Module 10: Trees and Hash Tables

Consider an example:

• Suppose we want to store the following data in a patient database: patient-name, age, height, weight, blood-type

• This might be a sample set of data records:

  

• What we'd like to do is associate a key with each record
       ⇒ Usually, this is what we'd use to search for the record.

• Let's use name as the key:

  

• The name becomes the key, while the entire record becomes the associated value
       ⇒ A map is a data structure that stores name-value associations.

An example with trees:

• Suppose we wish to store the following associations:

  

• In a program, this is how we'd like to make the associations:

  public class BinaryTreeMapExample {
  
      public static void main (String[] argv)
      {
          // Create an instance of the map data structure.
          BinaryTreeMap tree = new BinaryTreeMap ();
  
          // Add name and fierceness-rating (1-10)
          tree.add ("Ewok", 3);
          tree.add ("Aqualish", 6);
          tree.add ("Gungan", 2);
          tree.add ("Amanin", 8);
          tree.add ("Jawa", 6);
          tree.add ("Hutt", 7);
          tree.add ("Cerean", 4);
  
          int rating = tree.getValue ("Hutt");
          System.out.println ("Rating for Hutt: " + rating);
      }
  
  }
       

Let's examine the code for BinaryTreeMap:

import java.util.*;

class TreeNode {

    String key;        // The key-value pair.
    int value;
    
    TreeNode left;     // The usual left-child, right-child pointers.
    TreeNode right;
    
}


public class BinaryTreeMap {

    TreeNode root = null;
    int numItems = 0;


    public void add (String key, int value)
    {
        // If empty, create new root.
        if (root == null) {
            root = new TreeNode ();
            // Store both key and value:
            root.key = key;              
            root.value = value;
            numItems ++;
            return;
        }
        
        // Search to see if it's already there.
        if ( contains (key) ) {
            // Handle duplicates.
            return;
        }
        
        // If this is a new piece of data, insert into tree.
        recursiveInsert (root, key, value);
        
        numItems ++;
    }

    
    void recursiveInsert (TreeNode node, String key, int value)
    {
        // Compare input key with key in current node: comparisons are only with keys.

        if ( key.compareTo (node.key) < 0 ) {
            // It's less. Go left if possible, otherwise we've found the correct place to insert.
            if (node.left != null) {
                recursiveInsert (node.left, key, value);
            }
            else {
                node.left = new TreeNode ();
                node.left.key = key;              // Store both key and value.
                node.left.value = value;
            }
            
        }
        // Otherwise, go right.
        else {
            // It's greater. Go right if possible, otherwise we've found the correct place to insert.
            if (node.right != null) {
                recursiveInsert (node.right, key, value);
            }
            else {
                node.right = new TreeNode ();
                node.right.key = key;             // Store both key and value.
                node.right.value = value;
            }
        }
        
        
    }
    

    public int size ()
    {
        return numItems;
    }
    

    public boolean contains (String str)
    {
        if (numItems == 0) {
            return false;
        }
        
        TreeNode node = recursiveSearch (root, str);
        if (node == null) {
            return false;
        }

        return true;
    }


    public int getValue (String key)
    {
        if (numItems == 0) {
            return -1;
        }
        
        TreeNode node = recursiveSearch (root, key);
        if (node == null) {
            return -1;
        }

        return node.value;
    }
    
    
    TreeNode recursiveSearch (TreeNode node, String key)
    {
        // If input key is at current node, it's in the tree.
        if ( key.compareTo (node.key) == 0 ) {
            // Found.
            return node;
        }

        // Otherwise, navigate further.
        if ( key.compareTo (node.key) < 0 ) {
            // Go left if possible, otherwise it's not in the tree.
            if (node.left == null) {
                return null;
            }
            else {
                return recursiveSearch (node.left, key);
            }
        }
        else {
            // Go right if possible, otherwise it's not in the tree.
            if (node.right == null) {
                return null;
            }
            else {
                return recursiveSearch (node.right, key);
            }
        }
    }

} //end-BinaryTreeMap

• We store both the key and its associated value at the time of adding a key.

• The organization of the tree depends on the keys
       ⇒ Values play no role in searching or tree organization.
       ⇒ They are merely stored along with the associated keys.

