Group fractions that are equal

Question

Given a list of fractions as (numerator, denominator) pairs (denominators nonzero), group together all fractions that represent the same value. Return the groups. Do not compare every pair.

Accepted Answer

Comparing fractions by their floating-point value (num / den) is the tempting mistake: 1/3 and 2/6 should match, but rounding can make them differ in the last bit and split a group, or make two genuinely different fractions collide. The clean canonical form is the reduced fraction, computed with exact integer arithmetic. Divide numerator and denominator by their greatest common divisor, and push the sign onto the numerator so that (-1, 2) and (1, -2) reduce to the same key. On the example, (1,2), (2,4), (3,6) all reduce to key (1, 2) and (1,3), (2,6) reduce to (1, 3), giving the two groups. E…

Group fractions that are equal

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