex - 1 and right range pivotIndex + 1...high.
  • The trace starts from [4, 1, 5, 2, 3]: comparing 4 and 5 against pivot 3 leaves them on the right, while 1 and 2 swap left to produce [1, 2, 5, 4, 3].
  • The pivot swap moves 3 into index 2, yielding [1, 2, 3, 4, 5]; the replay then records already-sorted left [1, 2] and right [4, 5] recursions.
  • print(arr) uses Swift's array display form and outputs [1, 2, 3, 4, 5].