• In the above example, each key is a String and each value is an int.

Sometimes we wish to store a more complex value
     ⇒ An object, for instance.

• For example, suppose we wanted to store these associations:

  

• We will use an object called TribeInfo to store the three pieces of information:

  class TribeInfo {
  
      String name;
      int fierceness;
      String planet;
  
  
      // Constructor.
  
      public TribeInfo (String name, int fierceness, String planet)
      {
          this.name = name;
          this.fierceness = fierceness;
          this.planet = planet;
      }
  
  } 
       

• Then, we'd like to create key-value associations between tribe names and the associated object as follows:

  public class BinaryTreeMapExample2 {
  
      public static void main (String[] argv)
      {
          // Create an instance of our new object-version of a binary-tree map.
          BinaryTreeMap2 tree = new BinaryTreeMap2 ();
  
          // Put some key-value pairs inside.
          TribeInfo info = new TribeInfo ("Ewok", 3, "Endor");
          tree.add ("Ewok", info);
  
          info = new TribeInfo ("Aqualish", 6, "Ando");
          tree.add (info.name, info);
  
          info = new TribeInfo ("Gungan", 2, "Naboo");
          tree.add (info.name, info);
  
          info = new TribeInfo ("Amanin", 8, "Maridun");
          tree.add (info.name, info);
  
          info = new TribeInfo ("Jawa", 6, "Tatooine");
          tree.add (info.name, info);
  
          info = new TribeInfo ("Hutt", 7, "Varl");
          tree.add (info.name, info);
  
          info = new TribeInfo ("Cerean", 4, "Cerea");
          tree.add (info.name, info);
  
          // Note: a cast is needed for conversion from Object to TribeInfo
          // even though we know that a TribeInfo instance will be returned.
          TribeInfo tInfo = (TribeInfo) tree.getValue ("Hutt");
          System.out.println ("Info for Hutt: " + tInfo);
      }
  
  }
       

Let's now take a look at implementing the map:

import java.util.*;

class TreeNode {

    String key;
    Object value;      // The value is now a generic object.
    
    TreeNode left;
    TreeNode right;
    
}


public class BinaryTreeMap2 {

    TreeNode root = null;
    int numItems = 0;


    public void add (String key, Object value)
    {
        // ...
    }


    public int size ()
    {
        // ...
    }
    

    public boolean contains (String key)
    {
        // ...
    }
    

    public Object getValue (String key)    
    {
        // ...

        // Return value is an Object (the value)
    }
    
}

• The code changes only slightly
       ⇒ The value is now of type Object.

In-Class Exercise 14: Download BinaryTreeMapExample2.java and BinaryTreeMap2.java. What method should you add to TribeInfo for the printing in main() to print something useful?

What is an Object?

• This is a special class in the Java library, and is treated differently by the compiler.

• Every Java object is also an Object.

• Here's an example that explores the connection between Object and any other class we define:

  class MyOwnVeryObject {         // A silly little object
  
      int k;
      
      public String toString ()
      {
          return ("k=" + k);
      }
  
  }
  
  
  public class TestObject {
  
      public static void main (String[] argv)
      {
          // Create an instance of the class defined above and set a value for one of the members.
          MyOwnObject x = new MyOwnObject ();
          x.k = 5;
          
          // Invoke the toString() method:
          System.out.println (x);
          
          // Since MyOwnObject is also an Object, an Object variable can point to it.
          Object obj = x;
  
          // Invoke the toString() method: this calls the toString() method in x.
          System.out.println (obj);
  
          // Cast down from an Object variable into a MyOwnObject variable.
          MyOwnObject y = (MyOwnObject) obj;
          print (y);
  
          // Casting can occur in a method call too.
          print (x);
      }
  
  
      static void print (Object obj)
      {
          System.out.println (obj);
      }
      
  }
      

• This is why we needed the cast when we extracted the value in the map example:

          // Cast from return type (Object) into tInfo's type (TribeInfo).
          TribeInfo tInfo = (TribeInfo) tree.getValue ("Hutt");
      

