IPA FE Subject B 2024 Question 1

x > y and x > z — the first branch returns x, so its condition must hold exactly when x is the largest of the three; the elseif then only has to choose between y and z.

Since the three integers are different, x is the maximum exactly when it is greater than both others: x > y and x > z. If that is false, the maximum is y or z, and elseif (y > z) picks the larger of the two, which is correct whatever x is.

All six orders of the values 1, 2, 3 were run with each option; only x > y and x > z returns 3 every time. For example, maximum(3, 1, 2) returns 3 in the first branch, and maximum(2, 1, 3) fails the condition and returns z = 3.

Answer (b)

Why not others:

• •(a) x > y — returns x without comparing it with z: maximum(2, 1, 3) returns 2
• •(c) x > y and y > z — demands the order x, y, z, so a largest x with y < z falls through: maximum(3, 1, 2) returns 2
• •(d) x > z — ignores y: maximum(2, 3, 1) returns 2
• •(e) x > z and z > y — demands z > y, so a largest x with y > z falls through: maximum(3, 2, 1) returns 2
• •(f) z > y — says nothing about x: maximum(1, 2, 3) returns 1

Key rule: In an if/elseif chain, the first condition must test the full claim its branch makes (here, "x beats every other value"); the later branches may then assume it was false.

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