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Problem $2$:

Compare between the brute force implementation of matrix multiplication and the Strassen's Algorithm.

Analyze theoretically how Strassen's Algorithm reduces the time complexity and is better than the direct divide and conquer approach and the brute force approach.

Explain how this algorithm applies divide, transform and conquer.

Implement Strassen's algorithm as a function called strassen$\_$matrix$\_$multiply that takes two $2^k{2}^k$ matrices, where kin$\{0,1,2,$dots$\}$ and returns their multiplication.

Write the following helper functions:

a$.$ matrix$\_$add: Takes $2$ matrices & returns their addition.

b$.$ matrix$\_$subtract: Takes $2$ matrices & returns their subtraction.

c$.$ Matrix$\_$display: Takes a matrix & prints it on the screen.

Hint: You can represent matrices as vectors or $2$d arrays.

Compare between the brute force and the Strassen's implementation by calculating the number of multiplications for different n$($powers of $2)$ sizes of randomly initialized matrices. Save the results in an excel file.

Plot the curve to represent the difference between both implementations.