*****USING ECLIPSE Please don\'t just repost previous posts. For this exercise,
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*****USING ECLIPSE Please don't just repost previous posts.
For this exercise, you should create a random binary sort tree with 1023 nodes. The items in the tree can be real numbers, and you can create the tree by generating 1023 random real numbers and inserting them into the tree, using the usual treeInsert() method for binary sort trees. Once you have the tree, you should compute and output the average depth of all the leaves in the tree and the maximum depth of all the leaves. To do this, you will need three recursive subroutines: one to count the leaves, one to find the sum of the depths of all the leaves, and one to find the maximum depth. The latter two subroutines should have an int-valued parameter, depth, that tells how deep in the tree you've gone. When you call this routine from the main program, the depth parameter is 0; when you call the routine recursively, the parameter increases by 1. Build your solution on code and principles from section 9.4.2. Previous: Learning Journal AssignmentExit book Skip Table of contents Table of contents Overview Introduction Reading Assignment Discussion Forum question Assignment Learning Journal Assignment Exercises
Explanation / Answer
/**
* This program makes a random binary sort tree containing 1023 random
* real numbers. It then computes the height of the tree and the
* average depth of the leaves of the tree. Hopefully, the average
* depth will tend to be close to 9, which is what it would be
* if the tree were perfectly balanced. The height of the tree,
* which is the same as the maximum depth of any leaf, can be
* significantly larger.
*/
public class RandomSortTree {
static TreeNode root; // Pointer to the binary sort tree.
/**
* An object of type TreeNode represents one node in a binary tree of real numbers.
*/
static class TreeNode {
double item; // The data in this node.
TreeNode left; // Pointer to left subtree.
TreeNode right; // Pointer to right subtree.
TreeNode(double x) {
// Constructor. Make a node containing x.
item = x;
}
} // end class TreeNode
/**
* Add x to the binary sort tree to which the global variable "root" refers.
*/
static void treeInsert(double x) {
if ( root == null ) {
// The tree is empty. Set root to point to a new node
// containing the new item.
root = new TreeNode( x );
return;
}
TreeNode runner; // Runs down the tree to find a place for newItem.
runner = root; // Start at the root.
while (true) {
if ( x < runner.item ) {
// Since the new item is less than the item in runner,
// it belongs in the left subtree of runner. If there
// is an open space at runner.left, add a node there.
// Otherwise, advance runner down one level to the left.
if ( runner.left == null ) {
runner.left = new TreeNode( x );
return; // New item has been added to the tree.
}
else
runner = runner.left;
}
else {
// Since the new item is greater than or equal to the
// item in runner, it belongs in the right subtree of
// runner. If there is an open space at runner.right,
// add a new node there. Otherwise, advance runner
// down one level to the right.
if ( runner.right == null ) {
runner.right = new TreeNode( x );
return; // New item has been added to the tree.
}
else
runner = runner.right;
}
} // end while
} // end treeInsert()
/**
* Return the number of leaves in the tree to which node points.
*/
static int countLeaves(TreeNode node) {
if (node == null)
return 0;
else if (node.left == null && node.right == null)
return 1; // Node is a leaf.
else
return countLeaves(node.left) + countLeaves(node.right);
} // end countNodes()
/**
* When called as sumOfLeafDepths(root,0), this will compute the
* sum of the depths of all the leaves in the tree to which root
* points. When called recursively, the depth parameter gives
* the depth of the node, and the routine returns the sum of the
* depths of the leaves in the subtree to which node points.
* In each recursive call to this routine, depth goes up by one.
*/
static int sumOfLeafDepths( TreeNode node, int depth ) {
if ( node == null ) {
// Since the tree is empty and there are no leaves,
// the sum is zero.
return 0;
}
else if ( node.left == null && node.right == null) {
// The node is a leaf, and there are no subtrees of node, so
// the sum of the leaf depth is just the depths of this node.
return depth;
}
else {
// The node is not a leaf. Return the sum of the
// the depths of the leaves in the subtrees.
return sumOfLeafDepths(node.left, depth + 1)
+ sumOfLeafDepths(node.right, depth + 1);
}
} // end sumOfLeafDepths()
/**
* When called as maximumLeafDepth(root,0), this will compute the
* max of the depths of all the leaves in the tree to which root
* points. When called recursively, the depth parameter gives
* the depth of the node, and the routine returns the max of the
* depths of the leaves in the subtree to which node points.
* In each recursive call to this routine, depth goes up by one.
*/
static int maximumLeafDepth( TreeNode node, int depth ) {
if ( node == null ) {
// The tree is empty. Return 0.
return 0;
}
else if ( node.left == null && node.right == null) {
// The node is a leaf, so the maximum depth in this
// subtree is the depth of this node (the only leaf
// that it contains).
return depth;
}
else {
// Get the maximum depths for the two subtrees of this
// node. Return the larger of the two values, which
// represents the maximum in the tree overall.
int leftMax = maximumLeafDepth(node.left, depth + 1);
int rightMax = maximumLeafDepth(node.right, depth + 1);
if (leftMax > rightMax)
return leftMax;
else
return rightMax;
}
} // end maximumLeafDepth()
/**
* The main routine makes the random tree and prints the statistics.
*/
public static void main(String[] args) {
root = null; // Start with an empty tree. Root is a global
// variable, defined at the top of the class.
// Insert 1023 random items.
for (int i = 0; i < 1023; i++)
treeInsert(Math.random());
// Get the statistics.
int leafCount = countLeaves(root);
int depthSum = sumOfLeafDepths(root,0);
int depthMax = maximumLeafDepth(root,0);
double averageDepth = ((double)depthSum) / leafCount;
// Display the results.
System.out.println("Number of leaves: " + leafCount);
System.out.println("Average depth of leaves: " + averageDepth);
System.out.println("Maximum depth of leaves: " + depthMax);
} // end main()
} // end class RandomSortTree
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