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.swift
Replay: real traced execution (multi-file project)
func linearSearch(_ arr: [Int], _ target: Int) -> Int {
	for i in arr.indices {
		if arr[i] == target {
			return i
		}
	}
	return -1
}

let arr = [4, 7, 1, 9, 3, 8]
let target = 9
let result = linearSearch(arr, target)
print(result)

  1. arr ← [4, 7, 1, 9, 3, 8]

    10let arr = [4, 7, 1, 9, 3, 8]11let target = 9
    values this step[4, 7, 1, 9, 3, 8]arr

  2. target ← 9

    10let arr = [4, 7, 1, 9, 3, 8]11let target = 912let result = linearSearch(arr, target)
    values this step9target[4, 7, 1, 9, 3, 8]arr

  3. result ← -1

    11let target = 912let result = linearSearch(arr, target)13print(result)
    values this step-1result9target

  4. match ← no

    2for i in arr.indices {3	if arr[i] == target {4		return i
    values this stepnomatch0i4arr[i]9target

  5. match ← no

    2for i in arr.indices {3	if arr[i] == target {4		return i
    values this stepnomatch1i7arr[i]9target

  6. match ← no

    2for i in arr.indices {3	if arr[i] == target {4		return i
    values this stepnomatch2i1arr[i]9target

  7. match ← yes

    2for i in arr.indices {3	if arr[i] == target {4		return i
    values this stepyesmatch3i9arr[i]9target

  8. result ← 3

    3if arr[i] == target {4	return i5}
    values this step3result3i

  9. stdout ← 3

    12let result = linearSearch(arr, target)13print(result)
    values this step3stdout3result

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Swift: explicit for i in arr.indices with an early return i the moment arr[i] == target. The stdlib arr.firstIndex(of:) would hide the walk the lesson is teaching.
  • Function signature func linearSearch(_ arr: [Int], _ target: Int) -> Int documents the array contract; the -1 sentinel mirrors the language-neutral spec rather than returning Int?.
  • The replay shows the running index, the element being checked, and a match indicator on each frame.