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

The canonical input from the lesson spec is arr = [3, 1, 4, 1, 5, 9, 2, 6]. After eight passes the running total is 31.

linear scan Visit each element exactly once in index order.
running total `total` accumulates the sum as the loop advances.

Basic Implementation

basic.scala
Replay: real traced execution (multi-file project)
object Main {
	def main(args: Array[String]): Unit = {
		val arr = Array(3, 1, 4, 1, 5, 9, 2, 6)
		var total = 0
		for (i <- arr.indices) {
			total = total + arr(i)
		}
		println(total)
	}
}

  1. arr ← [3, 1, 4, 1, 5, 9, 2, 6]

    2def main(args: Array[String]): Unit = {3	val arr = Array(3, 1, 4, 1, 5, 9, 2, 6)4	var total = 0
    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr

  2. total ← 0

    3val arr = Array(3, 1, 4, 1, 5, 9, 2, 6)4var total = 05for (i <- arr.indices) {
    values this step0total[3, 1, 4, 1, 5, 9, 2, 6]arr

  3. total ← 3

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step0 → 3total0i3arr(i)

  4. total ← 4

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step3 → 4total1i1arr(i)

  5. total ← 8

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step4 → 8total2i4arr(i)

  6. total ← 9

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step8 → 9total3i1arr(i)

  7. total ← 14

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step9 → 14total4i5arr(i)

  8. total ← 23

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step14 → 23total5i9arr(i)

  9. total ← 25

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step23 → 25total6i2arr(i)

  10. total ← 31

    5for (i <- arr.indices) {6	total = total + arr(i)7}
    values this step25 → 31total7i6arr(i)

Trace Output

trace.scala
Replay: real traced execution (multi-file project)
object Main {
	def main(args: Array[String]): Unit = {
		val arr = Array(3, 1, 4, 1, 5, 9, 2, 6)
		var total = 0
		for (i <- arr.indices) {
			val before = total
			total = total + arr(i)
			println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
		}
		println(s"final total = $total")
	}
}

  1. total ← 3, stdout ← step 0: arr(0)=3 total 0 -> 3

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step3totalstep 0: arr(0)=3 total 0 -> 3stdout0before3arr(i)

  2. total ← 4, stdout ← step 1: arr(1)=1 total 3 -> 4

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step4totalstep 1: arr(1)=1 total 3 -> 4stdout3before1arr(i)

  3. total ← 8, stdout ← step 2: arr(2)=4 total 4 -> 8

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step8totalstep 2: arr(2)=4 total 4 -> 8stdout4before4arr(i)

  4. total ← 9, stdout ← step 3: arr(3)=1 total 8 -> 9

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step9totalstep 3: arr(3)=1 total 8 -> 9stdout8before1arr(i)

  5. total ← 14, stdout ← step 4: arr(4)=5 total 9 -> 14

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step14totalstep 4: arr(4)=5 total 9 -> 14stdout9before5arr(i)

  6. total ← 23, stdout ← step 5: arr(5)=9 total 14 -> 23

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step23totalstep 5: arr(5)=9 total 14 -> 23stdout14before9arr(i)

  7. total ← 25, stdout ← step 6: arr(6)=2 total 23 -> 25

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step25totalstep 6: arr(6)=2 total 23 -> 25stdout23before2arr(i)

  8. total ← 31, stdout ← step 7: arr(7)=6 total 25 -> 31

    6val before = total7total = total + arr(i)8println(s"step $i: arr($i)=${arr(i)} total $before -> $total")
    values this step31totalstep 7: arr(7)=6 total 25 -> 31stdout25before6arr(i)

  9. stdout ← final total = 31

    9	}10	println(s"final total = $total")11}
    values this stepfinal total = 31stdout31total

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Scala: use the explicit for (i <- 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 = Array(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.