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 Ruby DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.rb
Replay: real traced execution (multi-file project)
arr = [3, 1, 4, 1, 5, 9, 2, 6]
best = arr[0]
i = 1
while i < arr.length
	if arr[i] > best
		best = arr[i]
	end
	i += 1
end
puts best

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

    1arr = [3, 1, 4, 1, 5, 9, 2, 6]2best = arr[0]
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    4while i < arr.length5	if arr[i] > best6		best = arr[i]
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    1arr = [3, 1, 4, 1, 5, 9, 2, 6]2best = arr[0]
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • arr is a Ruby Array of integers, and the lesson reads it by index with arr[i] rather than using each or max.
  • best = arr[0] seeds the local variable with 3, so the while loop starts at i = 1.
  • The loop condition is i < arr.length, which keeps every indexed read inside the eight-element array.
  • best is reassigned only when arr[i] > best; equal or smaller values leave the local variable unchanged.
  • The trace shows replacements at index 2 (4), index 4 (5), and index 5 (9).
  • The array itself is never mutated; only best and i change during the scan.
  • puts best prints the final scalar result 9.