Programming Challenge 7.8 - Lo Shu Magic Square
/* Lo Shu Magic Square - The Lo Shu Magic Square is a grid with 3 rows
and 3 columns:
15
´
***** ***** *****
* 4 * * 9 * * 2 * > 15
***** ***** *****
* 3 * * 5 * * 7 * > 15
***** ***** *****
* 8 * * 1 * * 6 * > 15
***** ***** *****
v v v ` 15
15 15 15
The Lo Shu Magic Square has the following properties:
* The grid contains the numbers 1 through 9
* The sum of each row, each column, and each diagonal all add up
to the same number.
This program uses a two dimensional array to simulate the magic square.
It uses a function that accepts a two-dimensional array as an argument,
and determines whether the array is a Lo Shu Magic Square. The function
is tested in this program. */
#include "Utility.h"
/* Global Constants: Magic number X, Magic number Y, Array size */
const int MAGIC_NUM_X = 3,
MAGIC_NUM_Y = 3,
ARR_SIZE = 3;
/* Prototype: Show menu, Show intro, Get numbers, Lo Shu Magic */
void showMenu();
void showIntro();
void getNumbers(int loShuMagic[][MAGIC_NUM_Y], int ARR_SIZE);
void isLoShu(const int loShuMagic[][MAGIC_NUM_Y], int ARR_SIZE);
int main()
{
/* Call: showMenu */
showMenu();
pauseSystem();
return 0;
}
/* **********************************************************
Definition: showMenu
This function display a menu for the user to choose from.
********************************************************** */
void showMenu()
{
/* Constant: Menu */
const int MENU = 3;
/* Array variables: Menu, Lo Shu Magic */
int choice[MENU] = { 1, 2, 3 };
int loShuMagic[MAGIC_NUM_X][MAGIC_NUM_Y] = { { 0 }, { 0 } };
/* Variable: Menu */
int menu = choice[MENU];
do
{
/* Display: The menu */
cout << "\t\tLO SHU MAGIC SQUARE\n\n"
<< "Please select one of the following menu-items:\n\n"
<< " *1: View Introduction\n"
<< " *2: Enter Numbers\n"
<< " *3: Quit.\n\n"
<< "Your choice: ";
cin >> menu;
/* Validate: Input */
while (menu < 1 || menu > 3)
{
cout << "\nYou made an invalid menu selection!\n"
<< "Your choice: ";
cin >> menu;
}
/* Call: showIntro, showMenu, getNumbers, isLoShu*/
switch (menu)
{
case 1:
showIntro();
showMenu();
break;
case 2:
getNumbers(loShuMagic, ARR_SIZE);
isLoShu(loShuMagic, ARR_SIZE);
break;
case 3:
cout << "\nThis program will now exit.\n\n";
break;
}
} while (menu != 3);
}
/* **********************************************************
Definition: showIntro
This function display information about this program and
its purpose.
********************************************************** */
void showIntro()
{
cout << "\n\t\tLO SHU MAGIC SQUARE\n\n"
<< "\t\t\t 15\n"
<< "\t\t\t ´\n"
<< "\t ***** ***** ***** \n"
<< "\t * 4 * * 9 * * 2 * > 15\n"
<< "\t ***** ***** ***** \n"
<< "\t * 3 * * 5 * * 7 * > 15\n"
<< "\t ***** ***** ***** \n"
<< "\t * 8 * * 1 * * 6 * > 15\n"
<< "\t ***** ***** *****\n"
<< "\t v v v ` 15\n"
<< "\t 15 15 15\n\n"
<< "This program lets you enter a series of 9 numbers,\n"
<< "which are then displayed in a row and column oder.\n"
<< "Once you have finished entering your numbers, this\n"
<< "program will then determine whether it is actually\n"
<< "a magic square or not. This depends on the following\n"
<< "factors:\n\n"
<< " * When the sum of each row (left to right) is equal\n"
<< " * When the sum of each column (top to bottom) is equal\n"
<< " * When the sum of the diagonals, left-top, right-bottom\n"
<< " and vice versa is equal\n\n"
<< "If these conditions are met it is a 'Lo Shu Magic Square'.\n\n";
}
/* **********************************************************
Definition: getNumbers
This function gets the numbers for the Lo Shu magic square
and stores these in a two dimensional array.
********************************************************** */
void getNumbers(int loShuMagic[][MAGIC_NUM_Y], int size)
{
/* Variables: Input control, User numbers, Index x,
Index y (loop counters) */
idxX = 0,
idxY = 0,
inpCtrl = 0;
/* Get the user numbers */
cout << "\nPlease enter your numbers:\n\n";
for (idxX = 0; idxX < size; idxX++)
{
cout << "Col #" << (idxX + 1) << ":"
<< setw(5) << right << " "
<< "\n-------\n";
for (idxY = 0; idxY < size; idxY++)
{
cout << "Row #" << (idxY + 1) << ":"
<< setw(5) << right << " "
<< "-*-*-*- \t";
cin >> loShuMagic[idxX][idxY];
/* If the user enters a negative number, he or she is
informed about the mistake and asked to repeat the
input */
for (inpCtrl = 0; loShuMagic[idxX][idxY] <= 0; inpCtrl++)
{
cout << "\nInput Failure: You entered an invalid number.\n"
<< "Only positive values are allowed. Please repeat\n"
<< "your input.\n\n"
<< "Row #" << (idxY + 1) << ":"
<< setw(5) << right << " "
<< "-*-*-*- \t";
cin >> loShuMagic[idxX][idxY];
}
}
cout << endl;
}
/* Display: The numbers the user has entered as a square */
cout << "This is your square of numbers:\n\n";
for (idxX = 0; idxX < size; idxX++)
{
for (idxY = 0; idxY < size; idxY++)
{
cout << setw(5) << right << loShuMagic[idxX][idxY]
<< " \t" << setw(5) << right;
}
cout << "\n\n";
}
}
/* **********************************************************
Definition: isLoShu
This function accepts the following array as its argument:
* loShuMagic[][]
It determines whether the numbers entered form a Lo Shu
magic square or not.
********************************************************** */
void isLoShu(const int loShuMagic[][MAGIC_NUM_Y], int size)
{
/* Variables: Diagonal sum, Sum X, Sum Y, Sum XY, Sum YX
(accumulators), Index X, Index Y (loop counters) */
int sumX = 0,
sumY = 0,
sumXY = 0,
sumYX = 0,
idxX = 0,
idxY = 0,
diag = 0;
/* The sums of each row and each column are determined, vertically,
horizontally and in both diagonal directions */
for (idxX = 0; idxX < size; idxX++)
{
sumX = 0;
sumY = 0;
for (idxY = 0; idxY < size; idxY++)
{
sumX += loShuMagic[idxX][idxY];
sumY += loShuMagic[idxY][idxX];
if (diag == diag + idxY + idxX - 2)
{
sumXY += loShuMagic[idxY][idxX];
}
if (idxX == idxY)
{
sumYX += loShuMagic[idxY][idxX];
}
}
}
/* This ternary operator determines whether each row, each
column, and each diagonal sum match up or not */
((sumYX == sumX) && (sumYX == sumY)) &&
((sumXY == sumX) && (sumXY == sumY)) &&
((sumX == sumY) && (sumY == sumX)) ? cout << "This is a magic square!\n\n" :
cout << "This is no magic square ...\n\n";}
Example Output:
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