hdu 5050 Divided Land java

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本文介绍了一种解决二进制形式的土地长度和宽度的最大公约数(GCD)问题的算法，目的是将矩形土地均匀分割成尽可能大的正方形地块，确保没有浪费。使用Java实现，通过读取输入数据并利用BigInteger类进行高效计算。

It’s time to fight the local despots and redistribute the land. There is a rectangular piece of land granted from the government, whose length and width are both in binary form. As the mayor, you must segment the land into multiple squares of equal size for the villagers. What are required is there must be no any waste and each single segmented square land has as large area as possible. The width of the segmented square land is also binary.

Input

The first line of the input is T (1 ≤ T ≤ 100), which stands for the number of test cases you need to solve.

Each case contains two binary number represents the length L and the width W of given land. (0 < L, W ≤ 2 1000)

Output

For each test case, print a line “Case #t: ”(without quotes, t means the index of the test case) at the beginning. Then one number means the largest width of land that can be divided from input data. And it will be show in binary. Do not have any useless number or space.

Sample Input

3
10 100
100 110
10010 1100

Sample Output

Case #1: 10
Case #2: 10
Case #3: 110

题意：就是2进制求gcd；有java是超级简单

import java.math.*;
import java.util.*;

public class Main
{
    public static void main(String []args)
    {

         BigInteger [] b=new BigInteger [9];
         b[0]=BigInteger.ONE;
         b[1]=b[0].add(b[0]);
         for(int i=2;i<8;i++)
             b[i]=b[i-1].add(b[0]);
         Scanner cin=new Scanner(System.in);
         int T=cin.nextInt();
         for(int i=1;i<=T;i++)
         {
             String a=cin.next();
             String c=cin.next();
             BigInteger A=new BigInteger(a,2);//将字符串a当做2进制存入大数里
             BigInteger C=new BigInteger(c,2);
             A=A.gcd(C);//直接用gcd
             String B=A.toString(2);将大数A变成2进制放入字符串；
             System.out.printf("Case #%d: ",i);
             System.out.println(B);
         }
    }
}