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Author: Robert Baxter

Write a method construct that accepts an integer n as a parameter and that constructs a new tree of integers with n nodes numbered 0 through (n - 1) such that an in-order traversal of the tree will produce the values in sequential order. The tree should be balanced in that the number of values in any node's left subtree should always be within one of the number of values in its right subtree. If there is an extra value in one of a node's two subtrees, it should appear in the right subtree.

For example, given a variable tree of type IntTree, the call of tree.construct(7); should produce the first tree shown below. If the call had been tree.construct(10);, the tree's state should be that of the second tree shown below.

Call Tree
tree.construct(7); 
               +---+
               | 3 |
           ___ +---+ ___
         /               \
     +---+               +---+
     | 1 |               | 5 |
     +---+               +---+
    /     \             /     \
+---+     +---+     +---+     +---+
| 0 |     | 2 |     | 4 |     | 6 |
+---+     +---+     +---+     +---+
tree.construct(10); 
               +---+
               | 4 |
           ___ +---+ ___
         /               \
     +---+               +---+
     | 1 |               | 7 |
     +---+               +---+
    /     \             /     \
+---+     +---+     +---+     +---+
| 0 |     | 2 |     | 5 |     | 8 |
+---+     +---+     +---+     +---+
               \         \         \
               +---+     +---+     +---+
               | 3 |     | 6 |     | 9 |
               +---+     +---+     +---+

Your method should replace any existing tree. It should construct an empty tree if passed a value of 0 and should generate an IllegalArgumentException if passed a negative value.

Assume that you are adding this method to the IntTree class as defined below: 

public class IntTree {
    private IntTreeNode overallRoot;
    ...
}
Type your solution here:


This is a partial class problem. Submit code that will become part of an existing Java class as described. You do not need to write the complete class, just the portion described in the problem.

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