Please answer this question and give detailed reasons for your answer (explain). Thank you.

2. (20 pts.) Imagine a generalized version of binary heap where each non-leaf node has z children instead of 2. a. Show how you would represent such a heap using arrays. Show how to reach to the children nodes and parent nodes. Remember that for binary heap, given a node at position i, its left and right children are at positions 2i and 2i + 1, respectively. Also given a non-root node at position i, its parent node is at position [1/2]. Derive these formulas for your generic heap. Justify your answer. b. What is the height of the heap tree in terms of n and z where n is the total number of elements in the heap and z is the number of children each non- leaf node could have? Justify your answer. Remember that for binary heap, its height is [log2(n)]. 2. (20 pts.) Imagine a generalized version of binary heap where each non-leaf node has z children instead of 2. a. Show how you would represent such a heap using arrays. Show how to reach to the children nodes and parent nodes. Remember that for binary heap, given a node at position i, its left and right children are at positions 2i and 2i + 1, respectively. Also given a non-root node at position i, its parent node is at position [1/2]. Derive these formulas for your generic heap. Justify your answer. b. What is the height of the heap tree in terms of n and z where n is the total number of elements in the heap and z is the number of children each non- leaf node could have? Justify your answer. Remember that for binary heap, its height is [log2(n)]