Binary Tree    (insert level by level)

Hello,
I'm trying to program a binary tree. It's totally clear for me to insert new (Integer) Values in an ordinary binary tree.
I simply have to check if the root is equal (--> ready) smaller or larger than the value. I repeat this until I reached a leaf and then I insert a new node.
BUT:
My teacher gave me following problem: Inserting values level by level. The first element is the root, the leftson of the root is nuber2 the rightson of the root is number3
The leftson of root's leftson is number4, the rightson of root's leftson is number 5, the leftson of root's rightson is number 6 and so on.
I have NO idea how to program that.
For example: the 23rd element is in the tree: left, right, right, right, whilst the 24th element is right, left, left, left.
I cannot find a recursive structure, that solves the problem.
Perhaps YOU can save me from gettin' mad ;o)
I really hope so.

It's not quite clear what you mean by level-by-level (at least not to me). The structure of a binary tree depends in the insert order. If you insert 1,5,2,8 the tree will look different to when you insert 1,2,3,4. In the last case the tree actually has degenerated to a linked list (there are only rightsons).
Now, to minimize the number of levels (if that's what this is about) there's a technique called balancing. In a perfectly balanced binary tree each level is filled before a new level is started. This is quite complicated. Search the net or look in some data structures textbook for balanced binary trees.

Similar Messages

  • Binary tree    (level by level insert)

    Hello,
    I already posted this artivle in the Forum "Java Programming" because I'm new to the Forum and didn't see the Algorithms part.. Sorry for the double posting.
    I'm trying to program a binary tree. It's totally clear for me to insert new (Integer) Values in an ordinary binary tree.
    I simply have to check if the root is equal (--> ready) smaller or larger than the value. I repeat this until I reached a leaf and then I insert a new node.
    BUT:
    My teacher gave me following problem: Inserting values level by level. The first element is the root, the leftson of the root is nuber2 the rightson of the root is number3
    The leftson of root's leftson is number4, the rightson of root's leftson is number 5, the leftson of root's rightson is number 6 and so on.
    I have NO idea how to program that.
    For example: the 23rd element is in the tree: left, right, right, right, whilst the 24th element is right, left, left, left.
    I cannot find a recursive structure, that solves the problem.
    Perhaps YOU can save me from gettin' mad ;o)
    I really hope so.

    But can you think of a recursive code to solve the problem????????Ok, here's another hint -- take that node 23 again as an example. If you write out this number in binary (10111) and skip the leftmost 1 in this pattern (x0111), start reading from left to right, starting at the right of th 'x'. 0 denotes left, 1 denotes right. Does that ring a bell?
    Something like the following (pseudo code) should come up --
    insert(Node node, int val, int pattern, int bitmask) {
       if (bitmask == 1)                  // we have to insert now
          if ((pattern & bitmask) == 1)   // insert right
             node.right= new Node(val);
          else                            // insert left
             node.left= new Node(val);
       else if ((pattern & bitmask) == 1) // move right
          insert(Node.right, val, pattern, bitmask >> 1);
       else                               // move left
          insert(Node.left, val, pattern, bitmask >> 1);
    }Some bits and pieces are left as an exercise ;-)
    kind regards,
    Jos

  • Binary Tree: Number of Nodes at a Particular Level

    Hi, I'm trying to teach myself about binary tree but am having trouble writing an algorithm. The algorithm that I'm trying to write is one that will take a binary tree and output the number of nodes at each level of the tree (maybe in an array).
    I have no trouble writing an algorithm that does a breadth-first traversal, but I have lots of trouble trying to determine where each level ends.
    Thanks for the help

    Try something like this:
    class BTree {
        BTreeNode root;
        public int numberOfNodesAtLevel(int level) {
            if(root == null) return -1;
            return numberOfNodesAtLevel(root, level);
        private int numberOfNodesAtLevel(BTreeNode node, int level) {
            if(level == 0) {
                return 1;
            } else {
                return (node.left  == null ? 0 : numberOfNodesAtLevel(node.left, level-1)) +
                       (node.right == null ? 0 : numberOfNodesAtLevel(node.right,level-1));
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  • Binary tree per levels

    I must make a method that takes the variable "item" and put it in a string, for each element of the binary tree, but per levels..for example:
                  1
       2     3               6
    5                                4must return this string: 1 , 2 , 3 , 6 , 5 , 4
    The tree is something like:
    public class BinTree{
          private Node root;
          public class Node{
                public Node left;
                public Node right;
                public int item;
    }Thank you very much :)

