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Problem 4: Given a min-heap, which is a complete binary tree, you carn assign each node an index by starting at the root, progressively moving down through the levels, and going from left to right in each level. For example, the root has index 0, its left child has index 1, its right child has index 2, etc. Using these indices, you can store the tree in an array. (Recall that a complete binary tree has the property that every level must be full before starting on the next level) Consider the node at index j of the array (for simiplicity, suppose that array indices begin at 1). What is the index of the node's parent? What are the indices of the node's left and right children (if any)? Prove your answers Extra Credit (5 points): A binary tree is full if all vertices have either 0 or two children. Let Bn denote the number of full binary trees with n vertices. 1. What are the values of B3, B;, and B-? For general n, derive a recurrence relation for B. Include base cases 3. Show that Bn is S012(n-1)/2)