#include<iostream>
     using namespace std;

  const int N = 20;

  int maxint(int x, int y)
   {  
    if(x < y) return y;
    else return x;
   }

  struct treenode;

  typedef treenode*tree;

  struct treenode
   {
    int item;  
    tree left;
    tree right;
   };

  tree mainroot = 0;

  void inorder(tree t)
   {
    #include"inorder.tex"
   }

  void preorder(tree t)
   {
    #include"preorder.tex"
   }

  void postorder(tree t)
   {
    #include"postorder.tex"
   }

  int hite(tree t) // height
    // empty tree has hite -1
   {
    #include"hite.tex"
   }

  int numbr(tree t) // number of nodes of t
   {
    #include"numbr.tex"
   }

  void insrt(tree&t,int newitem)
   {
    if(t == 0)
     {
      t = new treenode();
      t->item = newitem;
     }
    else if(newitem < t->item) insrt(t->left,newitem);
    else insrt(t->right,newitem);
   }

  void insertrandom(int n)
   {
    // inserts n random 2 digit numbers into the binary search tree
    srand(0);
    for(int i = 0; i < n; i++)
     {
      int m = 10+rand()%90;
      insrt(mainroot,m);
      cout << m << " ";
     }
    cout << endl;
   }

  void levl(tree t, int ell)
   {
    if(t)
     if(ell == 0)
      cout << t->item << " ";
     else 
      {
       levl(t->left,ell-1);   
       levl(t->right,ell-1);   
      }
   }

  void levelorder(tree t)
   {
    for(int ell = 0; ell <= hite(t); ell++)
     levl(t,ell);
   }

  int main()
   {
    cout << "insert integers:" << endl;
    insertrandom(N);
    cout << "inorder:" << endl;
    inorder(mainroot);
    cout << endl;
    cout << "preorder:" << endl;
    preorder(mainroot);
    cout << endl;
    cout << "postorder:" << endl;
    postorder(mainroot);
    cout << endl;
    cout << "levelorder:" << endl;
    levelorder(mainroot);
    cout << endl;
    cout << "number of items = " << numbr(mainroot) << "   ";
    cout << "height = " << hite(mainroot) << endl;
    return 1;
   }