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 Fortran 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.f90 
program sort_quick_lomuto
    implicit none
    integer :: arr(5) = [4, 1, 5, 2, 3]
    call quick_sort(arr, 1, 5)
    print '(*(I0,1X))', arr
contains
    integer function partition(arr, low, high)
        integer, intent(inout) :: arr(:)
        integer, intent(in) :: low, high
        integer :: pivot, i, j, tmp
        pivot = arr(high)
        i = low - 1
        do j = low, high - 1
            if (arr(j) <= pivot) then
                i = i + 1
                tmp = arr(i); arr(i) = arr(j); arr(j) = tmp
            end if
        end do
        tmp = arr(i + 1); arr(i + 1) = arr(high); arr(high) = tmp
        partition = i + 1
    end function partition

    recursive subroutine quick_sort(arr, low, high)
        integer, intent(inout) :: arr(:)
        integer, intent(in) :: low, high
        integer :: pivot_index
        if (low < high) then
            pivot_index = partition(arr, low, high)
            call quick_sort(arr, low, pivot_index - 1)
            call quick_sort(arr, pivot_index + 1, high)
        end if
    end subroutine quick_sort
end program sort_quick_lomuto

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.