算法分析求最大公约数 gcd(int x,int y) (greatest common divisor )

package chapter5;
import java.util.Scanner;
public class Gcd {

 /**
  * 计算2个数的最大公约数
  */
 public static void main(String[] args) {
  
  　　int x;
 　　 int y;
 　　 int result;
 　　 System.out.println("please in put the x:");
 　　 Scanner input=new Scanner(System.in);
  　　x=input.nextInt();
  　　System.out.println("please in put the y:");
  　　Scanner input1=new Scanner(System.in);
  　　y=input1.nextInt();
  　　result=gcd(x,y);
  　　System.out.println(x+"和"+y+"的最大公约数为:"+result);
 }

  /*
   * 方法1: The “brute force” approach
   * /  
      private static int gcd(int x, int y) {
      　 int guess = Math.min(x, y);
          while (x % guess != 0 || y % guess != 0) {
                        guess--;
                 }
          return guess;
        }
   

  
 /*
  *  方法2:
  *  Euclid’s algorithm 欧几里德算法:
  *  1. Divide x by y and compute the remainder; call that remainder r.
  *  2. If r is zero, the procedure is complete, and the answer is y.
  *  3. If r is not zero, set x equal to the old value of y, set y equal to r, and repeat the entire
  */
 　　private static int gcd(int x, int y) {
   　　　int r = x % y;
    　　  while (r != 0) {
       　　   x = y;
         　　 y = r;
          　　r = x % y;
      　　}
      　　return y;
 　　}
}

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输入2个比较大的数字: 1,000,005 and 1,000,000  来验证2个方法实现的好坏:

分析:

1. 方法1 : the brute-force algorithm requires a million steps;

2. 方法2: Euclid’s algorithm requires only two steps;

结论:

　　方法2 比 方法1 算法优化很多