Problema
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.
Restricciones
2 ≤ n ≤ 10¹². The input 1 is excluded because it has no prime factor.
Ejemplos
Entrada:
n = 84
Salida esperada:
expected = 7Entrada:
long long n = 84;
Salida esperada:
long long expected = 7;Entrada:
long n = 84;
Salida esperada:
long expected = 7;Explicación
84 = 2 × 2 × 3 × 7, so the largest prime factor is 7.
Entrada:
n = 13
Salida esperada:
expected = 13Entrada:
long long n = 13;
Salida esperada:
long long expected = 13;Entrada:
long n = 13;
Salida esperada:
long expected = 13;Explicación
13 is prime, so it is its own largest prime factor.
Cómo abordarlo
Inténtalo primero por tu cuenta y luego abre las pistas una a una.
Pista 1
Remove small prime factors first; any remaining value can only shrink, and the last factor left is the answer.
Pista 2
Test divisors only up to the square root of the current remainder, and divide it out repeatedly when it fits.
Pista 3
If the remainder is still above 1 after checking smaller factors, that remainder is prime and is the largest factor.
Complejidad esperada
O(√n) time, O(1) extra space
Referencias
Este reto está adaptado para CodeUtility. Sigue el enunciado y las restricciones indicadas arriba.