This blog contains major algorithms implemented in python needed for competitive programming or to crack interviews.

Python familiarity is needed as this is not beginner friendly.

Algorithms are implemented from the book [Competitive Programing in Python](https://www.cambridge.org/tz/universitypress/subjects/computer-science/algorithmics-complexity-computer-algebra-and-computational-g/competitive-programming-python-128-algorithms-develop-your-coding-skills?format=PB&isbn=9781108716826).

### Matrices

### 1. [Frievald's Algorithm](https://en.wikipedia.org/wiki/Freivalds%27_algorithm)

To check matrix multiplication, $AB = C$ in $O(n^2)$ instead of $O(n^3)$ by randomly choosing a vector $x$ and testing $A(Bx) = Cx$.

```
from random import randint
from sys import stdin

def readint():

  return int(stdin.readline())

def readarray(typ):

  return list(map(typ, stdin.readline().split()))

def readmatrix(n):

  M = []

  for _ in range(n):

    row = readarray(int)

    assert len(row) == n

    M.append(row)

  return M

def mult(M, v):

  n = len(M)

  return [sum(M[i][j] * v[j] for j in range(n)) for i in range(n)]

def freivalds(A, B, C):

  n = len(A)

  x = [randint(0, 1000000) for j in range(n)]

  return mult(A, mult(B, x)) == mult(C, x)

if __name__ == "__main__":

  n = readint()

  A = readmatrix(n)

  B = readmatrix(n)

  C = readmatrix(n)

  print(freivalds(A, B, C))
```

Input:

```
2      # value of n in n by n matrices
1 2    # a11 a12
3 4    # a21 a22
5 6    # b11 b12
7 8    # b21 b22
9 10   # c11 c12
11 12  # c21 c22
```

Output: False

Algorithms

Relevant Coursework: Artificial Intelligence & Machine Learning, Data Structures & Algorithms, Industrial Robotics, Graph Theory, Probability & Statistics

Created a 3D robotic arm visualization tool with six interactive control points, featuring smooth multi-axis rotations across different arm segments, and a user-friendly camera system for viewing the arm from any angle within a grid environment.

Robotic Arm Visualizer

Built an interactive pathfinding visualization tool featuring multiple algorithms (Dijkstra's, A\*, BFS, DFS) with optimized performance for a 20x20 grid system, including maze generation capabilities that ensure valid solutions.

Pathfinding Visualizer

Built a browser-based code editor that runs Python, JavaScript, and C++ code in real-time, featuring support for Python libraries like numpy and matplotlib for data visualization, along with custom error handling and interactive user input capabilities.

Code Editor

Mobile robot remotely operated and capable of detecting, picking and sorting metallic and non-metallic objects

Capstone Project


1. [Office](https://dan10ish.github.io/Office/)

2. [Galaxy Generator](https://dan10ish.github.io/Galaxy/)

3. [3-DOF Robotic Arm](https://dan10ish.github.io/RoboticArm/)

React-three-fiber

* Developed fast and efficient C/C++ control software for a robotic arm, achieving reliable performance with processing times under one millisecond

* Created a motion planning system that generated smooth movement paths and could adjust trajectories in real-time

* Built well-organized software architecture with separate modules for movement calculations and control systems, supported by thorough testing

* Implemented a data monitoring system with CSV logging and visualization tools to track and analyze system performance

* Improved system efficiency by streamlining mathematical operations and calculations

Danish

2025