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.
Vincoli
2 ≤ n ≤ 10¹². The input 1 is excluded because it has no prime factor.
Esempi
Input:
n = 84
Output atteso:
expected = 7Input:
long long n = 84;
Output atteso:
long long expected = 7;Input:
long n = 84;
Output atteso:
long expected = 7;Spiegazione
84 = 2 × 2 × 3 × 7, so the largest prime factor is 7.
Input:
n = 13
Output atteso:
expected = 13Input:
long long n = 13;
Output atteso:
long long expected = 13;Input:
long n = 13;
Output atteso:
long expected = 13;Spiegazione
13 is prime, so it is its own largest prime factor.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
Remove small prime factors first; any remaining value can only shrink, and the last factor left is the answer.
Suggerimento 2
Test divisors only up to the square root of the current remainder, and divide it out repeatedly when it fits.
Suggerimento 3
If the remainder is still above 1 after checking smaller factors, that remainder is prime and is the largest factor.
Complessità attesa
O(√n) time, O(1) extra space
Riferimenti
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