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#include <iostream>
#include <vector>
#include <math.h>
using namespace std;
class Square {
public:
Square(int n);
Square();
void display();
void firstNumber(vector<int>& magicSq);
void rule1(vector<int>& magicSq);
void rule2(vector<int>& magicSq);
void rule3(vector<int>& magicSq);
void print(vector<int>& magicSq);
private:
int number, entryNumber, index, temp;
int indexBegin;
int indexEnd;
};
Square::Square(int n) {//Constructor initializes default values as well as an argument for number
number = n;
entryNumber = 1;
index = 0;
indexBegin = number / 2;
indexEnd = pow(number, 2);
temp = indexBegin; //Sets temp equal to the index number of insertion
}
Square::Square() {//Default constructor
number = 3;
entryNumber = 1;
index = 0;
indexBegin = number / 2;
indexEnd = pow(number, 2);
temp = indexBegin;
}
int main() {
Square magic(5);
magic.display();
return 0;
}
void Square::display() {
//Creates a vector the size of the number squared
vector<int> magicSq;
for (int i = 0; i < indexEnd; i++) {
magicSq.push_back(i);
}
firstNumber(magicSq);
rule1(magicSq);
cout << "The size of your square is: ";
cout << magicSq.size() << endl;
print(magicSq);
}
void Square::firstNumber(vector<int>& magicSq) {
//Inputs the first number
magicSq.erase(magicSq.begin() + indexBegin);
magicSq.insert(magicSq.begin() + indexBegin, entryNumber);
entryNumber++; //Increments, meaning next number input is 2
}
void Square::rule1(vector<int>& magicSq) {
while (entryNumber <= indexEnd){
/*The first rule states that if the index minus the number is less than
* zero, then the number must be inserted at an index greater than the
* original by adding the number multiplied by the number minus one to * one.
*/
if ((temp - number) < 0) {
temp = magicSq.at(temp + (number * (number - 1) + 1));
magicSq.erase(magicSq.begin() + temp);
magicSq.insert(magicSq.begin() + temp, entryNumber);
entryNumber++;
}
rule2(magicSq);
rule3(magicSq);
}
}
void Square::rule2(vector<int>& magicSq) {
/*Second rule of the magic square. If the index minus the number is greater than zero,
* then the number must be inserted at the original index minus the number minus one.
*/
if ((temp - number) >= 0) {
temp = magicSq.at(temp - (number - 1));
magicSq.erase(magicSq.begin() + temp);
magicSq.insert(magicSq.begin() + temp, entryNumber);
entryNumber++;
}
}
void Square::rule3(vector<int>& magicSq) {
/*Third rule for the magic square. If the index number minus the number minus one is
* equal to a multiple of the original number, then the number must be placed at an
* index equal to the number times two minus one.*/
int checkLeft = temp - (number - 1);
for (int i = 1; i <= number; i++) {
if (checkLeft == number * i) {
temp = magicSq.at(temp - ((number * 2) - 1));
magicSq.erase(magicSq.begin() + temp);
magicSq.insert(magicSq.begin() + temp, entryNumber);
entryNumber++;
}
}
}
void Square::print(vector<int>& magicSq) {
//Print function to output the square
int i = 0;
for (int a = 0; a <= number; a++) {
for (i; i < (number * a); i++) {
cout << magicSq[i];
cout << " ";
}
cout << endl;
}
}
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