"Blue Bridge Cup" Perfect Square Number (Java)

Question H

Violent enumeration, TLE, after 7 examples, you can probably get a score of 50%~70%.

import java.util.Scanner;

public class Main {
    
    
    public static void main(String[] args) {
    
    
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        for (long i = 1; i <= n; i++) {
    
    
            // 将这个数开根号之后转为整形 砍掉后面的小数位 判断是否等于这个数字
            if ((long) Math.sqrt(i * n) * (long) Math.sqrt(i * n) == i * n) {
    
    
                System.out.println(i);
                return;
            }
        }
    }
}

Correct solution : In fact, the test point of this question is to decompose the prime factors, $n\cdot x=m^2$，$What\; is\; the\; minimum\; multiplication\; of\; n$ , which can makennThe number of prime factors in n becomes even;$n$
$n=P_1^{\alpha }\times P_2^{\alpha }\times ...\times P_n^a$, if the degree of a prime factor $a_i$is an odd number, then we multiply by at least this prime factor, so this problem is to put $Decompose\; the\; prime\; factors\; of\; n$ , look at the degrees of all its terms, multiply all the prime factors with odd degrees, and that's the answer.

时间复杂度 $O(\sqrt{N})$

import java.util.Scanner;

public class Main {
    
    
    public static void main(String[] args) {
    
    
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long res = 1;
        for (long i = 2; i * i <= n; i++) {
    
    
            if (n % i == 0) {
    
    
                int s = 0;
                while (n % i == 0) {
    
     // 分解质因子求次数
                    s++; 
                    n /= i;
                }
                if (s % 2 == 1) res *= i; // 如果是奇数 则乘起来
            }
        }
        if (n > 1) res *= n; // 表示还有一个质因子 次数是1
        
        System.out.print(res);
    }
}

For $n>1$ For example,$24=2^3\times 3$ , at this time our$res=2$ , but there is also a factor of$3$ is not counted, because we arewhile(n % i == 0)in the last step of the coden /= i = 3, the last factor is left unconsidered, and the number is 1, so finally multiply by$n\; is$ enough,$res=2\times 3=6$。