Added Strassen's Matrix Multiplication in divide and conquer

[shuvojitss]

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Issue Title

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Strassen's Matrix Multiplication

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Info about the Related Issue

What's the goal of the project?
We are given with 2 matrix, our goal is to multiply them such that the time complexity of the calculation is O(n^2.81). We have used divide and conque approach to achieve the time complexity.

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Name

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Shuvojit Samanta

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GitHub ID

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shuvojitss

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shuvojitsamanta15@gmail.com

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GSSOC

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Closes

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Closes: #943

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Describe the Add-ons or Changes You've Made

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Algorithm Steps

1. Input Matrices: Given two n x n matrices, A and B.

2. Base Case:

   • If n = 1 , return the product A[0][0] x B[0][0] .

3. Divide:

   • Split each matrix into four n/2 x n/2 submatrices:

4. Compute Products:

   • Calculate the following seven products:
     1. P₁ = A₁₁ x (B₁₂ - B₂₂)
     2. P₂ = (A₁₁ + A₁₂) x B₂₂
     3. P₃ = (A₂₁ + A₂₂) x B₁₁
     4. P₄ = A₂₂ x (B₂₁ - B₁₁)
     5. P₅ = (A₁₁ + A₂₂) x (B₁₁ + B₂₂)
     6. P₆ = (A₁₂ - A₂₂) x (B₂₁ + B₂₂)
     7. P₇ = (A₁₁ - A₂₁) x (B₁₁ + B₁₂)

5. Combine Results:

   • Compute the four submatrices of the resulting product:
     • C₁₁ = P₅ + P₄ - P₂ + P₆
     • C₁₂ = P₁ + P₂
     • C₂₁ = P₃ + P₄
     • C₂₂ = P₅ + P₁ - P₃ - P₇

6. Combine Submatrices:

   • Construct the final resulting matrix C from the submatrices.

7. Output: Return the resulting matrix C .

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Type of Change

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• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Code style update (formatting, local variables)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

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How Has This Been Tested?

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I have tetsted it in all python editors and its working. I am providing a sample input output to describe it.

Sample Input:

Enter the elements of the first matrix (2x2):
5 10
15 20
Enter the elements of the second matrix (2x2):
6 8
9 2

Sample Output:

The resultant matrix is:
120     60
270     160

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Checklist

Please confirm the following:

• My code follows the guidelines of this project.
• I have performed a self-review of my own code.
• I have commented my code, particularly wherever it was hard to understand.
• I have made corresponding changes to the documentation.
• My changes generate no new warnings.
• I have added things that prove my fix is effective or that my feature works.
• Any dependent changes have been merged and published in downstream modules.

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