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.js 
function partition(arr, low, high) {
    const pivot = arr[high];
    let i = low - 1;
    for (let j = 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, low, high) {
    if (low < high) {
        const pivotIndex = partition(arr, low, high);
        quickSort(arr, low, pivotIndex - 1);
        quickSort(arr, pivotIndex + 1, high);
    }
}

const arr = [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

  • JavaScript stores the sortable data in a const Array of Number values. quickSort mutates that same array in place over inclusive low and high bounds, and recursion stops when low < high is false.
  • partition chooses arr[high] as the pivot, initializes let i = low - 1, and scans j while j < high. The arr[j] <= pivot test uses numeric Number comparison and sends values equal to the pivot to the left 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]]. Those writes mutate array slots in place; the right-hand destructuring arrays are short-lived runtime allocations.
  • The replay shows the first partition around pivot 3: 4 and 5 stay on the right, 1 and 2 swap left, and the pivot lands at index 2, producing [1, 2, 3, 4, 5] before the summarized recursive calls on [1, 2] and [4, 5].
  • console.log(JSON.stringify(arr)) prints the compact sorted output [1,2,3,4,5]. Aside from recursion stack frames, destructuring temporaries, and the output string, no replacement array is allocated.
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.