ShoupingShan / Algorithm

This repository is about three algoritms, such as strassen matrix, polynomial evaluation and Evolutionary calculation method. And C++ is used to calculate result tested in Ubuntu 18.04, Python and Matlab are used to plot the result.

Introduction

This repository is about three algoritms, such as strassen matrix, polynomial evaluation and Evolutionary calculation method. And C++ is used to calculate result tested in Ubuntu 18.04, Python and Matlab are used to plot the result.

How to Run

1. Strassen matrix

$ cd ./Matrix
$ make clean
$ make
$ ./main

2. Polynomial evaluation

$ cd ./Polynomial
$ make clean
$ make
$ ./main

3. Evolutionary calculation

$ cd ./chromosome
$ make clean
$ make
$ ./main

Details

Strassen matrix description

Matrix multiple problem can be devide into several blocks:

T(N)=O(N^2.81)

Result

    Round    1    Mode 1 costs   2e-06   seconds!
    Round    1    Mode 2 costs   1.1e-05   seconds!
    Round    1    Mode 3 costs   6e-06   seconds!
    Round    2    Mode 1 costs   4e-06   seconds!
    Round    2    Mode 2 costs   2.3e-05   seconds!
    Round    2    Mode 3 costs   2e-05   seconds!
    Round    3    Mode 1 costs   2.6e-05   seconds!
    Round    3    Mode 2 costs   0.000104   seconds!
    Round    3    Mode 3 costs   9.7e-05   seconds!
    Round    4    Mode 1 costs   0.000233   seconds!
    Round    4    Mode 2 costs   0.000771   seconds!
    Round    4    Mode 3 costs   0.000604   seconds!
    Round    5    Mode 1 costs   0.001751   seconds!
    Round    5    Mode 2 costs   0.004166   seconds!
    Round    5    Mode 3 costs   0.003808   seconds!
    Round    6    Mode 1 costs   0.012725   seconds!
    Round    6    Mode 2 costs   0.031629   seconds!
    Round    6    Mode 3 costs   0.026681   seconds!
    Round    7    Mode 1 costs   0.108709   seconds!
    Round    7    Mode 2 costs   0.245282   seconds!
    Round    7    Mode 3 costs   0.186738   seconds!
    Round    8    Mode 2 costs   2.16051   seconds!
    Round    8    Mode 3 costs   1.39623   seconds!
    Round    9    Mode 1 costs   15.8762   seconds!
    Round    9    Mode 2 costs   17.5623   seconds!
    Round    9    Mode 3 costs   9.89237   seconds!
    Round    10    Mode 1 costs   149.123   seconds!
    Round    10    Mode 2 costs   144.846   seconds!
    Round    10    Mode 3 costs   72.203   seconds!
    Round    11    Mode 1 costs   1326.32   seconds!
    Round    11    Mode 2 costs   1216.94   seconds!
    Round    11    Mode 3 costs   530.189   seconds!

Polynomial evaluation

Recursive method

begin
    1. P := a0; Q := 1;
    2. for i = 1 to n do
    3. Q = Qx
    4. P = P + aiQ
    end
end

T(N)=O(N)

Induction method

begin
    1. P := an
    2. for i = 1 to n do
    3. P = xP + an-i;
    end
end

T(N)=O(N)

Result

    Round    1    Mode    2    costs   2e-06   seconds!
    Round    1    Mode    3    costs   1e-06   seconds!
    Round    1    Mode    4    costs   1e-06   seconds!
    Round    2    Mode    1    costs   8e-06   seconds!
    Round    2    Mode    2    costs   6e-06   seconds!
    Round    2    Mode    3    costs   1e-06   seconds!
    Round    2    Mode    4    costs   1e-06   seconds!
    Round    3    Mode    1    costs   2e-05   seconds!
    Round    3    Mode    2    costs   2e-05   seconds!
    Round    3    Mode    3    costs   1e-06   seconds!
    Round    3    Mode    4    costs   1e-06   seconds!
    Round    4    Mode    1    costs   4.6e-05   seconds!
    Round    4    Mode    2    costs   4.5e-05   seconds!
    Round    4    Mode    3    costs   1e-06   seconds!
    Round    4    Mode    4    costs   2e-06   seconds!
    Round    5    Mode    1    costs   8.2e-05   seconds!
    Round    5    Mode    2    costs   8.2e-05   seconds!
    Round    5    Mode    3    costs   2e-06   seconds!
    Round    5    Mode    4    costs   2e-06   seconds!
    Round    6    Mode    1    costs   0.000188   seconds!
    Round    6    Mode    2    costs   0.000188   seconds!
    Round    6    Mode    3    costs   2e-06   seconds!
    Round    6    Mode    4    costs   3e-06   seconds!
    Round    7    Mode    1    costs   0.000338   seconds!
    Round    7    Mode    2    costs   0.000338   seconds!
    Round    7    Mode    3    costs   2e-06   seconds!
    Round    7    Mode    4    costs   3e-06   seconds!
    Round    8    Mode    1    costs   0.000554   seconds!
    Round    8    Mode    2    costs   0.000532   seconds!
    Round    8    Mode    3    costs   3e-06   seconds!
    Round    8    Mode    4    costs   4e-06   seconds!
    Round    9    Mode    1    costs   0.224067   seconds!
    Round    9    Mode    2    costs   0.224445   seconds!
    Round    9    Mode    3    costs   6.4e-05   seconds!
    Round    9    Mode    4    costs   9.6e-05   seconds!
    Round    10    Mode    1    costs   0.900165   seconds!
    Round    10    Mode    2    costs   0.903975   seconds!
    Round    10    Mode    3    costs   9.3e-05   seconds!
    Round    10    Mode    4    costs   0.00016   seconds!
    Round    11    Mode    1    costs   5.61629   seconds!
    Round    11    Mode    2    costs   5.5996   seconds!
    Round    11    Mode    3    costs   0.000229   seconds!
    Round    11    Mode    4    costs   0.000401   seconds!
    Round    12    Mode    1    costs   22.4098   seconds!
    Round    12    Mode    2    costs   22.4182   seconds!
    Round    12    Mode    3    costs   0.00047   seconds!
    Round    12    Mode    4    costs   0.000801   seconds!

Evolutionary calculation

Output

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