Question

(a) Draw the binary tree representation of the following arithmetic expression $(x + 10 \* d) + (g - 3 \* (a - b)) \* (4 + \frac{b}{2})$. (b) Consider the tree in the following figure: G W A Z H G F C K L Print the nodes of the tree based on: i. the inorder traversal, ii. the preorder traversal. (c) i. What is the maximum number of external nodes (leaves) of a binary tree of height $h$? (State the number without proof.) ii. Prove that a binary tree with $n!$ leaves must have height $\Omega(n \log n)$.

          (a) Draw the binary tree representation of the following arithmetic expression
$(x + 10 \* d) + (g - 3 \* (a - b)) \* (4 + \frac{b}{2})$.
(b) Consider the tree in the following figure:
G
W
A
Z
H
G
F
C
K
L
Print the nodes of the tree based on:
i. the inorder traversal,
ii. the preorder traversal.
(c)
i. What is the maximum number of external nodes (leaves) of a binary tree of
height $h$? (State the number without proof.)
ii. Prove that a binary tree with $n!$ leaves must have height $\Omega(n \log n)$.

(a) Draw the binary tree representation of the following arithmetic expression
(x + 10 d) + (g - 3 (a - b)) (4 + (b)/(2)).
(b) Consider the tree in the following figure:
G
W
A
Z
H
G
F
C
K
L
Print the nodes of the tree based on:
i. the inorder traversal,
ii. the preorder traversal.
(c)
i. What is the maximum number of external nodes (leaves) of a binary tree of
height h? (State the number without proof.)
ii. Prove that a binary tree with n! leaves must have height Ω(n log n).

Added by Gonzalo F.

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