Solve T(n) = 4T(n/2) + O(n°) using the recursion tree method. • Tree depth: • each subproblem size at depth d:

In CSE 143, you saw a recursive definition of trees. That definition looks a little different from what we saw in class. The following definition is analogous to what you saw in 143. We'll call them JTrees. Basis Step: null is a JTree. Recursive Step: If L, R are JTree then (L, data, R) is also a JTree. Show that for all JTree: if they have d – 1 copies of data then they have d copies of null. Remark: You're effectively showing here that a binary tree with d – 1 nodes has d null child pointers.

Construct a complete binary tree from the array: [ 0, 4, 3, 2, 1, 8, 7, 6, 5, 10, 9]?

Even in the worst case, a binary tree sort that uses a self-balancing binary search tree takes O(n log n) time, which is still slower than a merge sort.