[算法学习]欧几里德——求最大公约数

a和b的最大公约数

d = gcd(a,b) = gcd(b, a mod b) 当（a mod b） =0时， b极为所求。

同时， d=a*x+b*y（x，y为整数）；

代码如下：

#include<stdio.h>

long gcd(long a, long b, int* x, int* y)
{
	int t;
	long tmp;
	if(b==0)
	{
		*x=1; *y=0;
		return a;
	}
	else
	{
		tmp = gcd(b, a % b, x, y);
		t=*x; *x=*y; *y=t-(a/b)**y;
		return tmp;
	}

}
long a,b;
int x,y;

void main()
{
	long tmp;
 	printf("请输入a和b：");
	scanf("%ld%ld",&a,&b);
	tmp = gcd(a,b,&x,&y);
	printf("a和b的最大公约数是：%ld\n", tmp);
	printf("%ld=%ld*%d+%ld*%d\n",tmp,a,x,b,y);
}

program algorithm;

{$APPTYPE CONSOLE}

uses
  SysUtils;

{欧几里德算法———求最大公约数}
function gcd(a, b: longint; var x, y: Integer): longint;
var
  t: Integer;
begin
  if b = 0 then
  begin
    gcd := a;
    x := 1;
    y := 0;
  end
  else
  begin
    gcd := gcd(b, a mod b, x, y);
    t := x;
    x := y;
    y := t - (a div b) * y;
  end;
end;

var
  a, b, tmp: longint;
  x, y: Integer;

begin
  write('请输入a，b：');
  readln(a, b);
  tmp := gcd(a, b, x, y);
  writeln(a, '和', b, '的最大公约数是：', tmp);
  writeln(tmp, '=', a, '*', x, '+', b, '*', y);
  readln;

end.

package com.number;

import java.util.Scanner;

public class MainUnit {
	int x,y;
	public static void main(String[] args) {
		MainUnit mm= new MainUnit();
		System.out.println("请输入a和b：");
		Scanner sc=new Scanner(System.in);
		long a=sc.nextLong();
		long b=sc.nextLong();
		long tmp=mm.gcd(a,b);
		System.out.println(a+"和"+b+"的最大公约数是："+ tmp);
		System.out.println(tmp+"="+a+"*"+mm.x+"+"+b+"*"+mm.y);
	}
	
	public long gcd(long a, long b)
	{
		long tmp;
		if (b==0) {
			x=1; y=0;
			return a;
		}
		else {
			tmp= gcd(b, a%b);
			int t=x;
			x=y;
			y=t-(int)(a/b)*y;
			return tmp;
		}
			
	}
}