学步园

Chess Queen
Input: Standard Input

Output: Standard Output

Time limit: 2.000 seconds 

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 ofM andN (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 (MxN) board, where the values ofM andN came
from the input. All output values will fit in 64-bit signed integer.

找出递推的规律，然后转化为数学公式。

#include<cstdio>

using namespace std;

int main()
{
	long long n,m,s,i,min;

	while(scanf("%lld%lld",&n,&m)==2 && n!=0 || m!=0)
	{
		if(n==0 || m==0)
			s=0;
		else	if(n==1)
			s=m*(m-1);
		else	if(m==1)
			s=n*(n-1);
		else
		{
			s=12;
			for(i=3;i<=n;i++)
			{
				s=s+4*(i-1)+6;
			}
			 
			for(i=3;i<=m;i++)
			{
				min=i<n?i:n;
				if(n>i)
					s+=(n-i)*(min-1)*4;
				s=s+2*n*(i-1)+(min-1)*min*2+n*(n-1);
			}
		}
		printf("%lld\n",s);
	}

	return 0;
}

#include<cstdio>

using namespace std;

int main()
{
	long long n,m,s,i,tmp;

	while(scanf("%lld%lld",&n,&m)==2 && n!=0 || m!=0)
	{
		if(n<m)
		{
			tmp=m;	m=n;	n=tmp;
		}
		if(n==0 || m==0)
			s=0;
		else	if(n==1)
			s=m*(m-1);
		else	if(m==1)
			s=n*(n-1);
		else
		{
			s=12+(n+1)*(n-2)*2+6*(n-2);
		 
			s=s+n*(n-1)*(m-2)+n*(m+1)*(m-2);
			for(i=3;i<=m;i++)
			{
				s+=(n-i)*(i-1)*4;
				s+=(i-1)*i*2;
			}
		}
		printf("%lld\n",s);
	}

	return 0;
}

#include<iostream>
#include<algorithm>

using namespace std;

int main()
{
	unsigned long long n,m;
	while(cin>>n>>m,n||m){
		if(n>m)
			swap(n,m);
		cout<<n*m*(n+m-2)+2*n*(n-1)*(3*m-n-1)/3<<endl;
	}

	return 0;
}