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Algorithm Design\u003cbr\u003e 2024/2025 \u003c/h3\u003e\n\n---\n\u003ch3 align=\"center\"\u003e Collaborators \u0026#129309 \u003c/h2\u003e\n\n\u003cdiv align=\"center\"\u003e\n\n| Name          | Number      |\n|---------------|-------------|\n| Bárbara Gomes | up202305089 |\n| Tomás Morais  | up202304692 |\n| Tomás Silva   | up202307796 |\n\nGrade : 15,6\n\n\u003c/div\u003e\n\n# Delivery Truck Pallet Packing Optimization Tool Report\n\n- [Class Diagram](#class-diagram)  \n- [User Interface](#user-interface)  \n- [Reading the Dataset](#reading-the-dataset)  \n- [Programming Approaches](#programming-approaches)  \n  - [Brute-Force (Exhaustive)](#brute-force-exhaustive)  \n  - [Dynamic Programming](#dynamic-programming)  \n  - [Approximation (Greedy Approach)](#approximation-greedy-approach)  \n  - [Integer Linear Programming](#integer-linear-programming)  \n\n\u003ca id=\"class-diagram\"\u003e\u003c/a\u003e\n## Class Diagram\n\n\u003cdiv align=\"center\"\u003e\n\u003cimg width=\"1694\" height=\"786\" alt=\"Captura de ecrã de 2025-09-23 23-04-24\" src=\"https://github.com/user-attachments/assets/77e01a75-7744-461c-88da-635eceafa60e\" /\u003e\n\u003c/div\u003e\n\n\u003ca id=\"user-interface\"\u003e\u003c/a\u003e\n## User Interface\n\n- ✅ When starting the program, a menu is displayed with the options `Exit` (terminate program) and `Select Data Files`;  \n- ✅ If `Select Data Files` is chosen, all available datasets in the same directory as the source code are listed;  \n- ✅ After dataset selection, algorithmic approaches are shown for the user to choose from, with an option to return to `Select Data Files`;  \n- ✅ Once the algorithm runs, the solution is shown (including total profit) and an option to process another dataset is offered.  \n\n\u003ca id=\"reading-the-dataset\"\u003e\u003c/a\u003e\n## Reading the Dataset\n\nAfter the selection of the files to process:\n\n- ✅ `pair\u003cvector\u003cint\u003e, vector\u003cint\u003e\u003e extractPalletValues(const string\u0026 palletsFileName)`  \n  Opens and reads each line of the `Pallets` file, extracting each pallet’s `weight` and `profit`, storing them in vectors `weights` and `profits`. Returns a `pair` of these vectors for use in other functions.  \n\n- ✅ `int extractTruckCapacity(const string\u0026 truckFileName)`  \n  Extracts and returns the truck’s maximum weight capacity from the `Truck` file.  \n\n\u003ca id=\"programming-approaches\"\u003e\u003c/a\u003e\n## Programming Approaches\n\n\u003ca id=\"brute-force-exhaustive\"\u003e\u003c/a\u003e\n### Brute-Force (Exhaustive)\n\n- ✅ Iterates through all subsets of the given items;  \n- ✅ For each subset, calculates the total `weight` and `profit`;  \n- ✅ If the total weight is within the allowed capacity and profit is greater than the current best, updates the best subset;  \n- ✅ Outputs the indices, weights, profits of selected items, and the maximum achievable profit.  \n\n**Time Complexity:** `O(n 2^n)`  \n**Space Complexity:** `O(n)`  \n\n**Data Structures:**  \n- Input: 2 vectors (`profit`, `weight`) + integer (`maximum capacity`).  \n- Output: same 2 vectors + vector of selected indices + integer (`maximum profit`).  \n\n\u003ca id=\"dynamic-programming\"\u003e\u003c/a\u003e\n### Dynamic Programming\n\n- ✅ Takes as input profits, weights, and knapsack capacity;  \n- ✅ Builds a DP table to compute the maximum profit without exceeding capacity;  \n- ✅ Backtracks through the table to find items in the optimal solution;  \n- ✅ Outputs selected items (index, weight, profit) and total profit;  \n- ✅ More efficient than brute-force for larger inputs.  \n\n**Time Complexity:** `O(nW)`  \n**Space Complexity:** `O(nW)`  \n\n**Data Structures:**  \n- Input: 2 vectors (`profit`, `weight`) + integer (`maximum capacity`).  \n- Output: same 2 vectors + vector of selected indices + integer (`total profit`).  \n\n\u003ca id=\"approximation-greedy-approach\"\u003e\u003c/a\u003e\n### Approximation (Greedy Approach)\n\n**Greedy Algorithm A**  \n- ✅ Sort by `weight-to-profit` ratio (ascending).  \n- ✅ Select items while they fit in the truck.  \n\n**Greedy Algorithm B**  \n- ✅ Sort by `profit` (ascending).  \n- ✅ Select items while they fit in the truck.  \n\n**Approximation Algorithm**  \n- ✅ Picks the better solution between Greedy A and Greedy B.  \n\n**Time Complexity:** `O(n log n)`  \n**Space Complexity:** `O(n)`  \n\n**Data Structures:**  \n- Each greedy returns a `pair` (selected items, total profit).  \n- Approximation Algorithm returns the most profitable `pair`.  \n\n\u003ca id=\"integer-linear-programming\"\u003e\u003c/a\u003e\n### Integer Linear Programming\n\n#### Item Struct  \n- ✅ Stores `index`, `profit`, `weight`, and `profit-to-weight ratio`.  \n- ✅ Items are sorted in descending order.  \n\n#### Branch and Bound  \n- ✅ Explores item inclusion in the knapsack to maximise profit.  \n- ✅ Prunes unpromising branches.  \n\n#### knapsackILP` \n- ✅ Main function solving `0/1 knapsack` using Branch and Bound ILP approach.  \n\n**Time Complexity:** `O(n log n + 2^n)`  \n**Space Complexity:** `O(n)`  \n\n**Data Structures:**  \n- Branch and Bound: vectors of integers and `Items` (current solution + items).  \n- knapsackILP: vectors of `profits`, `weights`, current solution, and processed `Items`.  \n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftm-1-3%2Fdelivery-truck-pallet-packing-optimization-tool","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ftm-1-3%2Fdelivery-truck-pallet-packing-optimization-tool","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftm-1-3%2Fdelivery-truck-pallet-packing-optimization-tool/lists"}