This project implements a comparison between Dynamic Programming and CollapseGPT algorithms for the 01 Knapsack Problem, based on the "Self-referentially Complete Systems Necessarily Increase Entropy" axiom.

A Python virtual environment has been set up with all required dependencies:

# Activate the environment
source knapsack_env/bin/activate

# Or use the convenience script
./activate_env.sh

The following packages are installed in the virtual environment:

• numpy (2.3.1)
• matplotlib (3.10.3)
• seaborn (0.13.2)
• pandas (2.3.1)
• tqdm (4.67.1)

See requirements.txt for the complete list with exact versions.

# Make sure virtual environment is activated
source knapsack_env/bin/activate

# Run the experiment
python knapsack_collapse_experiment.py

The experiment generates:

• knapsack_comprehensive_analysis.png - Complete visualization analysis
• case_study.png - Detailed case study
• knapsack_experiment_results.csv - Raw experimental data

The experiment runs comparisons across different problem sizes (20, 50, 100, 200, 500 items) and shows:

• Speedup: CollapseGPT is ~360x faster on average
• Approximation: Achieves ~91% of optimal value
• Scalability: O(n log n) vs O(nW) complexity
• Memory: Minimal memory usage vs O(nW) for DP

To deactivate the virtual environment:

deactivate