# Question: We can sort a given set of n numbers by

We can sort a given set of n numbers by first building a binary search tree containing these numbers (using TREE-INSERT repeatedly to insert the numbers one by one) and then printing the numbers by an in order tree walk. What are the worst-case and best-case running times for this sorting algorithm?

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Let us define a relaxed red-black tree as a binary search tree that satisfies red- black properties 1, 3, 4, and 5. In other words, the root may be either red or black. Consider a relaxed red-black tree T whose root is red. ...Professor Teach is concerned that RB-INSERT-FIXUP might set color [nil [T]] to RED, in which case the test in line 1 would not cause the loop to terminate when z is the root. Show that the professor's concern is unfounded by ...Can the depths of nodes in a red-black tree be efficiently maintained as fields in the nodes of the tree? Show how, or argue why not.1 and aj < bj, or2. p < q and ai = bi for all i = 0, 1, ..., p.The QUICKSORT algorithm of Section 7.1 contains two recursive calls to itself. After the call to PARTITION, the left subarray is recursively sorted and then the right subarray is recursively sorted. The second recursive call ...Post your question