Problème
A prime is an integer greater than 1 with no positive divisors other than 1 and itself. Find the largest prime factor of n. When n is itself prime, return n.
Implement largest_prime_factor(n).
Input
n: The integer to factor.
Output
Return its largest prime divisor.
Contraintes
2 ≤ n ≤ 10¹². The input 1 is excluded because it has no prime factor.
Exemples
Entrée :
n = 84
Sortie attendue :
expected = 7Entrée :
long long n = 84;
Sortie attendue :
long long expected = 7;Entrée :
long n = 84;
Sortie attendue :
long expected = 7;Explication
84 = 2 × 2 × 3 × 7, so the largest prime factor is 7.
Entrée :
n = 13
Sortie attendue :
expected = 13Entrée :
long long n = 13;
Sortie attendue :
long long expected = 13;Entrée :
long n = 13;
Sortie attendue :
long expected = 13;Explication
13 is prime, so it is its own largest prime factor.
Comment l'aborder
Essayez d'abord seul, puis ouvrez les indices un par un.
Indice 1
Remove small prime factors first; any remaining value can only shrink, and the last factor left is the answer.
Indice 2
Test divisors only up to the square root of the current remainder, and divide it out repeatedly when it fits.
Indice 3
If the remainder is still above 1 after checking smaller factors, that remainder is prime and is the largest factor.
Complexité attendue
O(√n) time, O(1) extra space
Références
Ce défi a été adapté pour CodeUtility. Suivez l'énoncé et les contraintes ci-dessus.