Sorting

Quick Sort (Lomuto)

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

Algorithm

Basic Implementation

basic.ts 
function partition(arr: number[], low: number, high: number): number {
    const pivot: number = arr[high];
    let i: number = low - 1;
    for (let j: number = low; j < high; j++) {
        if (arr[j] <= pivot) {
            i++;
            [arr[i], arr[j]] = [arr[j], arr[i]];
        }
    }
    [arr[i + 1], arr[high]] = [arr[high], arr[i + 1]];
    return i + 1;
}

function quickSort(arr: number[], low: number, high: number): void {
    if (low < high) {
        const pivotIndex: number = partition(arr, low, high);
        quickSort(arr, low, pivotIndex - 1);
        quickSort(arr, pivotIndex + 1, high);
    }
}

const arr: number[] = [4, 1, 5, 2, 3];
quickSort(arr, 0, arr.length - 1);
console.log(JSON.stringify(arr));

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)

Complexity

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

Implementation notes

  • TypeScript declares partition to accept arr: number[], low: number, and high: number, returning number; quickSort uses the same typed bounds and returns void, so the checked code mutates one number[] in place.
  • partition stores const pivot: number = arr[high], initializes let i: number = low - 1, and scans let j: number = low while j < high.
  • The comparison arr[j] <= pivot uses numeric Number values through TypeScript's number type; equal values would be moved to the left side of the partition.
  • Swaps use destructuring assignment, [arr[i], arr[j]] = [arr[j], arr[i]] and then [arr[i + 1], arr[high]] = [arr[high], arr[i + 1]], mutating array slots in place through source-level two-element RHS array expressions that engines may optimize.
  • The replay partitions around pivot 3: 4 and 5 stay right, 1 and 2 swap left, and the pivot lands at index 2, yielding [1, 2, 3, 4, 5] before recursive calls on [1, 2] and [4, 5].
  • console.log(JSON.stringify(arr)) prints [1,2,3,4,5]; visible heap allocation is the initial array and JSON output string, while recursive call frames and partition indices are execution state.
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.