Problem #28

The majority of the work for this went to pencil-and-paper. I made a spiral 11x11, that gave me enough terms to create mathematical formulas for each of the directions. I then make a program to just calculate each of those directions outward until it got far enough.

#include <iostream>

#define MAX_SIZE_TO_GO_TO    1001
#define REALLY_SIZE_TO_GO    (MAX_SIZE_TO_GO_TO + 1) / 2

using namespace std;

int equationOne (int);
int equationTwo (int);
int equationThree (int);
int equationFour (int);

int main()
{
    unsigned long long int total = 0;

    // Left-Down
    total += equationOne (REALLY_SIZE_TO_GO);

    // Left-Up
    total += equationFour (REALLY_SIZE_TO_GO);

    // Right-Up
    total += equationTwo (REALLY_SIZE_TO_GO);
    total--;

    // Right-Down
    total += equationThree (REALLY_SIZE_TO_GO);

    cout << total << endl;

    system("pause");
    return 0;
}

int equationOne (int terms)
{
    int totalSum = 0;

    for (unsigned int i = 1; i <= terms; i++)
        totalSum += (2*i - 2) * (2*i - 2) + 1;

    return totalSum;
}

int equationTwo (int terms)
{
    int totalSum = 0;

    for (unsigned int i = 1; i <= terms; i++)
        totalSum +=(2*i - 1) * (2*i - 1);

    return totalSum;
}

int equationThree (int terms)
{
    int placeHolder = 0;
    int totalSum = 0;

    placeHolder = 1;
    for (unsigned int i = 1; i < terms; i++)
    {
        placeHolder = placeHolder + 2 + (i - 1) * 8;
        totalSum += placeHolder;
    }

    return totalSum;
}

int equationFour (int terms)
{
    int placeHolder = 0;
    int totalSum = 0;

    placeHolder = 1;
    for (unsigned int i = 1; i < terms; i++)
    {
        placeHolder = placeHolder + (6 + (i - 1)*8);
        totalSum += placeHolder;
    }

    return totalSum;
}