[Project Euler] Problem 28
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?
好吧,这道题我真不知道该怎样用C++编写
就说说计算思路吧
5X5的方阵计算如下:
1+(6+19)× 4 = (1+6+19)× 4 -3
= ((2*0)^2 +1 +(2*1)^2+2 +(2*2)^2 +3) *4 -3
=16*(0^2+1^2+2^2) + 4*(1+2+3) -3
好啦,平方和公式大家都知道吧 n*(n+1)*(2*n+1)/6
那1001×1001的方阵的对角和:
16*(500*501*1001)/6 + 4*(501*502)/2 -3
在python上简单的计算得到最后结果:
669171001
整个过程不超过1分钟。写这篇文章就花了3分钟