// Copyright 2010-2025 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// [START program]
// The Stigler diet problem.
// [START import]
using System;
using System.Collections.Generic;
using Google.OrTools.LinearSolver;
// [END import]

public class StiglerDiet
{
    static void Main()
    {
        // [START data_model]
        // Nutrient minimums.
        (String Name, double Value)[] nutrients =
            new[] { ("Calories (kcal)", 3.0), ("Protein (g)", 70.0),    ("Calcium (g)", 0.8),
                    ("Iron (mg)", 12.0),      ("Vitamin A (kIU)", 5.0), ("Vitamin B1 (mg)", 1.8),
                    ("Vitamin B2 (mg)", 2.7), ("Niacin (mg)", 18.0),    ("Vitamin C (mg)", 75.0) };

        (String Name, String Unit, double Price, double[] Nutrients)[] data = new[] {
            ("Wheat Flour (Enriched)", "10 lb.", 36, new double[] { 44.7, 1411, 2, 365, 0, 55.4, 33.3, 441, 0 }),
            ("Macaroni", "1 lb.", 14.1, new double[] { 11.6, 418, 0.7, 54, 0, 3.2, 1.9, 68, 0 }),
            ("Wheat Cereal (Enriched)", "28 oz.", 24.2, new double[] { 11.8, 377, 14.4, 175, 0, 14.4, 8.8, 114, 0 }),
            ("Corn Flakes", "8 oz.", 7.1, new double[] { 11.4, 252, 0.1, 56, 0, 13.5, 2.3, 68, 0 }),
            ("Corn Meal", "1 lb.", 4.6, new double[] { 36.0, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0 }),
            ("Hominy Grits", "24 oz.", 8.5, new double[] { 28.6, 680, 0.8, 80, 0, 10.6, 1.6, 110, 0 }),
            ("Rice", "1 lb.", 7.5, new double[] { 21.2, 460, 0.6, 41, 0, 2, 4.8, 60, 0 }),
            ("Rolled Oats", "1 lb.", 7.1, new double[] { 25.3, 907, 5.1, 341, 0, 37.1, 8.9, 64, 0 }),
            ("White Bread (Enriched)", "1 lb.", 7.9, new double[] { 15.0, 488, 2.5, 115, 0, 13.8, 8.5, 126, 0 }),
            ("Whole Wheat Bread", "1 lb.", 9.1, new double[] { 12.2, 484, 2.7, 125, 0, 13.9, 6.4, 160, 0 }),
            ("Rye Bread", "1 lb.", 9.1, new double[] { 12.4, 439, 1.1, 82, 0, 9.9, 3, 66, 0 }),
            ("Pound Cake", "1 lb.", 24.8, new double[] { 8.0, 130, 0.4, 31, 18.9, 2.8, 3, 17, 0 }),
            ("Soda Crackers", "1 lb.", 15.1, new double[] { 12.5, 288, 0.5, 50, 0, 0, 0, 0, 0 }),
            ("Milk", "1 qt.", 11, new double[] { 6.1, 310, 10.5, 18, 16.8, 4, 16, 7, 177 }),
            ("Evaporated Milk (can)", "14.5 oz.", 6.7, new double[] { 8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60 }),
            ("Butter", "1 lb.", 30.8, new double[] { 10.8, 9, 0.2, 3, 44.2, 0, 0.2, 2, 0 }),
            ("Oleomargarine", "1 lb.", 16.1, new double[] { 20.6, 17, 0.6, 6, 55.8, 0.2, 0, 0, 0 }),
            ("Eggs", "1 doz.", 32.6, new double[] { 2.9, 238, 1.0, 52, 18.6, 2.8, 6.5, 1, 0 }),
            ("Cheese (Cheddar)", "1 lb.", 24.2, new double[] { 7.4, 448, 16.4, 19, 28.1, 0.8, 10.3, 4, 0 }),
            ("Cream", "1/2 pt.", 14.1, new double[] { 3.5, 49, 1.7, 3, 16.9, 0.6, 2.5, 0, 17 }),
            ("Peanut Butter", "1 lb.", 17.9, new double[] { 15.7, 661, 1.0, 48, 0, 9.6, 8.1, 471, 0 }),
