扩展欧几里得专题（一）

HDU 1222

题解

code

//package adrui;

import java.util.*;

public class Main{
public static void main(String...args){
Scanner in = new Scanner(System.in);

int t = in.nextInt();
while(t-- > 0){
long m = in.nextLong(), n = in.nextLong();
long ans = expgcd(m, n);
String tmp = "YES";
if(ans == 1) tmp = "NO";
System.out.println(tmp);
}
in.close();
}

public static long expgcd(long a, long b){
if（b == 0）{
return a;
}
return expgcd(b, a % b);
}
}

HDU 1576

题解

code

//package adrui;

import java.util.*;

public class Main{
static long c;
public static void main(String...args){
Scanner in = new Scanner(System.in);

int t = in.nextInt();
while(t-- > 0){
c = in.nextLong();
long[] x = new long[1];/**数组实现引用*/
long[] y = new long[1];
long n = in.nextLong();
expgcd(9973, n, x, y);
y[0] = -y[0];
long ans = y[0] % 9973;
if(ans < 0) ans +=  9973;
System.out.println(ans);
}
in.close();
}

public static void expgcd(long a, long b, long[] x, long[] y){
if(b == 0){
x[0] = -c;
y[0] = 0;
return;
}
expgcd(b, a % b, y, x);
y[0] -= a / b * x[0];
}
}

HDU 2669

题解

code

/**
*@author : adrui
*/

import static java.lang.System.*;
import java.util.*;

public class Main{
static boolean f;/**静态全局*/
public static void main(String...args){
Scanner in = new Scanner(System.in);
while(in.hasNext()){
f = false;
int a = in.nextInt(), b = in.nextInt();
int[] x = new int[1];
int[] y = new int[1];
expgcd(a, b, x, y);
if(!f) out.println("sorry");
else{
int ans = x[0] % b;
if(ans < 0) ans += b;/** b = b / gcd(a, b) */
out.println(ans + " " + (1 - (long)ans * a) / b);/** ans * a 可能会爆int， 用通解也可以*/
}
}
}

public static void expgcd(int a, int b, int[] x, int[] y){
if(b == 0){
if(a == 1) {
x[0] = 1;
y[0] = 0;
f = true;/**有解标记*/
}
return;
}
expgcd(b, a % b, y, x);
y[0] -= a / b * x[0];
}
}

HDU 2504

code

/**
*@author : adrui
*/

import static java.lang.System.*;
import java.util.*;

public class Main{

public static void main(String...args){
Scanner in = new Scanner(System.in);
int n = in.nextInt();
while(n-- > 0){
int a = in.nextInt(), b = in.nextInt();
for(int i = b + b; ; i += b){
if(expgcd(a, i) == b){
out.println(i);
break;
}
}
}
}

public static int expgcd(int a, int b){
if(b == 0){
return a;
}
return expgcd(b, a % b);
}
}