HDOJ 5640-King's Cake【数学】

た入场券 2022-08-21 03:14 23阅读 0赞

# King's Cake #

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 0 Accepted Submission(s): 0

Problem Description

It is the king's birthday before the military parade . The ministers prepared a rectangle cake of size  n×m(1≤n,m≤10000)![Image 1][] . The king plans to cut the cake himself. But he has a strange habit of cutting cakes. Each time, he will cut the rectangle cake into two pieces, one of which should be a square cake.. Since he loves squares , he will cut the biggest square cake. He will continue to do that until all the pieces are square. Now can you tell him how many pieces he can get when he finishes.

Input

The first line contains a number  T(T≤1000)![Image 1][], the number of the testcases.  
  
For each testcase, the first line and the only line contains two positive numbers  n,m(1≤n,m≤10000)![Image 1][].

Output

For each testcase, print a single number as the answer.

Sample Input

2
    2 3
    2 5

Sample Output

3
    4
    
    hint:
    For the first testcase you can divide the into one cake of $2\times2$ , 2 cakes of $1\times 1$

Source

[BestCoder Round \#75 ][BestCoder Round _75]

解题思路：

一块蛋糕每次切下一个正方形，问能切几个正方形。

#include<stdio.h>
    #include<string.h>
    #include<algorithm>
    using namespace std;
    int main()
    {
        int T;
        scanf("%d",&T);
        while(T--)
        {
            int n,m;
            int ans=0;
            scanf("%d%d",&n,&m);
            for(;;)
            {
                
                int yy=max(n,m)/min(n,m);
                int xx=max(n,m)-min(n,m)*yy;
                ans+=yy;
                if(xx==0)
                break;
                if(max(n,m)!=min(n,m))
                {
                    if(max(n,m)==n)
                    {
                        n=n-m*yy;
                        continue;
                    }
                    if(max(n,m)==m)
                    {
                        m=m-n*yy;
                        continue;
                    }
                }
                else
                {
                    m=m-n*yy;
                }
            }    
            printf("%d\n",ans);
        }
        return 0;
    }

[Image 1]: 
[BestCoder Round _75]: http://acm.hdu.edu.cn/search.php?field=problem&key=BestCoder+Round+%2375&source=1&searchmode=source