跳跃表解决01背包问题

跳跃表解决01背包问题

挺有意思的题目

看算法设计与分析有跳跃点实现，解决空间复杂度，感觉好烧脑，就实现了一下

结果

代码

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;
using System.Text;
using System.Threading.Tasks;

namespace JumpPackage
{
    //一个物品信息
    public class Item
    {
        public int weight;//重量
        public int val;//价值
        public int id;//物品编号，名字

        public Item(int w, int v, int id) 
        {
            this.weight = w;
            this.val = v;
            this.id = id;
        }
    }

    //一个背包计划
    public class Plan
    {
        public int weight;//本计划总重量
        public int val;//本计划总价值
        public bool bControl;//是否受控，是则表名有同级更优计划，处理将抛弃
        public List<int> items = new List<int>();//计划物品，对应最优解

        public Plan()
        {
            weight = 0;
            val = 0;
            bControl = false;
        }

        public Plan(int w, int v)
        {
            weight = w;
            val = v;
            bControl = false;
        }
    }

    //背包问题
    public class Problem
    {
        public int content;//背包容量，输入获得
        public List<Item> items;//所有物品，输入获得
        public List<Plan> plns = new List<Plan>();//最后处理的计划集

        public Problem(int cet, List<Item> its)
        {
            content = cet;
            items = its;
        }

        public void Process()
        {
            List<Plan> right = new List<Plan>();
            plns.Add(new Plan(0,0));//没有任何物品的计划，
            foreach (Item it in items)
            {
                right = GenerateNext(plns, it);//产生下次计划
                plns = UnionPlan(plns, right);//去除受控计划
            }
        }

        public void Answer()
        {
            Console.WriteLine("最优方案 物品数量{0} 重量{1} 价值:{2}", 
                plns[plns.Count - 1].items.Count, plns[plns.Count - 1].weight, plns[plns.Count - 1].val);

            Console.Write("背包信息:");
            foreach (var item in plns[plns.Count - 1].items)
            {
                Console.Write("物品{0}:", item);
            }

            Console.WriteLine();
            Console.WriteLine("========跳跃表信息========");
            foreach (var item in plns)
            {
                Console.Write("({0},{1}) ", item.weight, item.val);
            }
            Console.WriteLine();
        }

        /// 

        /// 产生新计划
        /// 
        /// 旧计划
        /// 新的物品
        /// 新计划
        public List<Plan> GenerateNext(List<Plan> left, Item good)
        {
            List < Plan > next = new List<Plan>();

            foreach (var item in left)
            {
                if (item.weight + good.weight <= content)//不超重则录入
                {
                    Plan temp = new Plan(item.weight + good.weight, item.val + good.val);
                    temp.items.AddRange(item.items);
                    temp.items.Add(good.id);

                    next.Add(temp);
                }
            }

            return next;
        }

        /// 

        /// 合并计划
        /// 
        /// 旧计划集
        /// 新计划集
        /// 
        public List<Plan> UnionPlan(List<Plan> left, List<Plan> right)
        {
            List<Plan> plans = new List<Plan>();

            foreach (var lItem in left) 
            {
                foreach (var rItem in right)
                {
                    if (lItem.weight <= rItem.weight && lItem.val > rItem.val)//旧计划和新计划比较 轻或者一样重反而价值高，则标记新计划为受控计划
                    {
                        rItem.bControl = true;
                    }

                    if (rItem.weight <= lItem.weight && rItem.val > lItem.val)//新计划和旧计划比较 轻或者一样重反而价值高，则标记旧计划为受控计划
                    {
                        lItem.bControl = true;
                    }
                }
            }

            foreach (var lItem in left)
            {
                if (!lItem.bControl) 
                {
                    plans.Add(lItem);
                }
            }

            foreach (var rItem in right)
            {
                if (!rItem.bControl)
                {
                    plans.Add(rItem);
                }
            }

            plans.Sort((l, r) => {
                return l.weight < r.weight ? -1 : 1;
            });

            return plans;
        }
    }

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

            return val == "Y" || val == "y";
        }

        public static int ReadContent()
        {
            Console.Write("背包容量(正整数): ");
            string val = Console.ReadLine();
            int num;
            while (!int.TryParse(val, out num) || num <= 0)
            {
                Console.Write("输入错误,重新输入背包容量(正整数): ");
                val = Console.ReadLine();
            }

            return num;
        }

        public static int ReadCount()
        {
            Console.Write("物品数量(正整数): ");
            string val = Console.ReadLine();
            int num;
            while (!int.TryParse(val, out num) || num <= 0)
            {
                Console.Write("输入错误,重新输入物品数量(正整数): ");
                val = Console.ReadLine();
            }

            return num;
        }

        public static int ReadWeight(int idx)
        {
            Console.Write("物品{0}重量(正整数): ", idx);
            string val = Console.ReadLine();
            int num;
            while (!int.TryParse(val, out num) || num <= 0)
            {
                Console.Write("输入错误,重新输入物品{0}重量(正整数): ", idx);
                val = Console.ReadLine();
            }

            return num;
        }

        public static int ReadValue(int idx)
        {
            Console.Write("物品{0}价值(正整数): ", idx);
            string val = Console.ReadLine();
            int num;
            while (!int.TryParse(val, out num) || num <= 0)
            {
                Console.Write("输入错误,重新输入物品{0}价值(正整数): ", idx);
                val = Console.ReadLine();
            }

            return num;
        }

        static void Main(string[] args)
        {
            do
            {
                List<Item> items = new List<Item>();
                int content = ReadContent();
                int cnt = ReadCount();
                for (int idx = 0; idx < cnt; idx++)
                {
                    items.Add(new Item(ReadWeight(idx+1), ReadValue(idx+1), idx+1));
                }
                Problem problem = new Problem(content, items);
                problem.Process();
                problem.Answer();
            } while (IsContinue());
        }
    }
}

程序和代码已上传，可以下载直接test

程序和代码

参考

主要是看b站张老师的课程
跳跃点 背包问题