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 Scala 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.scala 
object Main {
	def partition(arr: Array[Int], low: Int, high: Int): Int = {
		val pivot = arr(high)
		var i = low - 1
		for (j <- low until high) {
			if (arr(j) <= pivot) {
				i = i + 1
				val tmp = arr(i); arr(i) = arr(j); arr(j) = tmp
			}
		}
		val tmp = arr(i + 1); arr(i + 1) = arr(high); arr(high) = tmp
		i + 1
	}

	def quickSort(arr: Array[Int], low: Int, high: Int): Unit = {
		if (low < high) {
			val pivotIndex = partition(arr, low, high)
			quickSort(arr, low, pivotIndex - 1)
			quickSort(arr, pivotIndex + 1, high)
		}
	}
	def main(args: Array[String]): Unit = {
		val arr = Array(4, 1, 5, 2, 3)
		quickSort(arr, 0, arr.length - 1)
		println(arr.mkString("[", ", ", "]"))
	}
}

Complexity

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

Implementation notes

  • val arr = Array(4, 1, 5, 2, 3) fixes the Scala Array[Int] reference, but partition and quickSort mutate its slots in place.
  • partition(arr: Array[Int], low: Int, high: Int): Int chooses the last slot with val pivot = arr(high).
  • var i = low - 1 marks the end of the left side. The scan for (j <- low until high) uses Scala's exclusive until, so j visits 0, 1, 2, and 3 while the pivot stays at index 4.
  • When arr(j) <= pivot, the code increments i and performs an explicit temporary-variable swap: val tmp = arr(i); arr(i) = arr(j); arr(j) = tmp.
  • The first partition compares against pivot 3: 4 stays right, 1 swaps left to make [1, 4, 5, 2, 3], 5 stays right, and 2 swaps left to make [1, 2, 5, 4, 3].
  • After the scan, a second explicit tmp swap moves the pivot into i + 1, producing [1, 2, 3, 4, 5] with pivot index 2.
  • quickSort recurses only when low < high; the replay then summarizes the already-sorted left side [1, 2] and right side [4, 5].
  • println(arr.mkString("[", ", ", "]")) prints the final array exactly as [1, 2, 3, 4, 5].