Number spiral diagonals Problem 28 Project Euler

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?

SOLUTION

Starting from the middle element if we add 2 

1+2=3

3+2=5

5+2=7

7+2=9

Now if we start adding 4 and proceed same way 4 times we will get next 4 elements than take six and go on you will get the result.

This is because each cycle increases two elements in a row and column and there will be 4 diagonal elements  so we add an elements 4 times.

C CODE:

#include<stdio.h>
static int a[5][5];
main()
{
int i=1,j;
int res=1;
int k=1,m=2;
while(k<=500)
{
for(j=0;j<4;j++)
{
    i=i+m;
    res=res+i;
}
m=m+2;
k++;
}
printf("%d",res);

}

TIME TAKEN

9ms

RESULT

669171001