Chess Queen(数学推断题）

最新推荐文章于 2021-12-18 14:48:30 发布

Modiz

最新推荐文章于 2021-12-18 14:48:30 发布

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分类专栏：数学+DP 基础

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本文介绍了一个关于在不同尺寸的棋盘上计算两个皇后处于互相攻击位置的方法。通过分析横纵斜线上的攻击模式，给出了适用于大规模数据集的有效算法实现。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

题意：有两个棋子，在同一行或者同一列或同一斜行中可以相互吃掉...然后给出棋盘大小，问有多少种情况...

解题思路：自己画图吧，先把横纵的算出来，在看斜行的规律...注意的是数据范围太大，必须lld，而且不知道为什么，我找到一个规律就是所有把变量加入乘法运算的都得用lld，不然只有wrong了...

Output: Standard Output

You probably know how the game of chess is played and how chess queen operates. Two chess queens are in attacking position when they are on same row, column or diagonal of a chess board. Suppose two such chess queens (one black and the other white) are placed on (2x2) chess board. They can be in attacking positions in 12 ways, these are shown in the picture below:

Figure: in a (2x2) chessboard 2 queens can be in attacking position in 12 ways

Given an (NxM) board you will have to decide in how many ways 2 queens can be in attacking position in that.

Input

Input file can contain up to 5000 lines of inputs. Each line contains two non-negative integers which denote the value of M and N (0< M, N10⁶) respectively.

Input is terminated by a line containing two zeroes. These two zeroes need not be processed.

Output

For each line of input produce one line of output. This line contains an integer which denotes in how many ways two queens can be in attacking position in an (MxN) board, where the values of M and N came from the input. All output values will fit in 64-bit signed integer.

Sample Input Output for Sample Input

2 2

100 223

2300 1000

0 0

10907100

11514134000

#include <stdio.h>
int main()
{
	long long n,m;
	while (~scanf("%lld%lld",&n,&m) && (n+m))
	{
		if (n<m) 
		{
			long long t=n;
			n=m;
			m=t;
		}
		long long t=n-m+1; 
		long long s=m*(m-1)*n+n*(n-1)*m+2*t*m*(m-1);//横纵加上斜多的 
		for (long long i=2;i<m;i++)
		s+=4*i*(i-1);
		printf("%lld\n",s); 
	} 
	return 0;
}