using System;
using System.Collections.Generic;
using System.Text;
namespace BackRack
{
 //要裝入書包的貨物節(jié)點(diǎn)
 class BagNode
 {
  public int mark;//貨物編號，從0開始記
  public int weight;//貨物重量
  public int value;//貨物價值
  public BagNode(int m, int w, int v)
  {
   mark = m;
   weight = w;
   value = v;   
  }
 }
//根據(jù)貨物的數(shù)目，建立相應(yīng)的滿二叉樹，如：3個貨物，需要建立15個節(jié)點(diǎn)的二叉樹，共三層（根節(jié)點(diǎn)所在的層記為0）
 class BulidFullSubTree
 {
  public static int treeNodeNum = 0;//滿二叉樹節(jié)點(diǎn)總數(shù)
  public int noleafNode = 0;//滿二叉樹出去葉子節(jié)點(diǎn)外所剩余的非葉子節(jié)點(diǎn)
   public static TreeNode[] treeNode;//存儲滿二叉樹所有節(jié)點(diǎn)的數(shù)組
  public BulidFullSubTree(int nodeNum)
  {
   treeNodeNum = Convert.ToInt32(Math.Pow(2,nodeNum+1)-1);
    noleafNode = Convert.ToInt32(treeNodeNum - Math.Pow(2,nodeNum));
    treeNode = new TreeNode[treeNodeNum];
    for (int i = 0; i < treeNodeNum; i++)
    {
     treeNode[i] = new TreeNode(i.ToString());
 //對二叉樹的所有節(jié)點(diǎn)初始化
    }
     for (int i = 0; i < noleafNode; i++)
     {
      //建立節(jié)點(diǎn)之間的關(guān)系
      treeNode[i].left = treeNode[2 * i + 1];
      treeNode[i].right = treeNode[2 * i + 2];
      treeNode[2 * i + 1].bLeftNode = true;
  //如果是左孩子，則記其標(biāo)識變量為true
      treeNode[2 * i + 2].bLeftNode = false;
     }
   treeNode[0].level=0;//約定根節(jié)點(diǎn)的層數(shù)為0
   //根據(jù)數(shù)組下標(biāo)確定節(jié)點(diǎn)的層數(shù)
   for (int i = 1; i <= 2; i++)
   {
    treeNode[i].level = 1;
   }
   for (int i = 3; i <= 6; i++)
   {
    treeNode[i].level = 2;
   }
   for (int i = 7; i <= 14; i++)
   {
    treeNode[i].level = 3;
   }
  }
 }
//利用回溯法尋找最優(yōu)解的類
 class DealBagProblem
 {
  public TreeNode[] treeNode = BulidFullSubTree.treeNode;
  //獲取建立好的二叉樹
  int maxWeiht = 0;//背包最大承重量
  int treeLevel =Convert.ToInt32(Math.Floor(Math.Log(BulidFullSubTree.treeNodeNum,2)))+1;
  //二叉樹的最大層數(shù)
  int []optionW=new int[100];//存儲最優(yōu)解的數(shù)組
  int[] optionV = new int[100];//存儲最優(yōu)解的數(shù)組
  int i = 0;//計數(shù)器，記錄相應(yīng)數(shù)組的下標(biāo)
  int midTw = 0;//中間變量，存儲程序回溯過程中的中間值
  int midTv = 0;//中間變量，存儲程序回溯過程中的中間值
  int midTw1 = 0;//中間變量，存儲程序回溯過程中的中間值
  int midTv2 = 0;//中間變量，存儲程序回溯過程中的中間值
  BagNode[] bagNode;//存儲貨物節(jié)點(diǎn)
  string[] solution=new string[3];
  //程序最終所得的最優(yōu)解，分別存儲：最優(yōu)價值，總重量，路徑 
  // int[] bestWay=new int[100];
  TraceNode[] Optiontrace=new TraceNode[100];//存儲路徑路徑
  public DealBagProblem(BagNode[] bagN,TreeNode[] treeNode,int maxW)
  {
   bagNode = bagN;
   maxWeiht = maxW;
   for (int i = 0; i < Optiontrace.Length; i++)
   {
    //將路徑數(shù)組對象初始化
    Optiontrace[i] = new TraceNode();
   }
  }
  //核心算法，進(jìn)行回溯
  //cursor:二叉樹下一個節(jié)點(diǎn)的指針;tw：當(dāng)前背包的重量；tv：當(dāng)前背包的總價值
