1. (20 marks) Binary trees' properties: recal the following concepts and then answer questions. a binary tree is full if each node in the tree is either a leaf or has exactly two child nodes. a binary tree with h levels is complete if all levels except possibly the last level (hth level are completely full, and the last level (hthlevel) has all its nodes filled into from the left side. If the level of the root ofa non-empty binary tree is level 0, the level ofthe root's children is level 1, etc., what is the maximum number of nodes on level i? If the height of a non-empty binary tree is h, what is the maximum number of nodes that the tree has in total? Express your answer in closed form (i.e. in terms of functions and mathematical operations, do not use "..." in your final answer). If a non-empty complete binary tree has n nodes, what is the height of this tree? Express your answer in closed form. Prove that the number of leaves in a non-empty full binary tree is 1 more than the number of non-leaves. When you prove this, don't just show an example. Write your proofin general for ANY non-empty full binary tree. If a non-empty binary tree has n nodes, what is the possible maximal height of the binary tree? What is the possible minimal height of the binary tree? a. b. c. d. e