前几天看到网上有人求助如何实现揹包问题，于是自己花了一个下午尝试解决：

问题：

有n个商品，每个商品价格是一个整数，给定一个整数，求所有商品价格和等于这个整数的组合。

解法：

定义商品类：

    /// <summary>
    /// 商品类
    /// </summary>
    public class Goods
    {
        public string Name { get; set; }
        public int Price { get; set; }
    }

定义测试类，可以得到商品组合的类：

 public class Test
    {
        private List<Goods> goodList;
        private int _totalprice;
        public Test(int totalprice)
        {
            //以下是自测试随机生成商品和价格列表，实际应用中可以用select语句获取所有单价小于totalprice的商品列表           
            goodList = new List<Goods>();
            for (int i = 0; i < 5; i++)
            {
                goodList.Add(new Goods()
                {
                    Name = string.Format(“第{0}个商品”, (i + 1).ToString()),
                    Price = (i+1)*10
                });
            }
            _totalprice=totalprice;
        }
        public List<List<Goods>> GetAllSelection()
        {
            List<Goods> nowgoods=new List<Goods>();
            List<List<Goods>> result = getSel(_totalprice, nowgoods);
            return result;
        }

        private List<List<Goods>> getSel(int total, List<Goods> nowgoods)
        {
            List<List<Goods>> goods = new List<List<Goods>>();         
            for (int i = 0; i < goodList.Count; i++)
            {
                if (goodList[i].Price == total)
                {
                    goods.Add(new List<Goods>());
                    goods[goods.Count – 1].AddRange(nowgoods);
                    goods[goods.Count – 1].Add(goodList[i]);
                }
                else if (goodList[i].Price < total)
                {
                    nowgoods.Add(goodList[i]);
                    goods.AddRange(getSel(total – goodList[i].Price, nowgoods));
                    nowgoods.RemoveAt(nowgoods.Count – 1);
                }
            }
            return goods;
        }
       
    }

调用类：

    /// <summary>
    /// MainWindow.xaml 的交互逻辑
    /// </summary>
    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();

            Test test = new Test(100);
            List<List<Goods>> resulttest = test.GetAllSelection();
            StringBuilder sb=new StringBuilder();
            for (int i = 0; i < resulttest.Count;i++ )
            {
                sb.Append(“\r\n”);
                for (int j = 0; j < resulttest[i].Count;j++ )
                {
                    sb.Append(resulttest[i][j].Price.ToString() + “,”);
                }
            }
            Console.WriteLine(sb.ToString());
        }
    }

测试通过。

问题有两个：

1.容易生成重复组合

2.当给定总额增加时，计算时间增加