Arrays and Iteration

Find Maximum

Scan the array once, keeping the largest value seen so far. The replay highlights when a candidate replaces the running maximum.

Algorithm

execution replay The checked-in replay follows the language-neutral state table for `array-find-max`.
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 array_find_max
    implicit none
    integer :: arr(8) = [3, 1, 4, 1, 5, 9, 2, 6]
    integer :: best, i
    best = arr(1)
    do i = 2, 8
        if (arr(i) > best) then
            best = arr(i)
        end if
    end do
    print '(I0)', best
end program array_find_max

  1. arr ← [3, 1, 4, 1, 5, 9, 2, 6], best ← 3

    1program array_find_max2    implicit none
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    6do i = 2, 87    if (arr(i) > best) then8        best = arr(i)
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    10    end do11    print '(I0)', best12end program array_find_max
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

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.