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