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

Basic Implementation

basic.go
Replay: real traced execution (multi-file project)
package main

import "fmt"

func main() {
	arr := []int{3, 1, 4, 1, 5, 9, 2, 6}
	best := arr[0]
	for i := 1; i < len(arr); i++ {
		if arr[i] > best {
			best = arr[i]
		}
	}
	fmt.Println(best)
}

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

    1package main
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    8for i := 1; i < len(arr); i++ {9	if arr[i] > best {10		best = arr[i]
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    1package main
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Go builds arr with the slice literal []int{3, 1, 4, 1, 5, 9, 2, 6}; the slice header points at a backing array holding those eight integers.
  • best := arr[0] assumes the checked slice is non-empty. An empty slice would panic on that index, but this lesson's literal is fixed.
  • The source uses for i := 1; i < len(arr); i++, not a range loop, so each step reads the current value through arr[i] and Go's normal bounds checks.
  • Only the scalar best mutates. The trace records replacements at i=2 (3 -> 4), i=4 (4 -> 5), and i=5 (5 -> 9), then no replacement for 2 or 6.
  • fmt.Println(best) formats the final integer with a newline, producing 9. The slice contents are never modified.