Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

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.

Basic Implementation

basic.f90

program sort_merge
    implicit none
    integer :: arr(5) = [5, 1, 4, 2, 8]
    call merge_sort(arr, 1, 5)
    print '(*(I0,1X))', arr
contains
    recursive subroutine merge_sort(arr, left, right)
        integer, intent(inout) :: arr(:)
        integer, intent(in) :: left, right
        integer :: mid
        if (left >= right) return
        mid = (left + right) / 2
        call merge_sort(arr, left, mid)
        call merge_sort(arr, mid + 1, right)
        call merge(arr, left, mid, right)
    end subroutine merge_sort

    subroutine merge(arr, left, mid, right)
        integer, intent(inout) :: arr(:)
        integer, intent(in) :: left, mid, right
        integer :: tmp(5), i, j, k, t
        i = left; j = mid + 1; k = 1
        do while (i <= mid .and. j <= right)
            if (arr(i) <= arr(j)) then
                tmp(k) = arr(i); i = i + 1
            else
                tmp(k) = arr(j); j = j + 1
            end if
            k = k + 1
        end do
        do while (i <= mid)
            tmp(k) = arr(i); i = i + 1; k = k + 1
        end do
        do while (j <= right)
            tmp(k) = arr(j); j = j + 1; k = k + 1
        end do
        do t = 1, k - 1
            arr(left + t - 1) = tmp(t)
        end do
    end subroutine merge
end program sort_merge

Complexity

Time: O(n log n)
Space: O(n)
Stable: yes

Implementation notes

Keep the explicit algorithmic steps instead of calling a standard-library sort. The replay is meant to expose comparisons, movement, and recursion.
The implementation is intentionally compact for learning and replay, not a production sorting utility.

divide and conquer Each recursive call solves a smaller sorted subproblem.

merge step Two sorted halves are combined by repeatedly taking the smaller front item.