We insert the following elements in the following order into an empty red-black tree: P, R, C, Z. Show the resulting tree after each insertion and if there are any violations of the red-black properties, show how that violation is fixed.
Added by Heather C.
Step 1
The resulting tree is: ``` P (black) ``` Show more…
Show all steps
Your feedback will help us improve your experience
Akash M and 99 other AP CS educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose we start with an empty red-black tree and insert n > 1 nodes (that is, after the insertion of these n nodes, there are at least two internal nodes). Pick n > 1 keys and either (a) show a sequence of inserts that results in a tree with only black nodes or (b) explain why this is impossible.
Akash M.
You are given a red-black tree T with 15 internal nodes (nodes that hold key values) that form a full binary tree of height 3 (i.e., a full binary tree of height 4 if you include the NIL leaves). Can you assign colors to the nodes so that a call to RB-Insert(T, z) for any new key value z.key will cause RB-Insert-Fixup(T, z) to change the color of the root to red before switching it back to black? The initial assignment of colors needs to obey the red-black properties. If such a color assignment exists, then provide a sequence of 15 numbers whose insertion (in that order) would lead to such a tree, along with a figure of the resulting tree. If not, then explain why such an assignment cannot exist, using the fact that the tree needs to satisfy the red-black properties.
QUESTION 3: Construct an AVL tree by using the following data: 14, 17, 11, 7, 53, 4, 13, 12, 8, 60, 19, 16, 20. NOTE: Show insertions and balance factor for every node inserted. Write every new insertion in a different step. QUESTION 4: Show the Red-Black tree after successfully inserting the keys 42, 39, 33, 14, 20, 9. NOTE: Show insertions and specify color for every node inserted. Write every new insertion in a different step. QUESTION 5: i) Which traversal outputs the data in a sorted order in a BST? ii) What is the worst-case time complexity to delete an element from a BST? iii) What is a BST whose leaves are external nodes? iv) Write all the properties of Red-Black Trees. v) What are the advantages of Tree Data Structures? vi) What is the maximum difference in heights between the leaves of an AVL Tree that is possible? vii) Write the pseudocode for double rotation (Right, Left) in an AVL Tree. viii) Write the algorithm for deleting the element (all cases) in a BST. ix) Why do we prefer Red-Black Trees over AVL Trees? x) What is the worst-case time complexity to perform an operation in Red-Black Trees?
Madhur L.
Recommended Textbooks
Computer Science and Information Technology
Introduction to Programming Using Python
Computer Science - An Overview
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD