I wrote an algorithm, that uses baysian estimation to estimate the volumes of the individual items. Then we use backtracking to solve the knapsack problem. We assume sergey doesnt want items twice!
Below you can find the solution the algo came up with:
Discovered 60 unique item IDs across both datasets. --- Bayesian Estimation of Individual Item Volumes --- Number of unique items to estimate: 60 Number of package observations: 1000 Assumed measurement error variance (sigma_epsilon^2): 2.0 Prior for each item volume: N(mean=14.19, variance=50.0)
Estimated Volume (Posterior Mean) for each item: A1: 22.01 liters A10: 14.54 liters A11: 22.77 liters A12: 14.96 liters A13: 21.54 liters A14: 29.66 liters A15: 11.04 liters A16: 15.96 liters A17: 6.87 liters A18: 8.36 liters A19: 15.18 liters A2: 14.46 liters A20: 22.10 liters A21: 26.43 liters A22: 25.79 liters A23: 7.28 liters A24: 25.77 liters A25: 9.48 liters A26: 20.58 liters A27: 7.52 liters A28: 6.84 liters A29: 20.85 liters A3: 8.46 liters A30: 19.33 liters A31: 6.88 liters A32: 0.93 liters A33: 5.95 liters A34: 13.25 liters A35: 4.98 liters A36: 25.11 liters A37: 12.50 liters A38: 9.90 liters A39: 1.56 liters A4: 23.95 liters A40: 10.54 liters A41: 23.03 liters A42: 11.57 liters A43: 5.01 liters A44: 4.82 liters A45: 22.43 liters A46: 17.58 liters A47: 26.03 liters A48: 7.22 liters A49: 11.18 liters A5: 16.61 liters A50: 11.39 liters A51: 26.98 liters A52: 23.00 liters A53: 5.63 liters A54: 11.65 liters A55: 16.51 liters A56: 10.44 liters A57: 18.70 liters A58: 25.48 liters A59: 16.19 liters A6: 0.39 liters A60: 12.36 liters A7: 8.84 liters A8: 3.55 liters A9: 0.97 liters (Note: Items only in items.json, not packages.json, will have volumes based primarily on the prior mean.)
--- Solving Knapsack Problem --- Backpack Capacity: 40.0 liters Number of items to consider (from items.json): 60
--- Best Gift Choices for Sergey's Birthday --- Maximum Total Price Achieved: 741.00 Euros Selected Item IDs: ['A6', 'A32', 'A9', 'A39', 'A35', 'A44', 'A8', 'A38', 'A48', 'A53']
Details of Selected Items:
- Name: A6, Price: 109.00€, Est. Volume: 0.39L (ID: A6)
- Name: A32, Price: 80.00€, Est. Volume: 0.93L (ID: A32)
- Name: A9, Price: 64.00€, Est. Volume: 0.97L (ID: A9)
- Name: A39, Price: 31.00€, Est. Volume: 1.56L (ID: A39)
- Name: A35, Price: 86.00€, Est. Volume: 4.98L (ID: A35)
- Name: A44, Price: 76.00€, Est. Volume: 4.82L (ID: A44)
- Name: A8, Price: 54.00€, Est. Volume: 3.55L (ID: A8)
- Name: A38, Price: 116.00€, Est. Volume: 9.90L (ID: A38)
- Name: A48, Price: 81.00€, Est. Volume: 7.22L (ID: A48)
- Name: A53, Price: 44.00€, Est. Volume: 5.63L (ID: A53)
Total Volume of Selected Items: 39.95 liters (Max Capacity: 40.0L) Total Price of Selected Items (for verification): 741.00 Euros