  public void BackTrace(TreeNode cursor,int tw,int tv)
  {
   if(cursor!=null)//如果當(dāng)前節(jié)點(diǎn)部位空值
   {
    midTv = tv;
    midTw = tw;
    if (cursor.left != null && cursor.right != null)
 //如果當(dāng)前節(jié)點(diǎn)不是葉子節(jié)點(diǎn)
    {
     //如果當(dāng)前節(jié)點(diǎn)是根節(jié)點(diǎn)，分別處理其左右子樹
     if (cursor.level == 0)
     {
      BackTrace(cursor.left, tw, tv);
      BackTrace(cursor.right, tw, tv);
     }
     //如果當(dāng)前節(jié)點(diǎn)不是根節(jié)點(diǎn)
     if (cursor.level > 0)
     {
      //如果當(dāng)前節(jié)點(diǎn)是左孩子
      if (cursor.bLeftNode)
      {
       //如果將當(dāng)前貨物放進(jìn)書包而不會超過背包的承重量
       if (tw + bagNode[cursor.level - 1].weight <= maxWeiht)
       {
        //記錄當(dāng)前節(jié)點(diǎn)放進(jìn)書包
        Optiontrace[i].mark = i;
        Optiontrace[i].traceStr += "1";
        tw = tw + bagNode[cursor.level - 1].weight;
        tv=tv+bagNode[cursor.level - 1].value;
        if (cursor.left != null)
        {
         //如果當(dāng)前節(jié)點(diǎn)有左孩子，遞歸
         BackTrace(cursor.left, tw, tv);
        }
        if (cursor.right != null)
        {
         //如果當(dāng)前節(jié)點(diǎn)有左、右孩子，遞歸
         BackTrace(cursor.right, midTw, midTv);
        }
       }
      }
       //如果當(dāng)前節(jié)點(diǎn)是其父節(jié)點(diǎn)的右孩子
      else
      {
       //記錄當(dāng)前節(jié)點(diǎn)下的tw,tv當(dāng)遞歸回到該節(jié)點(diǎn)時，以所記錄的值開始向當(dāng)前節(jié)點(diǎn)的右子樹遞歸
       midTv2 = midTv;
       midTw1 = midTw;
       Optiontrace[i].traceStr += "0";
       if (cursor.left != null)
       {
        BackTrace(cursor.left, midTw, midTv);
       }
       if (cursor.right != null)
       {
        //遞歸所傳遞的midTw1與midTv2是先前記錄下來的
        BackTrace(cursor.right, midTw1, midTv2);
       }
      }
     }
    }
    //如果是葉子節(jié)點(diǎn)，則表明已經(jīng)產(chǎn)生了一個臨時解
    if (cursor.left == null && cursor.right == null)
    {
     //如果葉子節(jié)點(diǎn)是其父節(jié)點(diǎn)的左孩子
     if (cursor.bLeftNode)
     {
      if (tw + bagNode[cursor.level - 1].weight <= maxWeiht)
      {
       Optiontrace[i].traceStr += "1";
       tw = tw + bagNode[cursor.level - 1].weight;
       tv = tv + bagNode[cursor.level - 1].value;
       if (cursor.left != null)
       {
        BackTrace(cursor.left, tw, tv);
       }
       if (cursor.right != null)
       {
        BackTrace(cursor.right, midTw, midTv);
       }
      }
     }
     //存儲臨時優(yōu)解
     optionV[i] = tv;
     optionW[i] = tw;
     i++;
     tv = 0;
     tw = 0;
    }
   }
  }
  //從所得到的臨時解數(shù)組中找到最優(yōu)解
  public string[] FindBestSolution()
  {
   int bestValue=-1;//最大價值
   int bestWeight = -1;//與最大價值對應(yīng)的重量
   int bestMark = -1;//最優(yōu)解所對應(yīng)得數(shù)組編號（由i確定）
   for (int i = 0; i < optionV.Length; i++)
