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

Basic Implementation

basic.php
Replay: real traced execution (multi-file project)
<?php
$arr = [3, 1, 4, 1, 5, 9, 2, 6];
$best = $arr[0];
for ($i = 1; $i < count($arr); $i++) {
	if ($arr[$i] > $best) {
		$best = $arr[$i];
	}
}
echo $best . "\n";

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

    1<?php2$arr = [3, 1, 4, 1, 5, 9, 2, 6];
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    4for ($i = 1; $i < count($arr); $i++) {5	if ($arr[$i] > $best) {6		$best = $arr[$i];
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    8}9echo $best . "\n";
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • $arr is a PHP array literal with the pinned values [3, 1, 4, 1, 5, 9, 2, 6].
  • $best = $arr[0] seeds the running maximum with 3 before the loop starts.
  • The scan uses an indexed for loop: $i = 1; $i < count($arr); $i++, so each later element is read as $arr[$i].
  • The array is never mutated; only $best and $i change during the scan.
  • The update condition is strict greater-than: if ($arr[$i] > $best) { $best = $arr[$i]; }.
  • The trace shows replacements at i = 2 (4), i = 4 (5), and i = 5 (9); later values 2 and 6 do not replace it.
  • echo $best . "\n"; prints the final scalar value 9 with a newline.