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.kt

fun main() {
	val arr = intArrayOf(3, 1, 4, 1, 5, 9, 2, 6)
	var total = 0
	for (i in arr.indices) {
		total = total + arr[i]
	}
	println(total)
}

trace.kt

fun main() {
	val arr = intArrayOf(3, 1, 4, 1, 5, 9, 2, 6)
	var total = 0
	for (i in arr.indices) {
		val before = total
		total = total + arr[i]
		println("step $i: arr[$i]=${arr[i]} total $before -> $total")
	}
	println("final total = $total")
}

Complexity

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

Implementation notes

Kotlin: use the explicit for (i in arr.indices) loop with var total = 0. The stdlib arr.sum() is fine for production but hides the loop the lesson spec is teaching.
val arr = intArrayOf(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.