King's Cake
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 736 Accepted Submission(s): 539
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) . 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), 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).
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 $1\times 1$
For the first testcase you can divide the into one cake of $2\times2$ , 2 cakes of $1\times 1$
题意：n*m的蛋糕，每次切一刀，要求有一块是正方形，问当最后所有蛋糕都是正方形时有多少块
题解：1、当长宽相等时 2、当长宽不等时要求长或宽有一个等1
#include<stdio.h>
#include<string.h>
#include<cstdio>
#include<string>
#include<math.h>
#include<algorithm>
#define LL long long
#define PI atan(1.0)*4
#define DD double
#define MAX 3000010
#define mod 100
#define dian 1.000000011
#define INF 0x3f3f3f
using namespace std;
int main()
{
LL n,m,j,i,k,sum,Max,Min;
int t;
scanf("%d",&t);
while(t--)
{
//printf("1\n");
scanf("%lld%lld",&n,&m);
if(n==m)
{
printf("1\n");
continue;
}
int x;
sum=0;k=0;
Min=min(n,m);
Max=max(n,m);
while(Max!=1&&Min!=1)
{
Max-=Min;
k++;
if(Max<Min)
{
x=Max;
Max=Min;
Min=x;
}
if(Max==Min)
break;
}
if(Max==Min)
printf("%lld\n",k+1);
else if(Max!=Min&&Min==1)
{
sum=sum+k+Max;
printf("%lld\n",sum);
}
}
return 0;
}