    Sorry, I didn't specify: I can use recursion,Level order traversals are normally performed using a queue.
    but in this case I don't know how to do it "per levels"..can
    someone help me? Sure: use a queue and try to do it first on a pice of paper.
    Also if you don't write the method,I won't. ; )
    What would you learn from that? Perhaps a little, but you'll learn far more by doing it yourself.
    just to tell me how to go through the tree in this
    case. ThanksHere's some pseudo code:
    LEVELORDER(root)
      queue.enqueue(root)
      WHILE queue not empty
        n = queue.dequeue()
        IF n.left  != null -> queue.enqueue(n.left )
        IF n.right != null -> queue.enqueue(n.right)
      END WHILE
    END LEVELORDERAnd an example. Take the following tree:     5
      3     8
    1   4 6   9No apply that pseudo code:
    queue = new queue
    queue.enqueue(5)
    while(queue is not empty) {
      n = queue.dequeue() = 5
      n.left  != null, so queue.enqueue(3)
      n.irght != null, so queue.enqueue(8)
      (queue is now [3,8])
      n = queue.dequeue() = 3
      n.left  != null, so queue.enqueue(1)
      n.irght != null, so queue.enqueue(4)
      (queue is now [8,1,4])
      n = queue.dequeue() = 8
      n.left  != null, so queue.enqueue(6)
      n.irght != null, so queue.enqueue(9)
      (queue is now [1,4,6,9])
      n = queue.dequeue() = 1
      n.left  == null
      n.irght == null
      (queue is now [4,6,9])
      n = queue.dequeue() = 4
      n.left  == null
      n.irght == null
      (queue is now [6,9])
      n = queue.dequeue() = 6
      n.left  == null
      n.irght == null
      (queue is now [9]) 
      n = queue.dequeue() = 9
      n.left  == null
      n.irght == null
      (queue is now [])
      queue is empty, end while.
    }As you can see, the items are dequeued in the following order: 5, 3, 8, 1, 4, 6, 9.
    Good luck.

  • Creating Insert Method for a binary tree

    I have code for a binary tree http://sourcepost.sytes.net/sourceview.aspx?source_id=5046
    I'm trying to create an insert method that will accept an element and insert it into my binary tree. The main purpose of this is to test my traversal functions, intrav(), postrav(), pretrav(). I have another class that will create 10 random numbers and call insert() to insert them into my tree. Can anyone help me write this method?

    anyone?

  • Implementing tree control in third level navigation

    Hello
    1. Is it possible to Implement a tree control inside third level navigation ?
    2. How can I make selecting one of the nodes change the display in another iview on the same page ?
    (How do they pass data to one another)
    3. Is it possible to select several nodes at once ?
    P.S
    Is there a how to guid out there ?
    Thanks
    Ziv.

    Hi,
    I undestand you want to hide/show tree nodes on demand.
    in the standard DTN (detailed navigation) it isn't possible.
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    Tal.
    Edited by: Tal Haviv on Aug 15, 2008 12:55 PM

  • How to traverse level by level in tree

    Wondering if there were any suggestions on how to efficiently traverse through a tree level by level.
    Here is my code for creating the tree.
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              String userInput = "";
              StringTokenizer tokenizedUserInput;
              int numAdd = 0;
              STree<Integer> completeTree = new STree<Integer>();
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              userInput = keyboard.nextLine();
              tokenizedUserInput = new StringTokenizer(userInput, ", ");
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    I have found a method to traverse through the tree level by level but it takes in a parameter of a node. I'm
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              String s = "";
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              while(!q.isEmpty())
                   p = q.pop();
                   s += p.nodeValue + " ";
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                        q.push(p.left);
                   if(p.right != null)
                        q.push(p.right);
              return s;
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  • Binary Tree Help

    I have a project where I need to build a binary tree with random floats and count the comparisons made. The problem I'm having is I'm not sure where to place the comaprison count in my code. Here's where I have it:
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              Node newNode = new Node();
              newNode.data = idata;
              if(root==null)
                   root = newNode;
              else
                   Node current = root;
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                   while(true)
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                             comp++;
                             current = current.leftc;
                             if(current == null)
                                  parent.leftc = newNode;
                                  return;
                        else
                             current = current.rightc;
                             if(current == null)
                                  parent.rightc = newNode;
                                  return;
         }//end insertDo I have it in the right place? Also, if I'm building the tree for 10,000 numbers would I get a new count for each level or would I get one count for comparisons?? I'd appreciate anyone's help on this.

    You never reset the comp variable, so each timeyou
    insert into the tree, it adds the number ofinserts
    to the previous value.Yes, or something like that. I'm not sure what theOP
    really means.Yeah, it's hard to be sure without seeing the rest of
    the code.Sorry, I thought I had already posted my code for you to look at.
    Here's a copy of it:
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         public float data;
         public Node leftc;
         public Node rightc;
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         private Node root;
         private int comp;
         public Btree(int value)
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                   root = newNode;
              else
                   Node current = root;
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                   while(true)
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                        if(idata < current.data)
                             current = current.leftc;
                             if(current == null)
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                                  return;
                        else
                             current = current.rightc;
                             if(current == null)
                                  parent.rightc = newNode;
                                  return;
         }//end insert
        public void display()
             //System.out.print();
             System.out.println("");     
             System.out.println(comp);
    } //end Btree
    class BtreeApp
         public static void main(String[] args)
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              Btree theTree = new Btree(value);
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                   float n = (int) (java.lang.Math.random() *99);
                   theTree.insert(n);
                   theTree.display();
    }