In-Class Exercise 15: What would happen if we mistakenly cast into the wrong type? Download BinaryTreeMapExample2.java and BinaryTreeMap2.java. Then add these lines to the end of main():

        String s = (String) tree.getValue ("Hutt");
        System.out.println ("Info for Hutt: " + s);
  

A separate key-value pair object

An alternative to handling keys and values separately is to create a single object that packages key-and-value:

• For example:

  public class KeyValuePair {
  
      String key;
      Object value;
  
      public KeyValuePair (String s, Object v)
      {
          key = s;
          value = v;
      }
  
  }
      

• Then, our map data structure is written to work with such objects:

  import java.util.*;
  
  class TreeNode {
  
      KeyValuePair kvp;      // A tree node now stores the Key-Value pair as an object.
      
      TreeNode left;         // The usual pointers.
      TreeNode right;
  
  }
  
  
  public class BinaryTreeMap3 {
  
      public void add (KeyValuePair kvp)
      {
          // ...
      }
  
      public boolean contains (String key)
      {
          // ...
      }
  
      public KeyValuePair getKeyValuePair (String key)
      {
          // ...
      }
  
  }
      

class TribeInfo {

    String name;
    int fierceness;
    String planet;

    public TribeInfo (String name, int fierceness, String planet)
    {
        this.name = name;
        this.fierceness = fierceness;
        this.planet = planet;
    }

} //end-TribeInfo


public class BinaryTreeMapExample3 {

    public static void main (String[] argv)
    {
        // Create an instance.
        BinaryTreeMap3 tree = new BinaryTreeMap3 ();

        // Put some key-value pairs inside.
        TribeInfo info = new TribeInfo ("Ewok", 3, "Endor");
        KeyValuePair kvp = new KeyValuePair ("Ewok", info);
        tree.add (kvp);

        info = new TribeInfo ("Aqualish", 6, "Ando");
        kvp = new KeyValuePair (info.name, info);
        tree.add (kvp);

        // This is more compact: create the instance in the method argument list.
        info = new TribeInfo ("Gungan", 2, "Naboo");
        tree.add ( new KeyValuePair (info.name, info) );

        info = new TribeInfo ("Amanin", 8, "Maridun");
        tree.add ( new KeyValuePair (info.name, info) );

        info = new TribeInfo ("Jawa", 6, "Tatooine");
        tree.add ( new KeyValuePair (info.name, info) );

        info = new TribeInfo ("Hutt", 7, "Varl");
        tree.add ( new KeyValuePair (info.name, info) );

        // A little harder to read, but even more compact:
        tree.add ( new KeyValuePair ("Cerean", new TribeInfo ("Cerean", 4, "Cerea") ) );

        KeyValuePair kvpResult = tree.getKeyValuePair ("Hutt");
        System.out.println ("Info for Hutt: " + kvpResult);
    }

}

public class OurHashMap {

    int numBuckets = 100;              // Initial number of buckets.
    OurLinkedListMap[] table;          // The hashtable.
    int numItems;                      // Keep track of number of items added.
    

    // Constructor.

    public OurHashMap (int numBuckets)
    {
        this.numBuckets = numBuckets;
        table = new OurLinkedListMap [numBuckets];
        numItems = 0;
    }


    public void add (KeyValuePair kvp)
    {
        if ( contains (kvp.key) ) {
            return;
        }
        
        // Compute hashcode and therefore, which table entry (list).
        int entry = Math.abs(kvp.key.hashCode()) % numBuckets;

        // If there's no list there, make one.
        if (table[entry] == null) {
            table[entry] = new OurLinkedListMap ();
        }

        // Add to list.
        table[entry].add (kvp);

        numItems ++;
    }
    

    public boolean contains (String key)
    {
        // Compute table entry using hash function.
        int entry = Math.abs(key.hashCode()) % numBuckets;

        if (table[entry] == null) {
            return false;
        }

        // Use the contains() method of the list.
        return table[entry].contains (key);
    }
    

    public KeyValuePair getKeyValuePair (String key)
    {
        // Similar to contains.
        int entry = Math.abs(key.hashCode()) % numBuckets;
        if (table[entry] == null) {
            return null;
        }
        return table[entry].getKeyValuePair (key);
    }
    
}