Question: programming language:c++ Lab 11 Is This Box a Magic Box? Objectives : Define a two dimensional array Understand how to traverse a two dimensional array
programming language:c++
Lab 11 Is This Box a Magic Box?
Objectives:
Define a two dimensional array
Understand how to traverse a two dimensional array
Code and run a program that processes a two dimensional array
Instructions:
A magic square is a matrix (two dimensional arrays) in which the sum of each row, sum of each column, sum of the main diagonal, and sum of the reverse diagonal are all the same value.
You are to code a program to determine if a given two-dimensional array (that will be read in from a file) is a magic square or not. The functions you will need to code are as follows:
Code a function/method for each of the following:
Read data into the matrix
Print the matrix on the screen
Sum a row given the index for that row
Sum a column given the index for that column
Sum the main diagonal
Sum the reverse diagonal
Determine if the two dimensional array is a magic square
The main method will read the size of the array outside of the while loop. Then inside the while loop it will call all the methods given above to read the data into the matrix, print the matrix, print all the row sums, print all the column sums, and print both diagonals. Then the program will determine if the matrix is a magic square and print an appropriate message. The next size should be read in at the end of the while loop. The main will continue with the next matrix in the data file, until a size of -1 is reached. See the Additional Notes on Two Dimension Arrays for more help with this assignment.
Sample Output:
The first part of the output should look similar to this:
=========
= Square 1=
=========
8 1 6
3 5 7
4 9 2
The sum of row 0 is 15
The sum of row 1 is 15
The sum of row 2 is 15
The sum of column 0 is 15
The sum of column 1 is 15
The sum of column 2 is 15
The main diagonal is 15
The other diagonal is 15
This matrix is a magic box!
Data File:
Paste everything below this block of text into a notepad file. Your input file must appear exactly as it below and include all of this data in the same file.
3
8 1 6
3 5 7
4 9 2
7
30 39 48 1 10 19 28
38 47 7 9 18 27 29
46 6 8 17 26 35 37
5 14 16 25 34 36 45
13 15 24 33 42 44 4
21 23 32 41 43 3 12
22 31 40 49 2 11 20
4
48 9 6 39
27 18 21 36
15 30 33 24
12 45 42 3
3
6 2 7
1 5 3
2 9 4
4
3 16 2 13
6 9 7 12
10 5 11 8
15 4 14 1
5
17 24 15 8 1
23 5 16 14 7
4 6 22 13 20
10 12 3 21 19
11 18 9 2 25
7
30 39 48 1 10 28 19
38 47 7 9 18 29 27
46 6 8 17 26 37 35
5 14 16 25 34 45 36
13 15 24 33 42 4 44
21 23 32 41 43 12 3
22 31 40 49 2 20 11
-1
Run:
Run the program to see if your results are correct.
Instructions for Lab 11
There are certain two-dimensional arrays that are magic. First of all, the array has to be a square array the number of rows and the number of columns must be the same, like a 4X4 or a 10X10 array. To be a magic array, a square array must have the sum of each row, the sum of each column, the sum of the main diagonal, and the sum of the reverse diagonal all equal. The main method will look like:
1.define square array and size as global
2.define a file (fin)
3.read a size from the file
4.while the size != -1
4.1 readData(fin)
4.2 printArray()
4.3 for (int i = 0; i < size; ++i)
4.3.1 print Row Total, i, sumRow(i)
4.4 for (int i = 0; i < size; ++i)
4.4.1 print Column Total, i, sumCol(i)
4.5print Main Diagonal is , mainDiagonal()
4.6print Reverse Diagonal is , reverseDiagonal()
4.7if (isMagic()
4.7.1 print Square is magic
4.8else
4.8.1print Square is not magic
4.9read a size from the file
5.close file
6.stop
To complete this lab, you must code:
void readData(ifstream fin)
void printArray()
int sumRow (int row)
{
int total = 0;
for (int j = 0; j < size; ++j)
total += square[row][j];
return total;
}
int sumCol (int col) //similar to sumRow
int mainDiagonal ()
{
int total = 0;
for (int i = 0; i < size; ++i)
total += square[i][i];
return total;
}
int reverseDiagonal() //similar to mainDiagonal but use a formula for second [i]
bool isMagic() // use reverse logic
if mainDiagonal() != reverseDiagonal(), return false
if mainDiagonal != to any of the sumRow(i), return false
if mainDiagonal != to any of the sumCol(i), return false
return true
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