  • CTE for Count the Binary Tree nodes

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    insert into #table(name,Mode,ReferId)values('Sujai','R',2)
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    2 2 L
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    4 3 L
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    See Itzik Ben-Gan examples for the subject
    REATE TABLE Employees
      empid   int         NOT NULL,
      mgrid   int         NULL,
      empname varchar(25) NOT NULL,
      salary  money       NOT NULL,
      CONSTRAINT PK_Employees PRIMARY KEY(empid),
      CONSTRAINT FK_Employees_mgrid_empid
        FOREIGN KEY(mgrid)
        REFERENCES Employees(empid)
    CREATE INDEX idx_nci_mgrid ON Employees(mgrid)
    SET NOCOUNT ON
    INSERT INTO Employees VALUES(1 , NULL, 'Nancy'   , $10000.00)
    INSERT INTO Employees VALUES(2 , 1   , 'Andrew'  , $5000.00)
    INSERT INTO Employees VALUES(3 , 1   , 'Janet'   , $5000.00)
    INSERT INTO Employees VALUES(4 , 1   , 'Margaret', $5000.00) 
    INSERT INTO Employees VALUES(5 , 2   , 'Steven'  , $2500.00)
    INSERT INTO Employees VALUES(6 , 2   , 'Michael' , $2500.00)
    INSERT INTO Employees VALUES(7 , 3   , 'Robert'  , $2500.00)
    INSERT INTO Employees VALUES(8 , 3   , 'Laura'   , $2500.00)
    INSERT INTO Employees VALUES(9 , 3   , 'Ann'     , $2500.00)
    INSERT INTO Employees VALUES(10, 4   , 'Ina'     , $2500.00)
    INSERT INTO Employees VALUES(11, 7   , 'David'   , $2000.00)
    INSERT INTO Employees VALUES(12, 7   , 'Ron'     , $2000.00)
    INSERT INTO Employees VALUES(13, 7   , 'Dan'     , $2000.00)
    INSERT INTO Employees VALUES(14, 11  , 'James'   , $1500.00)
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    The following CTE provides a solution to this request:
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      SELECT empid, empname, mgrid, 0
      FROM Employees
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      -- Recursive Member (RM)
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      SELECT empid, empname, mgrid, 0
      FROM Employees
      WHERE empid = 3
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      SELECT E.empid, E.empname, E.mgrid, M.lvl+1
      FROM Employees as E
        JOIN EmpCTEJanet as M
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      WHERE lvl < 2
    SELECT empid, empname
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    WHERE lvl = 2
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     For example, to make the query more generic, you can use 
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    SET @empid = 3 -- Janet
    SET @lvl   = 2 -- two levels
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    AS
      SELECT empid, empname, mgrid, 0
      FROM Employees
      WHERE empid = @empid
      UNION ALL
      SELECT E.empid, E.empname, E.mgrid, M.lvl+1
      FROM Employees as E
        JOIN EmpCTE as M
          ON E.mgrid = M.empid
      WHERE lvl < @lvl
    SELECT empid, empname
    FROM EmpCTE
    WHERE lvl = @lvl
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    and error 530 is generated. You might think of using the MAXRECURSION option 
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    Janet using the MAXRECURSION hint instead of the filter in the recursive member
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      SELECT empid, empname, mgrid, 0
      FROM Employees
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      UNION ALL
      SELECT E.empid, E.empname, E.mgrid, M.lvl+1
      FROM Employees as E
        JOIN EmpCTE as M
          ON E.mgrid = M.empid
    SELECT * FROM EmpCTE
    OPTION (MAXRECURSION 2)
    WITH EmpCTE(empid, empname, mgrid, lvl, sortcol)
    AS
      SELECT empid, empname, mgrid, 0,
        CAST(empid AS VARBINARY(900))
      FROM Employees
      WHERE empid = 1
      UNION ALL
      SELECT E.empid, E.empname, E.mgrid, M.lvl+1,
        CAST(sortcol + CAST(E.empid AS BINARY(4)) AS VARBINARY(900))
      FROM Employees AS E
        JOIN EmpCTE AS M
          ON E.mgrid = M.empid
    SELECT
      REPLICATE(' | ', lvl)
        + '(' + (CAST(empid AS VARCHAR(10))) + ') '
        + empname AS empname
    FROM EmpCTE
    ORDER BY sortcol
    (1) Nancy
     | (2) Andrew
     |  | (5) Steven
     |  | (6) Michael
     | (3) Janet
     |  | (7) Robert
     |  |  | (11) David
     |  |  |  | (14) James
     |  |  | (12) Ron
     |  |  | (13) Dan
     |  | (8) Laura
     |  | (9) Ann
     | (4) Margaret
     |  | (10) Ina
    Best Regards,Uri Dimant SQL Server MVP,
    http://sqlblog.com/blogs/uri_dimant/
    MS SQL optimization: MS SQL Development and Optimization
    MS SQL Consulting:
    Large scale of database and data cleansing
    Remote DBA Services:
    Improves MS SQL Database Performance
    SQL Server Integration Services:
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    CS312 Data Structures and Analysis of Algorithms
    (Here is a course about trees. Search and learn)
    http://www.calstatela.edu/faculty/jmiller6/cs312-winter2003/index.htm

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