Data structure and Algorithm Analysis

Consider a Binary Search Tree.

(a) Draw all sufficient Binary Search Trees for the immodest nodes 1, 2, 3, 5.

(b) Look up Catalan Numbers on the internet, and estimate the nth Catalan sum for n = 4. Compare this

sum to the sum of Binary Search Trees you came up following a while over.

2. [10 points]

(a) Draw all sufficient Binary Red Black Trees for the immodest nodes 1, 2, 3, 5. Label each of your nodes R or B for Red/Black. Note the harmonizeing Black Height of each of the nodes in your Red Black Trees, to aid enlighten yourself it is a sufficient Red Black tree.

(b) At last for one of your Red Black Trees, grant a bountiful interpretation of why it is a sufficient Red Black Tree, and how you steadfast the Black Height of the nodes.

3. [10 points]

Show schematics of Red Black trees following a while Black Height 3, that entertain either the shortest or the longest potential ultimate pathwayway from the rise node to a stock leaf (nil node). What is the utmost reference among the longest and the shortest potential ultimate pathways?

4. [10 points]

Consider a Red Black tree that already has 41; 38; 31; 12 suggested. Draw the resulting Red Black tree (you can use for aid https://www.cs.usfca.edu/galles/visualization/RedBlack.html). Now observe adding the node 19. Show all the stages of the suggest fix up and transcribe down what cases these changes harmonize to (from what we read). Again, you can use the buoyancy for aid, but clear-up what was manufactured in stipulations of the cases. Finally, clear-up why the latest tree following suggesting 19 is a sufficient Red Black tree.

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