I want to find the number of unique panels I need to cover a number of openings that have a min and max value for their width and height:

It includes 5 inputs that are used to calculate the max and min width and height. I used ChatGPT for a potential solution, unfortunately this one runs forever and eventually times out.

Any hints are highly appreciated

The data frame that gets inputed looks like this :

enter image description here

import pandas as pd
import numpy as np
from itertools import product
from datetime import datetime
from google.colab import files

def optimize_panels(df, max_lr, min_lr, max_top, min_top, bot):
    df['Widthmin'] = df['Width'] - 2 * max_lr
    df['Widthmax'] = df['Width'] - 2 * min_lr
    df['Heightmin'] = df['Height'] - 2 * max_top - bot
    df['Heightmax'] = df['Height'] - 2 * min_top - bot
    unique_ranges = df[['Widthmin', 'Widthmax', 'Heightmin', 'Heightmax']].drop_duplicates().reset_index(drop=True)
    potential_panels = list(product(unique_ranges['Widthmin'].unique(), unique_ranges['Heightmin'].unique()))
    coverage_matrix = np.zeros((len(unique_ranges), len(potential_panels)))
    for i, range_row in unique_ranges.iterrows():
        for j, panel in enumerate(potential_panels):
            if range_row['Widthmin'] <= panel[0] <= range_row['Widthmax'] and range_row['Heightmin'] <= panel[1] <= range_row['Heightmax']:
                coverage_matrix[i, j] = 1

    def find_min_covering_panels(coverage_matrix):
        covered = np.zeros(coverage_matrix.shape[0])
        selected_panels = []
        while not np.all(covered):
            coverage_counts = coverage_matrix.T @ (1 - covered)
            best_panel = np.argmax(coverage_counts)
            selected_panels.append(best_panel)
            covered = np.maximum(covered, coverage_matrix[:, best_panel])
        return selected_panels

    selected_panel_indices = find_min_covering_panels(coverage_matrix)
    selected_panel_details = [potential_panels[idx] for idx in selected_panel_indices]
    panel_to_number = {panel: idx + 1 for idx, panel in enumerate(selected_panel_details)}
    def assign_panel_number(row, panel_mapping):
        for panel, number in panel_mapping.items():
            if row['Widthmin'] <= panel[0] <= row['Widthmax'] and row['Heightmin'] <= panel[1] <= row['Heightmax']:
                return number, panel[0], panel[1]
        return None, None, None
    df['Panel Number'], df['Panel Width'], df['Panel Height'] = zip(*df.apply(lambda row: assign_panel_number(row, panel_to_number), axis=1))
    df['Joint width'] = df['Width'] - df['Panel Width']
    df['Joint height'] = df['Height'] - df['Panel Height']
    df['Panel ID'] = range(1, len(df) + 1)
    return df

def summarize_panels(df):
    panel_summary = df.groupby('Panel Number').agg(
        Usage_Count=('Panel Number', 'size'),
        Panel_Width=('Panel Width', 'first'),
        Panel_Height=('Panel Height', 'first')
    ).reset_index()
    return panel_summary.sort_values('Usage_Count', ascending=False)

def main():
    file_path = input("Enter the path to the CSV file: ")
    df = pd.read_csv(file_path)
    min_lr = float(input("Enter the minimum joint value left/right (fractional values allowed): "))
    max_lr = float(input("Enter the maximum joint value left/right (fractional values allowed): "))
    min_top = float(input("Enter the minimum joint value top (fractional values allowed): "))
    max_top = float(input("Enter the maximum joint value top (fractional values allowed): "))
    bot = float(input("Enter the bottom offset (fractional values allowed): "))
    
    optimized_df = optimize_panels(df, max_lr, min_lr, max_top, min_top, bot)
    panel_summary = summarize_panels(optimized_df)
    
    optimized_df = optimized_df.round(3)
    panel_summary = panel_summary.round(3)

    timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
    summary_filename = f"summary_{timestamp}.csv"
    panels_filename = f"panels_{timestamp}.csv"

    panel_summary.to_csv(summary_filename, index=False)
    optimized_df[['Panel ID', 'Panel Number', 'Width', 'Height', 'Widthmin', 'Widthmax', 'Heightmin', 'Heightmax', 'Panel Width', 'Panel Height', 'Joint width', 'Joint height']].to_csv(panels_filename, index=False)
    
    files.download(summary_filename)
    files.download(panels_filename)
    print("Optimization completed. Files are downloaded to your local machine.")

if __name__ == "__main__":
    main()