Arrays and Iteration

Array Sum (Linear Scan)

Walk an array once, accumulating each element into a running total. This is the canonical single-pass linear scan and the simplest possible loop invariant: after step i, total equals the sum of arr[0..i].

Algorithm

Trace Output

basic.js 
const arr = [3, 1, 4, 1, 5, 9, 2, 6];
let total = 0;
for (let i = 0; i < arr.length; i++) {
    total = total + arr[i];
}
console.log(total);
trace.js 
const arr = [3, 1, 4, 1, 5, 9, 2, 6];
let total = 0;
for (let i = 0; i < arr.length; i++) {
    const before = total;
    total = total + arr[i];
    console.log(`step ${i}: arr[${i}]=${arr[i]} total ${before} -> ${total}`);
}
console.log(`final total = ${total}`);

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • JavaScript: use the explicit for (let i = 0; i < arr.length; i++) loop and let total. Calling arr.reduce((a, b) => a + b, 0) would hide the iteration the lesson is teaching.
  • The replay shows i, arr[i], and total before and after each addition, matching the lesson spec's state-transition table.
linear scan Visit each element exactly once in index order.
running total `total` accumulates the sum as the loop advances.