            ("Mayonnaise", "1/2 pt.", 16.7, new double[] { 8.6, 18, 0.2, 8, 2.7, 0.4, 0.5, 0, 0 }),
            ("Crisco", "1 lb.", 20.3, new double[] { 20.1, 0, 0, 0, 0, 0, 0, 0, 0 }),
            ("Lard", "1 lb.", 9.8, new double[] { 41.7, 0, 0, 0, 0.2, 0, 0.5, 5, 0 }),
            ("Sirloin Steak", "1 lb.", 39.6, new double[] { 2.9, 166, 0.1, 34, 0.2, 2.1, 2.9, 69, 0 }),
            ("Round Steak", "1 lb.", 36.4, new double[] { 2.2, 214, 0.1, 32, 0.4, 2.5, 2.4, 87, 0 }),
            ("Rib Roast", "1 lb.", 29.2, new double[] { 3.4, 213, 0.1, 33, 0, 0, 2, 0, 0 }),
            ("Chuck Roast", "1 lb.", 22.6, new double[] { 3.6, 309, 0.2, 46, 0.4, 1, 4, 120, 0 }),
            ("Plate", "1 lb.", 14.6, new double[] { 8.5, 404, 0.2, 62, 0, 0.9, 0, 0, 0 }),
            ("Liver (Beef)", "1 lb.", 26.8, new double[] { 2.2, 333, 0.2, 139, 169.2, 6.4, 50.8, 316, 525 }),
            ("Leg of Lamb", "1 lb.", 27.6, new double[] { 3.1, 245, 0.1, 20, 0, 2.8, 3.9, 86, 0 }),
            ("Lamb Chops (Rib)", "1 lb.", 36.6, new double[] { 3.3, 140, 0.1, 15, 0, 1.7, 2.7, 54, 0 }),
            ("Pork Chops", "1 lb.", 30.7, new double[] { 3.5, 196, 0.2, 30, 0, 17.4, 2.7, 60, 0 }),
            ("Pork Loin Roast", "1 lb.", 24.2, new double[] { 4.4, 249, 0.3, 37, 0, 18.2, 3.6, 79, 0 }),
            ("Bacon", "1 lb.", 25.6, new double[] { 10.4, 152, 0.2, 23, 0, 1.8, 1.8, 71, 0 }),
            ("Ham, smoked", "1 lb.", 27.4, new double[] { 6.7, 212, 0.2, 31, 0, 9.9, 3.3, 50, 0 }),
            ("Salt Pork", "1 lb.", 16, new double[] { 18.8, 164, 0.1, 26, 0, 1.4, 1.8, 0, 0 }),
            ("Roasting Chicken", "1 lb.", 30.3, new double[] { 1.8, 184, 0.1, 30, 0.1, 0.9, 1.8, 68, 46 }),
            ("Veal Cutlets", "1 lb.", 42.3, new double[] { 1.7, 156, 0.1, 24, 0, 1.4, 2.4, 57, 0 }),
            ("Salmon, Pink (can)", "16 oz.", 13, new double[] { 5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0 }),
            ("Apples", "1 lb.", 4.4, new double[] { 5.8, 27, 0.5, 36, 7.3, 3.6, 2.7, 5, 544 }),
            ("Bananas", "1 lb.", 6.1, new double[] { 4.9, 60, 0.4, 30, 17.4, 2.5, 3.5, 28, 498 }),
            ("Lemons", "1 doz.", 26, new double[] { 1.0, 21, 0.5, 14, 0, 0.5, 0, 4, 952 }),
            ("Oranges", "1 doz.", 30.9, new double[] { 2.2, 40, 1.1, 18, 11.1, 3.6, 1.3, 10, 1998 }),
            ("Green Beans", "1 lb.", 7.1, new double[] { 2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862 }),
            ("Cabbage", "1 lb.", 3.7, new double[] { 2.6, 125, 4.0, 36, 7.2, 9, 4.5, 26, 5369 }),
            ("Carrots", "1 bunch", 4.7, new double[] { 2.7, 73, 2.8, 43, 188.5, 6.1, 4.3, 89, 608 }),
            ("Celery", "1 stalk", 7.3, new double[] { 0.9, 51, 3.0, 23, 0.9, 1.4, 1.4, 9, 313 }),
            ("Lettuce", "1 head", 8.2, new double[] { 0.4, 27, 1.1, 22, 112.4, 1.8, 3.4, 11, 449 }),
            ("Onions", "1 lb.", 3.6, new double[] { 5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184 }),
