Homework Answers
Please find your answer below.
Please find the solution in to
the Image.
DFS:This algorithm traverses a graph in a depthward direction and uses a stack to remember to get the next vertex to start a search, when a dead end occurs in any iteration.
It has following rules:
1.Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack.
2. If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.)
3.Repeat Rule 1 and Rule 2 until the stack is empty .
**Here i have solve the first question but you can solve the
second one in a same way only.
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Ex 3: Execute Depth-First Search on the following graphs (starting from node 0) by drawing the...
Figure 1: Graph for Problem 1 Problem 1 Consider a depth-first search on the graph shown in Figure 1, starting with nod...
Figure 1: Graph for Problem 1 Problem 1 Consider a depth-first search on the graph shown in Figure 1, starting with node c. Consider a node to be "visited" whenever there is a call to dfs with the node as the second argument a) Which nodes are visited, and in what order? Use the convention that graph.neighbors ) produces successors in ascending order of label b) Suppose you call dfs_times (graph, 'c') on the graph above. This function returns dictionaries...
Using Depth-First search for Undirected Graphs, complete the table starting at 0.
Using Depth-First search for Undirected Graphs, complete the
table starting at 0.
(8) Consider the following problem space with the node "A" as the starting state and the node "H" as the goal state. Please describe how breadth-first search and depth-first search is...
(8) Consider the following problem space with the node "A" as the starting state and the node "H" as the goal state. Please describe how breadth-first search and depth-first search is working with your problem space, and list the order that the nodes are traversed under these two search algorithms.
(8) Consider the following problem space with the node "A" as the starting state and the node "H" as the goal state. Please describe how breadth-first search and depth-first search...
Show the operation of depth-first search (DFS) on the graph of Figure 1 starting from vertex...
Show the operation of depth-first search (DFS) on the graph of Figure 1 starting from vertex q. Always process vertices in alphabetical order. Show the discovery and finish times for each vertex, and the classification of each edge. (b) A depth-first forest classifies the edges of a graph into tree, back, forward, and cross edges. A breadth-first search (BFS) tree can also be used to classify the edges reachable from the source of the search into the same four categories....
(a) Compute the Breadth-First Search tree for the following graph, using node a as the root....
(a) Compute the Breadth-First Search tree for the following
graph, using node a as the root. Please use alphabetic order to
make choice when you have multiple choices. You only need to show
the tree without showing the steps. (b) What is the height of the
tree?
Currently I have a tree of depth 3, a as the root, (b,g,h,k) as
depth 1, (c,j) under b (f) under g (e) under k for depth 2, and (d)
under c for...
1 Graph Search Consider the following graph G. 1.1 Draw the DFS tree for G when...
1 Graph Search Consider the following graph G. 1.1 Draw the DFS tree for G when starting in node 0. Assume that the adjacency lists are sorted in increasing order. Write the discovery and finish times for each node in the area marked by"_/_" next to each node. Solution:
2. Write a recursive algorithm which computes the number of nodes in a general tree. 3....
2. Write a recursive algorithm which computes the number of nodes in a general tree. 3. Show a tree achieving the worst-case running time for algorithm depth. 4. Let T be a tree whose nodes store strings. Give an efficient algorithm that computes and prints, for every node v of T, the string stored at v and the height of the subtree rooted at v. Hin Consider 'decorating' the tree, and add a height field to each node (initialized to...
7.[6] Consider the graph G below: a.[3] Find a Depth-First Search tree T for the above...
7.[6] Consider the graph G below: a.[3] Find a Depth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T. b.[3] Find a Breadth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T.
Exercise 3 (35 points) Depth-First Search Consider the following graph G=(V,E): a) Complete V= {z, ....)...
Exercise 3 (35 points) Depth-First Search Consider the following graph G=(V,E): a) Complete V= {z, ....) (Fill in the blanks. Sort V alphabetically in reverse z–a) b) Complete E = {(zz), ...} c) Complete the adjacency list as a table {sort Adiſul alphabetically in reverse zna} Vertices u Adj[u] {z, } y d) Execute Depth-First Search (DFS(G)) on Graph G. Respect the order of the adjacency list as completed in the previous question. Show all figures (a) through (p) just...
1- Give an example (by drawing or by describing) of the following undirected graphs (a) A...
1- Give an example (by drawing or by describing) of the following undirected graphs (a) A graph where the degree in each vertex is even and the total number of edges is odd (b) A graph that does not have an eulerian cycle. An eulerian cycle is a cycle where every edge of the graph is visited exactly once. (c) A graph that does not have any cycles and the maximum degree of a node is 2 (minimum degree can...
Figure 1: Graph for Problem 1 Problem 1 Consider a depth-first search on the graph shown in Figure 1, starting with node c. Consider a node to be "visited" whenever there is a call to dfs with the node as the second argument a) Which nodes are visited, and in what order? Use the convention that graph.neighbors ) produces successors in ascending order of label b) Suppose you call dfs_times (graph, 'c') on the graph above. This function returns dictionaries...
Using Depth-First search for Undirected Graphs, complete the
table starting at 0.
(8) Consider the following problem space with the node "A" as the starting state and the node "H" as the goal state. Please describe how breadth-first search and depth-first search is working with your problem space, and list the order that the nodes are traversed under these two search algorithms.
(8) Consider the following problem space with the node "A" as the starting state and the node "H" as the goal state. Please describe how breadth-first search and depth-first search...
Show the operation of depth-first search (DFS) on the graph of Figure 1 starting from vertex q. Always process vertices in alphabetical order. Show the discovery and finish times for each vertex, and the classification of each edge. (b) A depth-first forest classifies the edges of a graph into tree, back, forward, and cross edges. A breadth-first search (BFS) tree can also be used to classify the edges reachable from the source of the search into the same four categories....
(a) Compute the Breadth-First Search tree for the following
graph, using node a as the root. Please use alphabetic order to
make choice when you have multiple choices. You only need to show
the tree without showing the steps. (b) What is the height of the
tree?
Currently I have a tree of depth 3, a as the root, (b,g,h,k) as
depth 1, (c,j) under b (f) under g (e) under k for depth 2, and (d)
under c for...
1 Graph Search Consider the following graph G. 1.1 Draw the DFS tree for G when starting in node 0. Assume that the adjacency lists are sorted in increasing order. Write the discovery and finish times for each node in the area marked by"_/_" next to each node. Solution:
2. Write a recursive algorithm which computes the number of nodes in a general tree. 3. Show a tree achieving the worst-case running time for algorithm depth. 4. Let T be a tree whose nodes store strings. Give an efficient algorithm that computes and prints, for every node v of T, the string stored at v and the height of the subtree rooted at v. Hin Consider 'decorating' the tree, and add a height field to each node (initialized to...
7.[6] Consider the graph G below: a.[3] Find a Depth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T. b.[3] Find a Breadth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T.
Exercise 3 (35 points) Depth-First Search Consider the following graph G=(V,E): a) Complete V= {z, ....) (Fill in the blanks. Sort V alphabetically in reverse z–a) b) Complete E = {(zz), ...} c) Complete the adjacency list as a table {sort Adiſul alphabetically in reverse zna} Vertices u Adj[u] {z, } y d) Execute Depth-First Search (DFS(G)) on Graph G. Respect the order of the adjacency list as completed in the previous question. Show all figures (a) through (p) just...
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