binarysearchtree

 public class binarytree<Value> {
          private Node root = null;
          private  class Node{
                private Value val;
                private int key;
                private Node left,right;
                private int N;   //the number of the all nodes of its child nodes and itself
                //private int num;//the number
                public Node(Value val,int key,int N){
                    this.val = val; this.N = N;this.key = key;
                }

        }

         public  void walk(Node x) {   //O(n) time
             if(x!=null){
                 walk(x.left);
                 System.out.println(x.key);
                 walk(x.right);
             }
         }

         public Value get(Node x,int key){
             if(x == null){
                 return null;
             }

             if(x.key>key){
                 return get(x.left,key);
             }
             else if(x.key < key){
                 return get(x.right,key);
             }
             else{
                 return x.val;
             }
         }
          private Node min(Node x){
              if(x.left == null) return x;
              return min(x.left);
          }

          private Node deletemin(Node x){
          if(x.left == null){return x.right;}
          x.left = deletemin(x.left);
          x.N = size(x.left) + size(x.right) + 1;
          return x;
          }

          private Node delete(Node x,int key){
              if(key < x.key) x.left = delete(x.left,key);
               else if(key > x.key) x.right = delete(x.right,key);
               else{
                   if(x.left == null) return x.right;
                   if(x.right == null) return x.left;
                   Node t = x;
                   x = min(t.right);
                   x.right = deletemin(t.right);
                   x.left = t.left;
               }
              x.N = size(x.left) +size(x.right)+1;
              return x;

          }

          private  Node put(Node x,Value val,int key){
                if(x == null) return new Node(val,key,1);
                if(key < x.key) x.left = put(x.left,val,key);
                else if(key > x.key) x.right = put(x.right,val,key);
                else x.key = key;
                x.N = size(x.left) + size(x.right) + 1;
                return x;
            }
            private  int size(Node x){
                if(x == null){return 0;}
                else return x.N;
            }

            private Node select(Node x,int k){
                if(x == null) return null;
                int t = size(x.left);
                if (t>k) return select(x.left,k);
                else if(t<k) return select (x.right,k-t-1);
                else return x;
            }

     }