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?
1 #include <iostream>
2 using namespace std;
3
4 int main()
5 {
6 int sum = 1;
7 for(int i=3; i<=1001; i=i+2)
8 {
9 //top-right
10 sum += i*i;
11
12 //top-left
13 sum += i*i-i+1;
14
15 //bottom-left
16 sum += i*i-2*i+2;
17
18 //bottom-right
19 sum += i*i-3*i+3;
20 }
21
22 cout << sum << endl;
23 cin.get();
24 return 0;
25 }
2 using namespace std;
3
4 int main()
5 {
6 int sum = 1;
7 for(int i=3; i<=1001; i=i+2)
8 {
9 //top-right
10 sum += i*i;
11
12 //top-left
13 sum += i*i-i+1;
14
15 //bottom-left
16 sum += i*i-2*i+2;
17
18 //bottom-right
19 sum += i*i-3*i+3;
20 }
21
22 cout << sum << endl;
23 cin.get();
24 return 0;
25 }
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