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.swift

let arr = [3, 1, 4, 1, 5, 9, 2, 6]
var total = 0
for i in arr.indices {
	total = total + arr[i]
}
print(total)

trace.swift

let arr = [3, 1, 4, 1, 5, 9, 2, 6]
var total = 0
for i in arr.indices {
	let before = total
	total = total + arr[i]
	print("step \(i): arr[\(i)]=\(arr[i]) total \(before) -> \(total)")
}
print("final total = \(total)")

Complexity

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

Implementation notes

Swift: use an explicit for i in arr.indices loop with var total = 0. The stdlib arr.reduce(0, +) is fine for production but hides the loop the lesson spec is teaching.
let arr = [3, 1, 4, 1, 5, 9, 2, 6] documents the fixed-size array contract; arr.indices gives the explicit index range 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.