   {
    if (optionV[i] > bestValue)
    {
     bestValue=optionV[i];
     bestMark = i;
    }
   }
   bestWeight=optionW[bestMark];//重量應(yīng)該與最優(yōu)解的數(shù)組下標(biāo)對應(yīng)
   for (int i = 0; i < Optiontrace.Length; i++)
   {
    if (Optiontrace[i].traceStr.Length == bagNode.Length&&i==bestMark)
    {
     //找到與最大價值對應(yīng)得路徑
     solution[2]=Optiontrace[i].traceStr;
    }
   }
    solution[0] = bestWeight.ToString();
   solution[1] = bestValue.ToString();
   return solution;
  }
 }
class Program
 {
  static void Main(string[] args)
  {
   //測試數(shù)據(jù)（貨物）
   //Node[] bagNode = new Node[100];
   //BagNode bagNode1 = new BagNode(0, 5, 4);
   //BagNode bagNode2 = new BagNode(1, 3, 4);
   //BagNode bagNode3 = new BagNode(2, 2, 3);
   //測試數(shù)據(jù)（貨物）
   BagNode bagNode1 = new BagNode(0, 16, 45);
   BagNode bagNode2 = new BagNode(1, 15, 25);
   BagNode bagNode3 = new BagNode(2, 15, 25);
   BagNode[] bagNodeArr = new BagNode[] {bagNode1,bagNode2,bagNode3};
   BulidFullSubTree bfs = new BulidFullSubTree(3);
   //第3個參數(shù)為背包的承重
   DealBagProblem dbp = new DealBagProblem(bagNodeArr,BulidFullSubTree.treeNode,30);
   //找到最優(yōu)解并將其格式化輸出
   dbp.BackTrace(BulidFullSubTree.treeNode[0],0,0);
   string[] reslut=dbp.FindBestSolution();
   if (reslut[2] != null)
   {
    Console.WriteLine("該背包最優(yōu)情況下的貨物的重量為：{0}\n   貨物的最大總價值為：{1}", reslut[0].ToString(), reslut[1].ToString());
    Console.WriteLine("\n");
    Console.WriteLine("該最優(yōu)解的貨物選擇方式為：{0}", reslut[2].ToString());
    char[] r = reslut[2].ToString().ToCharArray();
    Console.WriteLine("被選擇的貨物有：");
    for (int i = 0; i < bagNodeArr.Length; i++)
    {
     if (r[i].ToString() == "1")
     {
      Console.WriteLine("貨物編號：{0},貨物重量：{1},貨物價值：{2}", bagNodeArr[i].mark, bagNodeArr[i].weight, bagNodeArr[i].value);
     }
    }
   }
   else
   {
    Console.WriteLine("程序沒有找到最優(yōu)解，請檢查你輸入的數(shù)據(jù)是否合適！");
   }
  }
 }
//存儲選擇回溯路徑的節(jié)點(diǎn)
public class TraceNode
 {
  public int mark;//路徑編號
  public string traceStr;//所走過的路徑（1代表取，2代表舍）
  public TraceNode(int m,string t)
  {
   mark = m;
   traceStr = t;
  }
  public TraceNode()
  {
   mark = -1;
   traceStr = "";
  }
 }
//回溯所要依附的滿二叉樹
 class TreeNode
 {
  public TreeNode left;//左孩子指針
  public TreeNode right;//右孩子指針
  public int level;//數(shù)的層，層數(shù)代表貨物的標(biāo)識
  string symb;//節(jié)點(diǎn)的標(biāo)識，用其所在數(shù)組中的下標(biāo)，如：“1”，“2”
  public bool bLeftNode;//當(dāng)前節(jié)點(diǎn)是否是父節(jié)點(diǎn)的左孩子
  public TreeNode(TreeNode l, TreeNode r, int lev,string sb,bool ln)
  {
   left = l;
   right = r;
   level = lev;
   symb = sb;
   bLeftNode = ln;
  }
  public TreeNode(string sb)
  {
   symb = sb;
  }
 }
}