            ("Potatoes", "15 lb.", 34, new double[] { 14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522 }),
            ("Spinach", "1 lb.", 8.1, new double[] { 1.1, 106, 0, 138, 918.4, 5.7, 13.8, 33, 2755 }),
            ("Sweet Potatoes", "1 lb.", 5.1, new double[] { 9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912 }),
            ("Peaches (can)", "No. 2 1/2", 16.8, new double[] { 3.7, 20, 0.4, 10, 21.5, 0.5, 1, 31, 196 }),
            ("Pears (can)", "No. 2 1/2", 20.4, new double[] { 3.0, 8, 0.3, 8, 0.8, 0.8, 0.8, 5, 81 }),
            ("Pineapple (can)", "No. 2 1/2", 21.3, new double[] { 2.4, 16, 0.4, 8, 2, 2.8, 0.8, 7, 399 }),
            ("Asparagus (can)", "No. 2", 27.7, new double[] { 0.4, 33, 0.3, 12, 16.3, 1.4, 2.1, 17, 272 }),
            ("Green Beans (can)", "No. 2", 10, new double[] { 1.0, 54, 2, 65, 53.9, 1.6, 4.3, 32, 431 }),
            ("Pork and Beans (can)", "16 oz.", 7.1, new double[] { 7.5, 364, 4, 134, 3.5, 8.3, 7.7, 56, 0 }),
            ("Corn (can)", "No. 2", 10.4, new double[] { 5.2, 136, 0.2, 16, 12, 1.6, 2.7, 42, 218 }),
            ("Peas (can)", "No. 2", 13.8, new double[] { 2.3, 136, 0.6, 45, 34.9, 4.9, 2.5, 37, 370 }),
            ("Tomatoes (can)", "No. 2", 8.6, new double[] { 1.3, 63, 0.7, 38, 53.2, 3.4, 2.5, 36, 1253 }),
            ("Tomato Soup (can)", "10 1/2 oz.", 7.6, new double[] { 1.6, 71, 0.6, 43, 57.9, 3.5, 2.4, 67, 862 }),
            ("Peaches, Dried", "1 lb.", 15.7, new double[] { 8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57 }),
            ("Prunes, Dried", "1 lb.", 9, new double[] { 12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257 }),
            ("Raisins, Dried", "15 oz.", 9.4, new double[] { 13.5, 104, 2.5, 136, 4.5, 6.3, 1.4, 24, 136 }),
            ("Peas, Dried", "1 lb.", 7.9, new double[] { 20.0, 1367, 4.2, 345, 2.9, 28.7, 18.4, 162, 0 }),
            ("Lima Beans, Dried", "1 lb.", 8.9, new double[] { 17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0 }),
            ("Navy Beans, Dried", "1 lb.", 5.9, new double[] { 26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0 }),
            ("Coffee", "1 lb.", 22.4, new double[] { 0, 0, 0, 0, 0, 4, 5.1, 50, 0 }),
            ("Tea", "1/4 lb.", 17.4, new double[] { 0, 0, 0, 0, 0, 0, 2.3, 42, 0 }),
            ("Cocoa", "8 oz.", 8.6, new double[] { 8.7, 237, 3, 72, 0, 2, 11.9, 40, 0 }),
            ("Chocolate", "8 oz.", 16.2, new double[] { 8.0, 77, 1.3, 39, 0, 0.9, 3.4, 14, 0 }),
            ("Sugar", "10 lb.", 51.7, new double[] { 34.9, 0, 0, 0, 0, 0, 0, 0, 0 }),
            ("Corn Syrup", "24 oz.", 13.7, new double[] { 14.7, 0, 0.5, 74, 0, 0, 0, 5, 0 }),
            ("Molasses", "18 oz.", 13.6, new double[] { 9.0, 0, 10.3, 244, 0, 1.9, 7.5, 146, 0 }),
            ("Strawberry Preserves", "1 lb.", 20.5, new double[] { 6.4, 11, 0.4, 7, 0.2, 0.2, 0.4, 3, 0 })
        };
        // [END data_model]

