CS 367: Introduction to Data Structures

HOMEWORK 5

Due Date: 30th July

1. Show the red-black tree that results from inserting each sequence of integers into a tree that is initially empty. In your answer, you can grapically draw red nodes with their data and use R_ as the prefix and black nodes with B_ as the prefix. An example for this is shown below.

   1. 55, 99, 33, 44, 11, 77, 88, 66, 22

   2. 77, 66, 55, 22, 33, 88, 11, 44, 99

   
   Here is an example of the RBT from lecture:

   
                        B_14
                      /      \
                    B_7      R_20
                   /  \      /   \
                 R_1  R_11 B_18  B_23
                                   \
                                   R_29
   
   

2. Consider the following directed graph, which is given in adjacency list form:

   1 : 2, 5, 7
   2 : 3, 4, 5
   3 : 1
   4 : 3, 6
   5 : 8
   6 : 1, 4, 9
   7 : 2, 9
   8 : 6
   9 : 3
   

   (I.e., the first line says that the graph contains a directed edge from node 1 to node 2, an edge from 1 to 5, and so on.)

   Part A:

   1. Show the order that nodes are visited for breadth-first search on the graph above starting at 1 and visiting successors in increasing numerical order (i.e., follow the CS 367 conventions). (e.g., if a node has edges to vertices 3, 7, and 9, your search should visit node 3 before 7 and 7 before 9).
   2. Give the corresponding BFS spanning tree in adjacency list form.
      Note: List add nodes in the adjacency list even if there are no edges from that particular node.

   Part B:

   1. Repeat part A but for depth-first search, again visiting successors in increasing numerical order.
   2. Give the corresponding DFS spanning tree in adjacency list form.
      Note: List add nodes in the adjacency list even if there are no edges from that particular node.
   
   

SUBMISSION

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