Question

Write a programme to find multiplication
of matrices of order 4*4 and find the total number of comparison, total no. of
assignments, total number of multiplications and total number of addition
operations required in the programme. 

Answer 1

I write the algorithm. Please write the program in the language of your choice.  

Integer M = 4 , N  = 4 , P  = 4 ;
Integer A [0..M-1, 0.. N-1] ,  B [0..N-1, 0..P-1], AB[ 0..M-1, 0..P-1] ;

Multiply(INPUT M, N, P, A, B ; OUTPUT AB)
Begin
   Integer I, J, K ;
 
      I = 0 ;
      While (I < M) do
           K = 0 ;
           While ( K < P) do
                  AB[I, K] = 0   ;  J = 0  ;
                  while ( J < N ) do
                       AB[I, K] = AB[I, K] + A[I, J] * B[J, K]   ;
                 end while
                 K = K + 1
           end while 
           I = I + 1 ;
      end while
end program

============================
M = 4,  N = 4 , P = 4

Number of assignments = 1 + M [ 2 + P { 3 + N } ] = 1 + M (2 + 3 P +  N P )
                                        = 1 + 2 M + 3 M P + M N P = 1 + 8 + 48 + 64 = 121

Number of comparisons = M * [ P ( N + 1 ) + 1 ]  + 1 = M (PN + P + 1) + 1
                                        = M N P + M P + M + 1 = 4³ + 4² + 4 + 1 = 85

Number of additions = M [ 1 + P ( 1 + N ) ]  = M + M P + M P N = 4 + 16 + 64 = 84

Number of Multiplications = M [ P ( N )  ] = M N P = 64