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

Basic Implementation

basic.py
Replay: real traced execution (multi-file project)
arr = [3, 1, 4, 1, 5, 9, 2, 6]
best = arr[0]
for i in range(1, len(arr)):
    if arr[i] > best:
        best = arr[i]
print(best)

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

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

  2. replaced ← no

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

    3for i in range(1, len(arr)):4    if arr[i] > best:5        best = arr[i]
    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    5        best = arr[i]6print(best)
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Python stores arr as a list object containing references to immutable int objects. best = arr[0] and later best = arr[i] rebind the local name; the list itself is never mutated.
  • The checked-in loop is index based: range(1, len(arr)) creates the replayed indexes, and each arr[i] > best comparison uses Python integer ordering.
  • No new per-iteration containers are allocated beyond the range iterator machinery, so GC is not part of the visible state. The trace shows only i, arr[i], whether best was replaced, and the final printed 9.