ITPEC FE Subject B April 2025 Question 1

Leap Year Algorithm — fill in conditions for a leap year checker using modular arithmetic.

The leap year rule has three tiers, checked from most specific to least:

1. Divisible by 400 → leap year (year mod 400 = 0 → return true)
2. Divisible by 100 → NOT a leap year (year mod 100 = 0 → return false)
3. Divisible by 4 → leap year (year mod 4 = 0 → return true)
4. Otherwise → NOT a leap year (return false)

The program checks the 400 case first (slot A = year mod 400 = 0), returns true (slot B), then checks the 100 case (slot C = year mod 100 = 0) and returns false. The remaining mod 4 branch is already provided.

Verification with known years:
- 2000: 2000 mod 400 = 0 → true ✓ (leap)
- 1900: mod 400 ≠ 0, mod 100 = 0 → false ✓ (not leap)
- 2024: mod 400 ≠ 0, mod 100 ≠ 0, mod 4 = 0 → true ✓ (leap)

Why not others:
- (a) A = mod 100, B = false — would return false for year 1900 (correct) but also false for year 2000 (wrong, 2000 is a leap year)
- (b) A = mod 100, B = true — returns true for all centurial years, making the mod 400 check in C useless
- (c) Same as (a) but with ≠ in C, breaks the 400-year exception logic
- (d) A = mod 100 ≠ 0, B = true — would return true for non-centurial years without checking mod 4
- (e) A = mod 400, B = false — returns false for years divisible by 400 (wrong, they are leap years)
- (g) A = mod 400 ≠ 0 — the first check catches all years NOT divisible by 400, which is almost every year
- (h) A = mod 400 ≠ 0, B = true — returns true for nearly all years

Key rule: When implementing leap year logic, always check divisibility by 400 first, then 100, then 4 — from most specific to least specific.

AI-generated — may contain errors