문제
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.
제약 조건
2 ≤ n ≤ 10¹². The input 1 is excluded because it has no prime factor.
예시
입력:
n = 84
예상 출력:
expected = 7입력:
long long n = 84;
예상 출력:
long long expected = 7;입력:
long n = 84;
예상 출력:
long expected = 7;설명
84 = 2 × 2 × 3 × 7, so the largest prime factor is 7.
입력:
n = 13
예상 출력:
expected = 13입력:
long long n = 13;
예상 출력:
long long expected = 13;입력:
long n = 13;
예상 출력:
long expected = 13;설명
13 is prime, so it is its own largest prime factor.
접근 방법
먼저 스스로 풀어 본 뒤 힌트를 하나씩 열어 보세요.
힌트 1
Remove small prime factors first; any remaining value can only shrink, and the last factor left is the answer.
힌트 2
Test divisors only up to the square root of the current remainder, and divide it out repeatedly when it fits.
힌트 3
If the remainder is still above 1 after checking smaller factors, that remainder is prime and is the largest factor.
예상 복잡도
O(√n) time, O(1) extra space
참고 자료
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