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

Basic Implementation

Basic.java
Replay: real traced execution (multi-file project)
public class Basic {
    public static void main(String[] args) {
        int[] arr = {3, 1, 4, 1, 5, 9, 2, 6};
        int best = arr[0];
        for (int i = 1; i < arr.length; i++) {
            if (arr[i] > best) {
                best = arr[i];
            }
        }
        System.out.println(best);
    }
}

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

    1public class Basic {2    public static void main(String[] args) {
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    5for (int i = 1; i < arr.length; i++) {6    if (arr[i] > best) {7        best = arr[i];
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    9    }10    System.out.println(best);11}
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Java stores the input as a primitive int[], so each arr[i] read copies an int value out of the array slot rather than returning an object reference.
  • best is seeded from arr[0], then an index loop starts at i = 1 and runs while i < arr.length. Those loop bounds keep every indexed read inside the array's checked range.
  • The update is a direct primitive comparison: when arr[i] > best, the local best variable is overwritten with that value; otherwise the array and best stay unchanged.
  • The replay exposes the scan state as i, arr[i], best, and a replaced flag, with replacements at values 4, 5, and 9. Aside from the initial array allocation, the scan uses local primitives and does not create GC pressure.