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

Basic Implementation

basic.js
Replay: real traced execution (multi-file project)
const arr = [3, 1, 4, 1, 5, 9, 2, 6];
let best = arr[0];
for (let i = 1; i < arr.length; i++) {
  if (arr[i] > best) {
    best = arr[i];
  }
}
console.log(best);

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

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

  2. replaced ← no

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    3for (let i = 1; i < arr.length; i++) {4  if (arr[i] > best) {5    best = arr[i];
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    1const arr = [3, 1, 4, 1, 5, 9, 2, 6];2let best = arr[0];
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • JavaScript stores the input in a const Array whose elements are Number values. The array binding is constant, but the scan does not mutate the array or allocate a replacement.
  • let best = arr[0] seeds the running maximum from the first slot, then the index loop starts at i = 1 and runs while i < arr.length.
  • Each arr[i] > best comparison uses numeric Number values from the array; when the comparison is true, best = arr[i] rebinds the local variable to that value, otherwise best stays unchanged.
  • The replay exposes i, arr[i], best, and whether replacement happened, with updates at values 4, 5, and 9. console.log(best) prints the final number 9; aside from the initial array, the scan creates no ongoing GC pressure.