## HOMEWORK 5

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.