CareerCup

import java.util.ArrayList;

/*
This program makes a random 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 Example
{
static TreeNode root; // Pointer to the binary sort tree.
static class TreeNode
{
// An object of type TreeNode represents one node
// in a binary tree of real numbers.
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

static void treeInsert(double x)
{
// Add x to the binary sort tree to which the
// global variable "root" refers.
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()


static int countLeaves(TreeNode node)
{
// Return the number of leaves in the tree to which node points.
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()





static int sumOfLeafDepths( TreeNode node, int depth )
{
// 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.
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 sumOfLeafDepth()


static int maximumLeafDepth( TreeNode node, int depth )
{
// 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.
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 sumOfLeafDepth()


public static void main(String[] args)
{
// The main routine makes the random tree and prints
// the statistics.

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()


}

"

" can you tell me how did you proceed in finding the solution of this  question, are there any more number which are following this pattern "

"

"

" you can figure out that for any given door, say door #42, you will visit it for every divisor it has. so 42 has 1 & 42, 2 & 21, 3 & 14, 6 & 7. so on pass 1 i will open the door, pass 2 i will close it, pass 3 open, pass 6 close, pass 7 open, pass 14 close, pass 21 open, pass 42 close. for every pair of divisors the door will just end up back in its initial state. so you might think that every door will end up closed? well what about door #9. 9 has the divisors 1 & 9, 3 & 3. but 3 is repeated because 9 is a perfect square, so you will only visit door #9, on pass 1, 3, and 9... leaving it open at the end. only perfect square doors will be open at the end.  "

"