ITPEC FE Morning April 2022 Question 8
For two non-negative integers x and y, which of the following is the result of the procedure shown in the flowchart below?
Explanation
q is the quotient and r the remainder of x ÷ y — the flowchart divides by repeated subtraction.
- •Start: q ← 0, r ← x
- •While r ≥ y: subtract y from r and add 1 to q
- •Stop when r < y
So q counts how many times y fits into x, and r is what is left, smaller than y. Example with x = 13, y = 4: r goes 13, 9, 5, 1 while q goes 0, 1, 2, 3, ending with q = 3, r = 1, and 13 = 4 × 3 + 1.
Answer (a)
Why not others:
- •(b) — the dividend is x, because r starts at x, and the divisor is y, the amount subtracted; this reverses them
- •(c) — swaps the roles: q counts the subtractions, so it is the quotient, and r holds the leftover
- •(d) — both reverses the division and swaps quotient and remainder
Key rule: In a repeated-subtraction loop, the counter is the quotient and the value left when the loop stops is the remainder.
Algorithm and Programming · AI-written, may contain errors
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