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 Dart 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.dart 
int partition(List<int> arr, int low, int high) {
  final pivot = arr[high];
  var i = low - 1;
  for (var j = low; j < high; j++) {
    if (arr[j] <= pivot) {
      i++;
      final tmp = arr[i];
      arr[i] = arr[j];
      arr[j] = tmp;
    }
  }
  final tmp = arr[i + 1];
  arr[i + 1] = arr[high];
  arr[high] = tmp;
  return i + 1;
}

void quickSort(List<int> arr, int low, int high) {
  if (low < high) {
    final pivotIndex = partition(arr, low, high);
    quickSort(arr, low, pivotIndex - 1);
    quickSort(arr, pivotIndex + 1, high);
  }
}

void main() {
  final arr = <int>[4, 1, 5, 2, 3];
  quickSort(arr, 0, arr.length - 1);
  print(arr);
}

Complexity

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

Implementation notes

  • Keep the explicit algorithmic steps instead of calling a standard-library sort. This checked-in replay shows each comparison and swap in the first partition, then summarizes the recursive calls on already-sorted sides.
  • The implementation is intentionally compact for learning and replay, not a production sorting utility.