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Write a program to find whether a given matrix is magic or not.
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Overview
A Magic matrix has the following properties :
a. n x n matrix of distinct element from 1 to n2 .
b. Sum of any row, column, prime diagonal and secondary diagonal is always equal.
Example :
The following matrix is a magic matrix:
4 9 2
3 5 7
8 1 6
This matrix has all the properties of a magic matrix :
· All the elements in the matrix are unique
· Sum of any row = 15
· Sum of any column = 15
· Sum of any prime diagonal =15
· Sum of any secondary diagonal = 15
Algorithm
Algorithm:
Input:
A matrix
Output:
Displays if the given matrix is a magic matrix or not
Algo:
Step 1: Start
Step 2:Defining magicMatrix function
int magicMatrix(int n, int matrix[][n])
Set primeDiagonalSum <= 0
for i = 0 to i < n repeat
Set primeDiagonalSum <= primeDiagonalSum + matrix[i][i]
Set I <= i + 1
Set secondaryDiagonalSum <= 0
for i = 0 to i < n repeat
Set secondaryDiagonalSum <= secondaryDiagonalSum + matrix[i][n-1-i]
Set i <= i + 1
Check if(primeDiagonalSum ≠ secondaryDiagonalSum)
Return 0
End if
for i = 0 to i < n repeat
Set rowSum <= 0
for j = 0 to j < n repeat
Set rowSum <= rowSum + matrix[i][j]
Set j <= j + 1
Check if(rowSum ≠ primeDiagonalSum)
Return 0
End if
Set i <= i + 1
for i = 0 to i < n repeat
Set columnSum <= 0
for j = 0 to j < n repeat
Set columnSum <= columnSum + matrix[i][j]
Set j <= j + 1
Check if(columnSum ≠ primeDiagonalSum)
Return 0
End if
Set i <= i + 1
Return 1
Step 3: Defining main function
Set int matrix[100][100] <= null
Set int i <= null
Set int j <= null
Set int n <= null
Display “Enter the Size of the Matrix”
Read n
Display “Enter the matrix”
for i = 0 to i < n repeat
for j = 0 to j < n repeat
Read matrix[i][j]
Set j <= j + 1
Set i <= i + 1
Display “The matrix is”
for i = 0 to i < n repeat
Display “\n”
for j = 0 to j < n repeat
Display matrix[i][j]
Set j <= j + 1
Set i <= i + 1
Check if(Call magicMatrix(n, matrix))
Display “The given matrix is a magic matrix”
Else
Display “The given matrix is not a magic matrix”
End if
Return 0
Step 13: Stop
Code
Applications:
a. It is used in cryptography and the creation of ciphers.
b. Also it is played as a game.
Advantage:
1. No extra space is required for this program as dynamic memory allocation is used here.
Disadvantage:
2. Time complexity is quite high, O(n*n).
Time complexity:
If the size of the matrix is n x n . Then the time complexity will be O(n*n) as we need to iterate over the row and columns of the matrix.
Space Complexity:
No extra space is required in this code, so space complexity O(1) .
