Problem 28

问题描述：

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?

 

解决问题：

观察规律。

1 = 1*1

9 = 3*3

25 = 5*5

以1为原点的左上的数字都是(2*n+1)*(2*n+1) (n=0,1,2...)

 

 

public static int sum(int number){
		int total = 0;
		
		int tmp;
		for(;number>1;number-=2){
			tmp = number*number;
			total+=tmp;
			tmp-=number-1;
			total+=tmp;
			tmp-=number-1;
			total+=tmp;
			tmp-=number-1;
			total+=tmp;
			tmp-=number-1;
		}
		total += 1;
		return total;
	}