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 Rust 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.rs 
fn partition(arr: &mut [i32], low: usize, high: usize) -> usize {
	let pivot = arr[high];
	let mut i = low;
	for j in low..high {
		if arr[j] <= pivot {
			arr.swap(i, j);
			i += 1;
		}
	}
	arr.swap(i, high);
	i
}

fn quick_sort(arr: &mut [i32], low: usize, high: usize) {
	if low < high {
		let pivot_index = partition(arr, low, high);
		if pivot_index > 0 {
			quick_sort(arr, low, pivot_index - 1);
		}
		quick_sort(arr, pivot_index + 1, high);
	}
}

fn main() {
	let mut arr = [4, 1, 5, 2, 3];
	let last = arr.len() - 1;
	quick_sort(&mut arr, 0, last);
	println!("{:?}", arr);
}

Complexity

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

Implementation notes

  • The checked source uses a fixed mutable array, let mut arr = [4, 1, 5, 2, 3], and passes it as &mut [i32]; it does not allocate a Vec.
  • partition(arr: &mut [i32], low: usize, high: usize) -> usize receives the mutable slice plus bounds, chooses pivot = arr[high], and returns the final pivot index.
  • quick_sort(arr: &mut [i32], low: usize, high: usize) mutates in place and returns (). It recurses only when low < high.
  • The source keeps i as the next left-side write slot and scans for j in low..high. On arr[j] <= pivot, arr.swap(i, j) moves that value left and then increments i.
  • After the scan, arr.swap(i, high) places the pivot. The recursive left call is guarded by if pivot_index > 0 so pivot_index - 1 cannot underflow as a usize.
  • The trace records the first partition around pivot 3: keep 4, swap 1 left, keep 5, swap 2 left, then swap the pivot into index 2, yielding [1, 2, 3, 4, 5]. Its i labels the left boundary, while the Rust variable holds the next write slot.
  • Recursive calls on [1, 2] and [4, 5] are summarized in the trace. The final println!("{:?}", arr) uses debug formatting and prints [1, 2, 3, 4, 5].