Give the preorder, inorder, postorder and levelorder
traversals for the tree below.
H
/ \
/ \
B K
/ \ /
F E D
/ / \
J G A
/ \ \
L C I
Draw a binary tree whose preorder traversal is A B C D E F G H I.
Draw a binary tree whose inorder traversal is A B C D E F G H I.
Draw a binary tree whose postorder traversal is A B C D E F G H I.
Draw a binary tree whose levelorder traversal is A B C D E F G H I.
Draw the most filled-in binary tree with height 2 you can (that is, the tree with the most
nodes). Show the picture. How many nodes does the tree have?
Draw the most filled-in binary tree with height 3 you can (that is, the tree with the most
nodes). Show the picture. How many nodes does the tree have?
What is the maximum number of nodes in a binary tree of height h?
(Look for a pattern in (a) and (b) and convince yourself that it holds for
all heights.)
Draw the least filled-in binary tree with height 2 you can (that is, the tree with the fewest
nodes). Show the picture. How many nodes does the tree have?
Draw the least filled-in binary tree with height 3 you can (that is, the tree with the fewest
nodes). Show the picture. How many nodes does the tree have?
What is the minimum number of nodes in a binary tree of height h?
Draw the least filled-in complete binary tree of height 2 you can (that is, the tree with the fewest
nodes). Show the picture. How many nodes does the tree have?
Draw the least filled-in complete binary tree of height 3 you can (that is, the tree with the fewest
nodes). Show the picture. How many nodes does the tree have?
What is the minimum number of nodes in a complete binary tree of height h?
Draw the tallest binary tree you can using 2 nodes. Show the tree. What is
its height?
Draw the tallest binary tree you can using 3 nodes. Show the tree. What is
its height?
What is the maximum height of a binary tree with n nodes?