HDoj Chessboard 5100(数学幾何学的法則)

Chessboard
Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 913    Accepted Submission(s): 385
Problem Description
Consider the problem of tiling an n×n chessboard by polyomino pieces that are k×1 in size; Every one of the k pieces of each polyomino tile must align exactly with one of the chessboard squares. Your task is to figure out the maximum number of chessboard squares tiled.
 
Input
There are multiple test cases in the input file.
First line contain the number of cases T (
T≤10000 ).
 
In the next T lines contain T cases , Each case has two integers n and k. (
1≤n,k≤100 )
 
Output
Print the maximum number of chessboard squares tiled.
 
Sample Input

   
   
   
   

    
    
    
    2
6 3
5 3
   
   
   
   

 
Sample Output

   
   
   
   

    
    
    
    36
24
   
   
   
   
   
   
   
   

    
    
    
    //  ：
   
   
   
   
   
   
   
   

    
    
    
        n,  k,       n*n    ，   k*1   ，           ，              。
   
   
   
   
   
   
   
   

    
    
    
    //  ：
   
   
   
   
   
   
   
   

    
    
    
                 ： m=n%k, m<=k/2 ，      n*n-m*m; m>k/2 ，      n*n-(k-m)*(k-m).
   
   
   
   
   
   
   
   

    
    
    
    
#include<stdio.h>
#include<string.h>
#include<algorithm>
#define INF 0x3f3f3f3f
#define ll long long
#define N 100010
#define M 1000000007
using namespace std;
int main()
{
	int t,n,k;
	scanf("%d",&t);
	while(t--)
	{
		int sum;
		scanf("%d%d",&n,&k);
		if(n<k)
		{
			printf("0
");
			continue;
		}
		int m=n%k;
		if(m<=k/2)
			sum=n*n-m*m;
		else
			sum=n*n-(k-m)*(k-m);
		printf("%d
",sum);
	}
	return 0;
}