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

Basic Implementation

basic.cpp
Replay: real traced execution (multi-file project)
#include <iostream>
#include <unordered_map>
#include <vector>

int main() {
    std::vector<int> arr{3, 1, 4, 1, 5, 9, 2, 6};
    int best = arr[0];
    for (std::size_t i = 1; i < arr.size(); ++i) {
        if (arr[i] > best) {
            best = arr[i];
        }
    }
    std::cout << best << "\n";
    return 0;
}

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

    1#include <iostream>2#include <unordered_map>
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

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

  3. best ← 4, replaced ← yes

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

  4. replaced ← no

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

  5. best ← 5, replaced ← yes

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

  6. best ← 9, replaced ← yes

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

  7. replaced ← no

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

  8. replaced ← no

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

  9. stdout ← 9

    1#include <iostream>2#include <unordered_map>
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • In C++, the input is a std::vector<int> initialized with {3, 1, 4, 1, 5, 9, 2, 6}; the scan reads elements by index and never mutates the vector.
  • int best = arr[0] copies the first element into a scalar local. Later updates assign another int value into best, not a reference to the vector slot.
  • The loop index is std::size_t i, starts at 1, and stops at i < arr.size(), so each arr[i] access stays inside the vector bounds.
  • The comparison is the explicit integer test arr[i] > best; the trace shows replacements at i=2 (4), i=4 (5), and i=5 (9), with later values leaving best unchanged.
  • std::cout << best << "\n" writes the final 9. Visible allocation is the vector storage from the initializer list; the replayed state mutation is only the scalar best.