Matrix Practice Problems

Sort the given matrix

Given a n x n matrix. The problem is to sort the given matrix in strict order. Here strict order means that the matrix is sorted in a way such that all elements in a row are sorted in increasing order and for row ‘i’, where 1 <= i <= n-1, the first element of row ‘i’ is greater than or equal to the last element of row ‘i-1’.

Examples:

Input : mat[][] = { {5, 4, 7},
                    {1, 3, 8},
                    {2, 9, 6} }
Output : 1 2 3
         4 5 6
         7 8 9

Solution

# Python program for the above approach
# driver code
v = [[5,4,7], [1,3,8], [2,9,6]]
n = len(v)
 
x = []
for i in range(n):
    for j in range(n):
        x.append(v[i][j])
 
x.sort()
k = 0
for i in range(n):
    for j in range(n):
        v[i][j] = x[k]
        k += 1
 
print("Sorted Matrix will be: ")
for i in range(n):
    for j in range(n):
        print(v[i][j], end=" ")
    print("")
 
# THIS CODE IS CONTRIBUTED BY Dhairya Gothi(dhairyagothi)

Output

Sorted Matrix Will be:

1 2 3 
4 5 6 
7 8 9 

Time Complexity: O(n2log2n), O(nn) for traversing, and O(n2log2n) for sorting the vector x, which has a size of n2. So overall time complexity is O(n2log2n). Auxiliary Space: O(nn), For vector.

Program for scalar multiplication of a matrix

Given a matrix and a scalar element k, our task is to find out the scalar product of that matrix.

Examples:

Input : mat[][] = {{2, 3}
                   {5, 4}}
        k = 5
Output : 10 15 
         25 20 
We multiply 5 with every element.

Input : 1 2 3 
        4 5 6
        7 8 9
        k = 4
Output :  4 8  12
          16 20 24
          28 32 36 
The scalar multiplication of a number k(scalar), multiply it on every entry in the matrix. and a matrix A is the matrix kA.

# Python 3 program to find the scalar 
# product of a matrix
 
# Size of given matrix
N = 3
 
def scalarProductMat( mat, k):
 
    # scalar element is multiplied 
    # by the matrix
    for i in range( N):
        for j in range( N): 
            mat[i][j] = mat[i][j] * k     
 
# Driver code
if __name__ == "__main__":
     
    mat = [[ 1, 2, 3 ],
           [ 4, 5, 6 ],
           [ 7, 8, 9 ]]
    k = 4
 
    scalarProductMat(mat, k)
 
    # to display the resultant matrix
    print("Scalar Product Matrix is : ")
    for i in range(N):
        for j in range(N):
            print(mat[i][j], end = " ")
        print()
 
# This code is contributed by dhairya

Output:

Scalar Product Matrix is : 
4 8 12 
16 20 24 
28 32 36

ime Complexity: O(n2),

Auxiliary Space: O(1), since no extra space has been taken.