Searching

Binary Search (Recursive)

Use the same binary-search window as the iterative lesson, but pass lo and hi through recursive calls.

Algorithm

execution replay The checked-in replay follows the language-neutral state table for `search-binary-recursive`.
cross-language comparison This Fortran DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.f90
Replay: real traced execution (multi-file project)
program search_binary_recursive
    implicit none
    integer :: arr(7) = [1, 3, 5, 7, 9, 11, 13]
    integer :: target
    target = 11
    print '(I0)', search(arr, target, 0, 6)
contains
    recursive integer function search(arr, target, lo, hi) result(pos)
        integer, intent(in) :: arr(7), target, lo, hi
        integer :: mid, value
        if (lo > hi) then
            pos = -1
            return
        end if
        mid = lo + (hi - lo) / 2
        value = arr(mid + 1)
        if (value == target) then
            pos = mid
        else if (value < target) then
            pos = search(arr, target, mid + 1, hi)
        else
            pos = search(arr, target, lo, mid - 1)
        end if
    end function search
end program search_binary_recursive

  1. lo ← 0, hi ← 6, target ← 11

    1program search_binary_recursive2    implicit none
    values this step0lo6hi11target

  2. mid ← 3, arr[mid] ← 7, next call ← (4, 6)

    9integer, intent(in) :: arr(7), target, lo, hi10integer :: mid, value11if (lo > hi) then
    values this step3mid7arr[mid](4, 6)next call0lo6hi

  3. mid ← 5, arr[mid] ← 11, result ← 5

    9integer, intent(in) :: arr(7), target, lo, hi10integer :: mid, value11if (lo > hi) then
    values this step5mid11arr[mid]5result4lo6hi

  4. stdout ← 5

    5    target = 116    print '(I0)', search(arr, target, 0, 6)7contains
    values this step5stdout5result

Complexity

  • Time: O(log n)
  • Space: O(log n) call stack

Implementation notes

  • Keep the explicit control flow. Library shortcuts would hide the state changes this lesson is meant to replay.
  • The final output is intentionally small and deterministic for cross-language comparison.