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

Basic Implementation

basic.swift
Replay: real traced execution (multi-file project)
let arr = [3, 1, 4, 1, 5, 9, 2, 6]
var best = arr[0]
for i in 1..<arr.count {
	if arr[i] > best {
		best = arr[i]
	}
}
print(best)

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

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

  2. replaced ← no

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    3for i in 1..<arr.count {4	if arr[i] > best {5		best = arr[i]
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    7}8print(best)
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Swift infers arr as an [Int] from let arr = [3, 1, 4, 1, 5, 9, 2, 6]; the let binding means the array is not mutated or rebound.
  • var best = arr[0] seeds the running maximum from the first element, so the loop can start at index 1 without optional or sentinel state.
  • The scan uses for i in 1..<arr.count, visiting indexes 1 through 7 and reading each candidate with arr[i].
  • if arr[i] > best performs a strict Int comparison; equal values do not replace the current maximum.
  • Only best mutates during the loop. The trace records replacements at i=2 (3 -> 4), i=4 (4 -> 5), and i=5 (5 -> 9), with later values leaving best at 9.
  • print(best) writes the final Int as 9.