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 R 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.R 
partition <- function(arr, low, high) {
	pivot <- arr[high]
	i <- low - 1
	for (j in low:(high - 1)) {
		if (arr[j] <= pivot) {
			i <- i + 1
			tmp <- arr[i]; arr[i] <- arr[j]; arr[j] <- tmp
		}
	}
	tmp <- arr[i + 1]; arr[i + 1] <- arr[high]; arr[high] <- tmp
	list(arr = arr, pivot = i + 1)
}

quick_sort <- function(arr, low, high) {
	if (low < high) {
		part <- partition(arr, low, high)
		arr <- part$arr
		pivot_index <- part$pivot
		arr <- quick_sort(arr, low, pivot_index - 1)
		arr <- quick_sort(arr, pivot_index + 1, high)
	}
	arr
}

arr <- quick_sort(c(4, 1, 5, 2, 3), 1, 5)
cat("[", paste(arr, collapse = ", "), "]
", sep = "")

Complexity

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

Implementation notes

  • The checked input is the R vector c(4, 1, 5, 2, 3).
  • quick_sort(arr, low, high) returns the sorted vector; the source reassigns arr after partitioning and after each recursive call.
  • R vector indexes are 1-based, so the top-level call is quick_sort(..., 1, 5).
  • partition(arr, low, high) chooses the last slot as the pivot: pivot <- arr[high], so the first pivot is 3.
  • i <- low - 1 starts at 0 for the first partition.
  • The comparison loop is for (j in low:(high - 1)), so this run checks R indexes 1 through 4.
  • The condition is arr[j] <= pivot; values less than or equal to the pivot move to the left side.
  • Swaps use a temporary scalar: tmp <- arr[i]; arr[i] <- arr[j]; arr[j] <- tmp.
  • Final pivot placement also uses tmp, swapping arr[i + 1] with arr[high].
  • partition returns list(arr = arr, pivot = i + 1), and quick_sort unpacks that with part$arr and part$pivot.
  • The trace reports zero-based partition labels, so its j=0 corresponds to R index 1, and its final pivot index 2 corresponds to R index 3.

First partition replay

start:             [4, 1, 5, 2, 3], pivot = 3
compare 4 <= 3:   [4, 1, 5, 2, 3]
compare 1 <= 3:   [1, 4, 5, 2, 3]
compare 5 <= 3:   [1, 4, 5, 2, 3]
compare 2 <= 3:   [1, 2, 5, 4, 3]
place pivot 3:    [1, 2, 3, 4, 5]
  • The replay then summarizes the left side [1, 2] and right side [4, 5], both already sorted after the first pivot lands.
  • The final cat call combines "[", paste(arr, collapse = ", "), and a closing bracket string that contains the newline, so it prints [1, 2, 3, 4, 5].