a) Write a C++ program that uses a 3 3 array and randomly places each integer fr

Question

a) Write a C++ program that uses a 3 3 array and randomly places each integer from 1 to 9 into one of the nine squares. Then, the program calculates the magic number by adding all the numbers in the array and then dividing the sum by 3. Finally, the program outputs the number of times a magic square occurred. Your program must contain the following functions:

Function fillBoard that randomly fills the array with numbers from 1 to 9 placed randomly;

Function isMagic that determines if the array is a magic square;

Function showBoard that prints out the array that is found to be a magic square.

Explanation / Answer

Solution:

code:

#include <iostream>
#include <time.h>
#include <fstream>

#define N 3

using namespace std;

//Function that checks for row totals
int checkRows(int **matrix, int total)
{
    int i, j, sum = 0, cnt = 0;

    //Iterating over rows
    for(i=0; i<N; i++)
    {
        sum = 0;

        //Iterating over columns
        for(j=0; j<N; j++)
        {
            //Finding row sum
            sum += matrix[i][j];
        }

        //If row sum is equal to total, increment counter
        if(sum == total)
            cnt++;
    }

    //If all rows produces actual total, return 1 (Pass)
    if(cnt == N)
        return 1;
    else
        //Fail
        return 0;
}

//Function that checks for column totals
int checkColumns(int **matrix, int total)
{
    int i, j, sum = 0, cnt = 0;

    //Iterating over rows
    for(i=0; i<N; i++)
    {
        sum = 0;

        //Iterating over columns
        for(j=0; j<N; j++)
        {
            //Finding column sum
            sum += matrix[j][i];
        }

        //If row sum is equal to total, increment counter
        if(sum == total)
            cnt++;
    }

    //If all columns produces actual total, return 1 (Pass)
    if(cnt == N)
        return 1;
    else
        //Fail
        return 0;
}

//Function that checks for primary diagonal total
int checkprimaryDiagonal1(int **matrix, int total)
{
    int i, j, sum = 0;

    //Iterating over rows
    for(i=0; i<N; i++)
    {
        //Iterating over columns
        for(j=0; j<N; j++)
        {
            //Handling primary diagonal elements
            if(i==j)
                //Finding column sum
                sum += matrix[i][j];
        }
    }

    //If sum is equal to total
    if(sum == total)
        //Pass
        return 1;
    else
        //Fail
        return 0;
}

//Function that checks for primary diagonal2 total
int checkprimaryDiagonal2(int **matrix, int total)
{
    int i, j, sum = 0;

    //Iterating over rows
    for(i=0,j=N-1; i<N && j>-1; i++, j--)
    {
        //Finding column sum
        sum += matrix[i][j];
    }

    //If sum is equal to total
    if(sum == total)
        //Pass
        return 1;
    else
        //Fail
        return 0;
}

//Function that gets magic number from given matrix
int getMagicNumber(int **matrix)
{
    int i, j, sum=0;

    //Iterating over rows
    for(i=0; i<N; i++)
    {
        //Iterating over columns
        for(j=0; j<N; j++)
        {
            //Finding sum
            sum += matrix[i][j];
        }
    }

    //Return magic number
    return (sum/N);
}

//Filling array with random values
void fillArray(int **matrix)
{
    int i, j;

    //Iterating over rows
    for(i=0; i<N; i++)
    {
        //Iterating over columns
        for(j=0; j<N; j++)
        {
            //Generating a random number
            matrix[i][j] = rand()%9 + 1;
        }
    }
}

//Displaying array
void showBoard(int **matrix)
{
    int i, j;

    //Iterating over rows
    for(i=0; i<N; i++)
    {
        //Iterating over columns
        for(j=0; j<N; j++)
        {
            //Displaying matrix element
            cout << matrix[i][j] << " ";
        }

        cout << " ";
    }
}

//Checking for magic
bool isMagic(int **square, int magic)
{
    //Checking for magic
    if( (checkRows(square, magic) == 1) && (checkColumns(square, magic) == 1) && (checkprimaryDiagonal1(square, magic) == 1) && (checkprimaryDiagonal2(square, magic) == 1) )
    {
        return true;
    }
    else
    {
        return false;
    }
}

//Main function
int main()
{
    int i, cnt=0, magic;

    //Initializing random number
    srand(time(NULL));

    //Creating dynamic array of size N
    int** square = new int*[N];

    //Allocating memory
    for(i = 0; i < N; ++i)
    {
        square[i] = new int[N];
    }

    //Iterating for 1000 times
    for(i=1; i<=1000; i++)
    {
        //Filling matrix
        fillArray(square);

        //Getting magic number
        magic = getMagicNumber(square);

        //Checking for magic square
        if(isMagic(square, magic))
        {
            cout << " Following Matrix is a magic square: " ;

            //Displaying board
            showBoard(square);

            //Incrementing count
            cnt += 1;
        }
    }

    if(cnt == 0)
    {
        cout << " No Magic Squares generated.... ";
    }

    cout << " ";
    return 0;
}

I hope this helps, if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.