Problema
Return the greatest common divisor of a and b. Euclid's algorithm repeatedly replaces (a, b) with (b, a mod b) until b is 0.
Implement gcd(a, b).
Input
a: The first number. b: The second number.
Output
Return gcd(a, b). gcd(0, 0) is 0.
Vincoli
0 ≤ a, b ≤ 10¹⁸
Esempi
Esempio 1
Input:
a = 48
b = 18
Output atteso:
expected = 6Input:
long long a = 48;
long long b = 18;
Output atteso:
long long expected = 6;Input:
long a = 48;
long b = 18;
Output atteso:
long expected = 6;Spiegazione
48 mod 18 = 12, 18 mod 12 = 6, 12 mod 6 = 0, so the answer is 6.
Esempio 2
Input:
a = 17
b = 5
Output atteso:
expected = 1Input:
long long a = 17;
long long b = 5;
Output atteso:
long long expected = 1;Input:
long a = 17;
long b = 5;
Output atteso:
long expected = 1;Spiegazione
17 and 5 share no factor other than 1.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
The gcd does not change when you replace a pair with the remainder step.
Suggerimento 2
Keep swapping the roles of the two numbers until the second becomes zero.
Suggerimento 3
Be sure to handle the case where both inputs are zero.
Complessità attesa
O(log min(a, b)) time, O(1) extra space
Riferimenti
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