Arrays and Iteration

Linear Search

Walk an array once looking for a target value. Return the index of the first match, or -1 if none. The simplest possible search loop.

Algorithm

Canonical input arr = [4, 7, 1, 9, 3, 8] with target = 9 finishes after four compares; the matching index is 3.

early exit Return the index the moment `arr[i]` equals the target. Walking past it would defeat the point.
sentinel return A no-match walk falls off the loop and returns `-1`.

Basic Implementation

basic.rb
Replay: real traced execution (multi-file project)
def linear_search(arr, target)
	i = 0
	while i < arr.length
		if arr[i] == target
			return i
		end
		i = i + 1
	end
	-1
end

arr = [4, 7, 1, 9, 3, 8]
target = 9
result = linear_search(arr, target)
puts result

  1. arr ← [4, 7, 1, 9, 3, 8]

    12arr = [4, 7, 1, 9, 3, 8]13target = 9
    values this step[4, 7, 1, 9, 3, 8]arr

  2. target ← 9

    12arr = [4, 7, 1, 9, 3, 8]13target = 914result = linear_search(arr, target)
    values this step9target[4, 7, 1, 9, 3, 8]arr

  3. result ← -1

    13target = 914result = linear_search(arr, target)15puts result
    values this step-1result9target

  4. match ← no

    3while i < arr.length4	if arr[i] == target5		return i
    values this stepnomatch0i4arr[i]9target

  5. match ← no

    3while i < arr.length4	if arr[i] == target5		return i
    values this stepnomatch1i7arr[i]9target

  6. match ← no

    3while i < arr.length4	if arr[i] == target5		return i
    values this stepnomatch2i1arr[i]9target

  7. match ← yes

    3while i < arr.length4	if arr[i] == target5		return i
    values this stepyesmatch3i9arr[i]9target

  8. result ← 3

    4if arr[i] == target5	return i6end
    values this step3result3i

  9. stdout ← 3

    14result = linear_search(arr, target)15puts result
    values this step3stdout3result

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Ruby: explicit while i < arr.length with an early return i the moment arr[i] == target. The stdlib arr.index(target) or arr.find_index { |x| x == target } would hide the walk the lesson is teaching.
  • Method signature def linear_search(arr, target) documents the array contract; the -1 sentinel mirrors the language-neutral spec rather than returning nil.
  • The replay shows the running index, the element being checked, and a match indicator on each frame.