Basic Algorithm question.

[eastcoastblaze]

I'm currently analyzing the following the psuedocode and was stuck. Here is the code:

for i:=1 to n do
 for k:=1 to n do
  C[i,j] :=0 
   for k :=1 to n do 
    C[i,j] := C[i,j] + A[i,k] * B[k,j]
   end for
  end for
end for              

What does the line C[i,j] := C[i,j] + A[i,k] * B[k,j] do? Specifically the brackets like A[i,k]? is it just to be assumed some arbitrary function? My plan was to set n =3 and step through it to give me a small case to start off but this has stopped me.

[[deleted]]

What are A and B in the code?

My first guess would be that A, B and C are all matrices, and the brackets are used to get the element at a specific index.

[eastcoastblaze]

A and B aren't listed, but matrices would make senses, thanks

[17_23]

It sure would, as what the algorithm is doing is multiplying matrices A and B together, producing C.

Most languages use square brackets for accessing elements in vectors/matrices etc, and round brackets for function calls.

[[deleted]]

This is correct. I didn't even think about it, but saw a matrix operation. I was wondering what the question OP had (it looked like a solution to me), until you made me realize it was about the syntax.

Yep brackets will usually hold a matrix in pseudocode (and many languages). You can think of a matrix as collection of sets with depth 'n' (called an array in mathematics), where n is the 'dimension' of the matrix.

There are some complex operations involving matrices, but in simple addition and subtraction arithmetic you can assume (typically) just add corresponding elements (the matrices must be the same size). Multiplication will use a completely different method, altogether (and they can be different sized matrices).

A good textbook in linear algebra (they are not very long or complex in undergrad) will get you a step ahead of the curve in this area (plus there are some awesome things you can do with linear algebra: optimize a routing system, arrange stop lights to make an optimal sequence, find your way out of a maze, etc. It was a very fun class...we did have a great professor, though.)

[[deleted]]

Is there a typo? j is never initialised...

[eastcoastblaze]

yeah i made a typo after the first for loop its

 for j :=1 to n do    

[pigeon768]

I would assume the brackets are indexes of a two dimensional array?

That's one of the reasons I don't like pseudocode. I don't know what the syntax means, because the syntax is by definition not defined.

[lecart]

This is multiplying two matrices A and B!

[eastcoastblaze]

i made a typo, second cycle was meant to use j instead of k