UVA - 11538 Chess Queen

最新推荐文章于 2019-12-07 23:16:16 发布

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本文介绍了一道关于计算两个国际象棋皇后在N*M棋盘上处于攻击位置的方法数量的题目。通过简单的数学推导即可求解，需注意可能产生的中间数据溢出问题。

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11538 Chess Queen
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 (2 2) chess board. They can be
in attacking positions in 12 ways, these are shown in the picture below:
Figure: in a (2 2) chessboard 2 queens can be in attacking position in 12 ways
Given an (N M) board you will have to decide in how many ways 2 queens can be in attacking
position in that.
Input
Input le 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; N 106
) 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 (M N) board, where the values of M and
N came from the input. All output values will t in 64-bit signed integer.
Sample Input
2 2
100 223
2300 1000
0 0
Sample Output
12
10907100

11514134000

分析：

刘汝佳大白书里的水题。排列组合，简单数学推导就可以解决。

需要注意的是这种题可能会产生中间数据溢出，当然这个题没有这种情况。具体注意事项见大白书。

ac代码：

#include <iostream>
#include<cstdio>
#include<algorithm>
using namespace std;

int main()
{
long long n,m;
while(scanf("%lld%lld",&n,&m))
{
if(!n&&!m) break;
if(n>m) swap(n,m);
printf("%lld\n",n*m*(m+n-2)+2*n*(n-1)*(3*m-n-1)/3);
}
return 0;
}