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?
找规律。
右上角(2n+1)^2
左上角(2n+1)^2-(2n+1)+1
左下角(2n+1)^2-4*n
右下角(2n+1)^2-6*n
2n+1<=1001 n<=500
#include <iostream>
#include <string>
using namespace std;
int main()
{
int n = 500;
long long res = 1;
for (int i = 1; i <= 500; i++)
{
int tmp = (2 * i + 1)*(2 * i + 1);
res += tmp*4 - (2 * i + 1) + 1 - 4 * i - 6 * i;
}
cout << res << endl;
system("pause");
return 0;
}
版权声明：本文博主原创文章，博客，未经同意不得转载。