Problem 1
Mark the following statements as true or false. a. \(A\) binary tree must be nonempty. b. The level of the root node is 0 c. If a tree has only one node, the height of this tree is 0 because the number of levels is 0 d. The inorder traversal of a binary tree always outputs the data in ascending order.
Problem 24
Insert 28,25,26,42,47,30,45,29,5 into an initially empty binary search tree. Draw the final binary search tree.
Problem 25
Prove that a binary tree with \(n\) nodes has exactly \(n+1\) empty subtree (NULL pointers).
Problem 26
Suppose that you are given two sequences of elements corresponding to the inorder sequence and the preorder sequence. Prove that it is possible to reconstruct a unique binary tree.
Problem 28
Given the nodes of a binary tree in the preorder sequence and the postorder sequence, show that it may not be possible to reconstruct a unique binary tree.
