https://github.com/am-ash-or-am-i/algorithm-analysis

https://github.com/am-ash-or-am-i/algorithm-analysis

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• Host: GitHub
• URL: https://github.com/am-ash-or-am-i/algorithm-analysis
• Owner: AM-ash-OR-AM-I
• Created: 2022-11-24T11:31:25.000Z (about 2 years ago)
• Default Branch: main
• Last Pushed: 2023-09-23T08:07:03.000Z (over 1 year ago)
• Last Synced: 2024-12-22T11:42:17.873Z (3 days ago)
• Language: Java
• Size: 5.6 MB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Algorithm analysis

This repository contains my notes and implementations of algorithms and data structures in CSW-II and AD-I/II.

## AD-I:

  - [Practical comparision for Karatsuba's fast multiplication](./src/divide_conquer/README.md)

  - [Sorting](./src/sorting/)

  - [Graphs](./src/csw/graph/)

  - [Greedy Algorithms](./src/greedy/)

  - [Divide and Conquer](./src/divide_and_conquer/)

  - [Dynamic Programming](./src/dp/)

## AD-II

### Randomised Algorithms

#### Quick Sort

- The worst case of quick sort is when the pivot is the smallest or the largest element in the array. This can be avoided by choosing a random pivot.

- Here are codes:

  - [Quicksort Randomised](./src/sorting/quick_sort_randomised.py)

  - [Randomised select](./src/sorting/select_randomised.py)

  - [Comparison between quicksort and randomised quicksort](./src/sorting/compare_quick_sort_randomised.py)

### Local Search

#### Metropolis Algorithm - Simulated Annealing

  - Boltzmann distribution in desmos: https://www.desmos.com/calculator/pwjyj4yoyg

### Approximation Algorithms

#### 0/1 Knapsack

- Approximation algorithms are used to find a solution to a problem that is close to the optimal solution.

  - [0/1 Knapsack optimal](./src/dp/Knapsack01.java)

  - [0/1 Knapsack approximation](./src/dp/Knapsack01.java)

### SAT

- SAT game: http://www.cril.univ-artois.fr/~roussel/satgame/satgame.php?level=2&lang=eng

- SAT solver: https://developers.google.com/optimization/cp/cp_solver

- SAT in machine learning: https://www.borealisai.com/research-blogs/tutorial-9-sat-solvers-i-introduction-and-applications/

- 

### NP vs NP-Hard

- Are there any problems that are NP but not NP-Hard and not in P?

- This is an open problem, which is equivalent to P != NP

- If proven, it would mean that there are problems that are hard to solve but easy to verify

- If (P = NP) => NP = NP-Complete, Modern cryptography would be broken because it uses SAT and other NP-hard problems.

## CSW-II codes:

  - [Code](./src/csw/)