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.cs

using System;

class Program {
	static void Main() {
		int[] arr = new int[] { 3, 1, 4, 1, 5, 9, 2, 6 };
		int total = 0;
		for (int i = 0; i < arr.Length; i++) {
			total = total + arr[i];
		}
		Console.WriteLine(total);
	}
}

trace.cs

using System;

class Program {
	static void Main() {
		int[] arr = new int[] { 3, 1, 4, 1, 5, 9, 2, 6 };
		int total = 0;
		for (int i = 0; i < arr.Length; i++) {
			int before = total;
			total = total + arr[i];
			Console.WriteLine(
				$"step {i}: arr[{i}]={arr[i]} total {before} -> {total}");
		}
		Console.WriteLine($"final total = {total}");
	}
}

Complexity

Time: O(n)
Space: O(1)

Implementation notes

C#: use the explicit for (int i = 0; i < arr.Length; i++) loop with int total = 0;. LINQ's arr.Sum() is fine for production but hides the loop the lesson spec is teaching.
int[] arr = new int[] { 3, 1, 4, 1, 5, 9, 2, 6 }; documents the fixed-size array contract; arr.Length gives the explicit count without leaning on a helper that hides the iteration.
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.