ITPEC IP October 2025 Question 8

Topic: Algorithm and Programming

In the program below, the function subTotal receives an integer array inputarr as an argument, returns an array arr in which the sum of all elements of original array inputarr up to that location is stored in the same location. Which of the following is the correct combination of pieces of code to be inserted into A and B in the program. Here, the size of the array inputarr is greater than 1, and elements outside the bounds of the array must not be accessed, and the array index starts at 1.

[Program]
○ integer []:subTotal(integer []: inputarr)
integer: i
integer: n ← the number of elements in inputarr
integer []: arr ← {0, ⋯, 0} // Number of elements is n.
// All the elements of the array are 0.
arr[1] ← inputarr[1]
for (increase i from A to n by 1)
arr[i] ← inputarr[i] + B
endfor
return arr
OptionAB

Explanation

A: 2, B: arr[i − 1] — arr[1] is set before the loop, so the loop starts at 2 and adds each input to the running sum stored just before it.

The sum up to position i is the sum up to i − 1 plus the element at i: arr[i] ← inputarr[i] + arr[i − 1]. For inputarr = {3, 1, 4, 2}:

  • •arr[1] = 3 (before the loop)
  • •i = 2: 1 + 3 = 4
  • •i = 3: 4 + 4 = 8
  • •i = 4: 2 + 8 = 10

The result {3, 4, 8, 10} holds every running total, and no index outside 1 to n is touched.

Answer (d)

Why not others:

  • •(a) — starting at 1 recomputes arr[1], and arr[i + 1] is still 0 when read; at i = n it reads arr[n + 1], outside the array
  • •(b) — at i = 1 it reads arr[0], which does not exist in an array whose index starts at 1
  • •(c) — arr[i + 1] has not been computed yet (it is still 0), so each element just copies the input, and at i = n it reads outside the array

Key rule: A running (prefix) sum builds each element from the one before it, arr[i] = arr[i − 1] + value[i], so the first element is set on its own and the loop starts at the second.

Algorithm and Programming · AI-written, may contain errors

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