（Problem 28）Number spiral diagonals

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7   8   9  10
19  6   1   2  11
18  5   4   3  12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

原题大意：

从数字1开始向右顺时针方向移动，可以得到如下的5×5的螺旋：

21 22 23 24 25
20  7   8   9  10
19  6   1  2  11
18  5   4   3  12
17 16 15 14 13

可以算出对角线上数字之和是101.        1001×1001的螺旋中对角线上数字之和是多少？

//（Problem 28）Number spiral diagonals 

// Completed on Thu, 25 Jul 2013, 14:31

// Language: C

//

// 版权所有（C）acutus   (mail: [email protected]) 

// 博客地址：http://www.cnblogs.com/acutus/



#include<stdio.h>

void countSum()

{

    int i=3;

    int sum=1;

    int n=(1001+1)/2-1;

    while(n--)

    {

        int t=i*i;

        sum+=(4*t-(i-1)*6);

        i=i+2;

    }

    printf("%d\n",sum);

}



int main()

{

    countSum();

    return 0;

}

Answer:

669171001