        // [START solver]
        // Create the linear solver with the GLOP backend.
        Solver solver = Solver.CreateSolver("GLOP");
        if (solver is null)
        {
            return;
        }
        // [END solver]

        // [START variables]
        List<Variable> foods = new List<Variable>();
        for (int i = 0; i < data.Length; ++i)
        {
            foods.Add(solver.MakeNumVar(0.0, double.PositiveInfinity, data[i].Name));
        }
        Console.WriteLine($"Number of variables = {solver.NumVariables()}");
        // [END variables]

        // [START constraints]
        List<Constraint> constraints = new List<Constraint>();
        for (int i = 0; i < nutrients.Length; ++i)
        {
            Constraint constraint =
                solver.MakeConstraint(nutrients[i].Value, double.PositiveInfinity, nutrients[i].Name);
            for (int j = 0; j < data.Length; ++j)
            {
                constraint.SetCoefficient(foods[j], data[j].Nutrients[i]);
            }
            constraints.Add(constraint);
        }
        Console.WriteLine($"Number of constraints = {solver.NumConstraints()}");
        // [END constraints]

        // [START objective]
        Objective objective = solver.Objective();
        for (int i = 0; i < data.Length; ++i)
        {
            objective.SetCoefficient(foods[i], 1);
        }
        objective.SetMinimization();
        // [END objective]

        // [START solve]
        Solver.ResultStatus resultStatus = solver.Solve();
        // [END solve]

        // [START print_solution]
        // Check that the problem has an optimal solution.
        if (resultStatus != Solver.ResultStatus.OPTIMAL)
        {
            Console.WriteLine("The problem does not have an optimal solution!");
            if (resultStatus == Solver.ResultStatus.FEASIBLE)
            {
                Console.WriteLine("A potentially suboptimal solution was found.");
            }
            else
            {
                Console.WriteLine("The solver could not solve the problem.");
                return;
            }
        }

        // Display the amounts (in dollars) to purchase of each food.
        double[] nutrientsResult = new double[nutrients.Length];
        Console.WriteLine("\nAnnual Foods:");
        for (int i = 0; i < foods.Count; ++i)
        {
            if (foods[i].SolutionValue() > 0.0)
            {
                Console.WriteLine($"{data[i].Name}: ${365 * foods[i].SolutionValue():N2}");
                for (int j = 0; j < nutrients.Length; ++j)
                {
                    nutrientsResult[j] += data[i].Nutrients[j] * foods[i].SolutionValue();
                }
            }
        }
        Console.WriteLine($"\nOptimal annual price: ${365 * objective.Value():N2}");

        Console.WriteLine("\nNutrients per day:");
        for (int i = 0; i < nutrients.Length; ++i)
        {
            Console.WriteLine($"{nutrients[i].Name}: {nutrientsResult[i]:N2} (min {nutrients[i].Value})");
        }
        // [END print_solution]

        // [START advanced]
        Console.WriteLine("\nAdvanced usage:");
        Console.WriteLine($"Problem solved in {solver.WallTime()} milliseconds");
        Console.WriteLine($"Problem solved in {solver.Iterations()} iterations");
        // [END advanced]
    }
}
// [END program]