01背包问题 动态规划

很有意思的问题。

写了点代码 C#实现

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Net.Mime.MediaTypeNames;

namespace Package
{
    public class Item
    {
        public int weight;
        public int value;

        public Item(int w, int val) 
        {
            weight = w;
            value = val;
        }
    }

    public class Problem
    {
        //背包容量
        int content;
        int item_cnt;
        Item[] items;
        int[,] dps;

        public Problem()
        {
        }

        public void Init()
        {
            Console.Write("请输入背包容量(正整数):");
            string con = Console.ReadLine();
            while (!int.TryParse(con, out content) || content < 0) 
            {
                Console.Write("输入错误，请输入背包容量(正整数):");
                con = Console.ReadLine();
            }

            Console.Write("请输入物品数量(正整数):");
            con = Console.ReadLine();
            while (!int.TryParse(con, out item_cnt) || item_cnt < 0)
            {
                Console.Write("输入错误，请输入物品数量(正整数):");
                con = Console.ReadLine();
            }

            items = new Item[item_cnt];
            int temp_weight = 0, temp_val = 0;
            for (int idx  = 0; idx < items.Length; idx++) 
            {
                Console.Write("请输入物品{0}重量(正整数):", idx+1);
                con = Console.ReadLine();
                while (!int.TryParse(con, out temp_weight) || temp_weight < 0)
                {
                    Console.Write("输入错误，请输入物品{0}重量(正整数):", idx + 1);
                    con = Console.ReadLine();
                }

                Console.Write("请输入物品{0}价值(正整数):", idx + 1);
                con = Console.ReadLine();
                while (!int.TryParse(con, out temp_val) || temp_val < 0)
                {
                    Console.Write("输入错误，请输入物品{0}价值(正整数):", idx + 1);
                    con = Console.ReadLine();
                }

                items[idx] = new Item(temp_weight, temp_val);
            }
        }

        public void Display()
        {
            Console.WriteLine("========问题信息========");
            Console.WriteLine("背包容量:{0} 物品数量:{1}", content, item_cnt);
            for (int idx = 0; idx < items.Length; idx++) 
            {
                Console.WriteLine("物品{0} (重量:{1} 价值:{2})", idx+1, items[idx].weight, items[idx].value);
            }
        }

        public void Cal()
        {
            int h_cnt = item_cnt + 1;
            int l_cnt = content + 1;
            dps = new int[h_cnt, l_cnt];
            for (int item = 0;item < h_cnt; item++) 
            {
                for (int cidx = 0; cidx < l_cnt; cidx++) 
                {
                    if (item == 0) 
                    {
                        dps[item, cidx] = 0;
                    }
                    else
                    {
                        if (cidx < items[item - 1].weight)//背包在此容量下压根就装不上
                        {
                            dps[item, cidx] = dps[item - 1, cidx];
                        }
                       else//能装 装和不装取最大
                        {
                            dps[item, cidx] = Math.Max(dps[item-1, cidx], dps[item-1, cidx-items[item-1].weight] + items[item-1].value);
                        }
                    }
                }
            }
        }

        public void Answer()
        {
            Console.WriteLine("========dp table========");
            for (int h = 1; h < item_cnt + 1; h++)
            {
                for (int l = 0; l < content + 1; l++)
                {
                    Console.Write("{0}   ", dps[h, l]);
                }
                Console.WriteLine();
            }

            Console.WriteLine("最大价值:{0}", dps[item_cnt, content]);
            Console.Write("背包信息:");
            Plan(item_cnt, content);
            Console.WriteLine();
        }

        void Plan(int h, int l)
        {
            if (l <= 0 || h <= 0)
                return;

            if (dps[h - 1,l] != dps[h,l])
            {
                Plan(h-1, l - items[h-1].weight);
                Console.Write("物品{0} ", h);
            }
            else
            {
                Plan(h-1, l);
            }
        }
    }

    internal class Program
    {
        static bool IsContinue()
        {
            Console.WriteLine("是否继续(Y/N)?");
            string val = Console.ReadLine();
            while (val != "Y" && val != "y" && val != "N" && val != "n")
            {
                Console.WriteLine("是否继续(Y/N)?");
                val = Console.ReadLine();
            }

            if (val == "Y" || val == "y")
            {
                return true;
            }
            else
            {
                return false;
            }
        }

        static void Main(string[] args)
        {
            Problem problem = new Problem();
            do
            {
                problem.Init();
                problem.Display();
                problem.Cal();
                problem.Answer();
            } while (IsContinue());
         }
    }
}

程序运行结果

代码和程序已经上传

代码和程序