求公因数的本质——扩展欧几里得算法,递归逼近,反正又是一个不打算弄懂的东西,记个模板顶多了

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import java.util.*;  
public class Main {
static long x,y,r;
public static void main(String[] args) {
Scanner sc= new Scanner(System.in);
while(sc.hasNext()){
long a=sc.nextInt();
long b=sc.nextInt();
System.out.println(gcd(a,b));
exgcd(a,b);
System.out.println(x+"*"+a+y+"*"+b+"="+r);
}
}

static long gcd (long a,long b){
return a==0?b:gcd(b%a,a);
}
static void exgcd(long a,long b){
if(b==0){
x=1;
y=0;
r=a; //r为余数
}
else{
exgcd(b,a%b);
long temp=x;
x=y;
y=temp-(a/b)*y;
}
}

}