How many times is the comparison i ≥ n performed in the following program? int…
2022
How many times is the comparison i ≥ n performed in the following program? int i = 200, n = 110; main() { while (i ≥ n) { i = i - 1; n = n + 1; } }
- A.
46
- B.
47
- C.
48
- D.
90
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Correct answer: B
Short answer: 47 comparisons.
Initial values: i = 200, n = 110 → difference (gap) = i - n = 90.
Each iteration decreases i by 1 and increases n by 1, so the gap decreases by 2 each iteration.
After m iterations the gap = 90 - 2m. The loop runs while i ≥ n, i.e., while gap ≥ 0. Find smallest m with gap < 0: 90 - 2m < 0 ⇒ m > 45, so the smallest integer m = 46. Therefore the loop executes 46 iterations.
The condition i ≥ n is evaluated once before each iteration and one final time when it fails. Total comparisons = iterations + 1 = 46 + 1 = 47.
Conclusion: The comparison i ≥ n is performed 47 times.
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