HDU 5100 Chessboard 用 k × 1 的矩形覆盖 n × n 的正方形棋盘

Posted 2020-09-27 gavanwanggw

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Chessboard

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 335    Accepted Submission(s): 168

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

 

Source

BestCoder Round #17

 

用 k × 1 的小矩形覆盖一个 n × n 的正方形棋盘，问正方形棋盘最多能被覆盖多少。

规律就是：假设n<k。肯定不行。

定义mod=n%k;

假设(mod<=k/2),结果为：n*n-mod*mod；

否则结果为：n*n-(k-mod)*(k-mod)；

点此证明

//0MS	228K
#include<stdio.h>
int main()
{
    int t,n,k;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&k);
        if(n<k){printf("0\n");continue;}
        int mod=n%k;
        if(mod<=k/2)printf("%d\n",n*n-mod*mod);
        else printf("%d\n",n*n-(k-mod)*(k-mod));
    }
    return 0;
}