for this graph starting at vertex H. Ties should be resolved by whichever vertex is alphabetically earlier.
list the order the vertices are removed during Dijkstra's
algorithm for this graph starting at vertex H. Also list any update
to the known distance values for neighboring vertices (including
the initial update from infinity to a known value). Also include a
list of edges (pairs of vertices) in the tree that is formed as
part of the traversal in Dijkstra's algorithm. Ties should be
resolved by whichever vertex is lower numbered.
Homework Answers
- Note the weight of the edge, if there is no edge, put infinity
- Find the least weighted vertex1 in row 1 and note the weight as well
- Now consider the vertices from above vertex1 and add above weight with current weight from vertex1 to other vertices
- If any are lesser, replace values, else let them be the same
- Do this until no vertices are left
Add Answer to:
for this graph starting at vertex H. Ties should be resolved by
whichever vertex is alphabetically...
Draw the DFS search tree with starting vertex E and break ties alphabetically. Assuming unit edge...
Draw the DFS search tree with starting vertex E and break ties alphabetically. Assuming unit edge length (i.e., ignore edge weight), draw the BFS search tree with starting vertex E and break ties alphabetically. Suppose the Dijkstras algorithm is run on the graph with starting vertex E: (i) draw a table showing the intermediate distance values of all vertices at each iteration of the algorithm; (ii) show the final shortest-path tree.
Algorithm Question 5. Below is a graph with edge lengths. Apply Dijkstra's algorithm to find the shortest paths, starting at vertex A, to all other vertices. Write down the sequence in which the...
Algorithm Question
5. Below is a graph with edge lengths. Apply Dijkstra's algorithm to find the shortest paths, starting at vertex A, to all other vertices. Write down the sequence in which the edges are chosen, breaking ties by using vertices at the same length in alphabetic orde. 3 Ga 2
5. Below is a graph with edge lengths. Apply Dijkstra's algorithm to find the shortest paths, starting at vertex A, to all other vertices. Write down the sequence in...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in the order they were added to the minimum spanning tree. Demonstrate Dijkstra's algorithm on the graph, using vertex A as the source. Write the vertices in the order which they are marked and compute all distances at each step.
You're running Dijkstra's algorithm to find all shortest paths starting with vertex A in the graph...
You're running Dijkstra's algorithm to find all shortest paths
starting with vertex A in the graph below, but you pause after
vertex E has been added to the solution (and the relaxation step
for vertex E has been performed). Annotate the graph as follows:
(1) label each node with its current dist value, (2)
darken the edges that are part of the current spanning tree (i.e.,
the parent links), (3) draw a dotted circle around the
"cloud'' of vertices that...
Run Dijkstra's algorithm on the graph G below, where s is the source vertex.
Run Dijkstra's algorithm on the graph G below, where s is the source vertex. Draw a table that shows the vertices in Q at each iteration. Write thed and I values of each vertex. Color the edges in the shortest-path tree, similar to the example from the notes. List the order in which vertices are added to S. Use the algorithm learned in class.
Using the following graph and Dijkstra's algorithm, calculate the shortest distance to each other vertex starting...
Using the following graph and Dijkstra's algorithm, calculate the shortest distance to each other vertex starting from vertex A. Label all vertices with the total distance (from A). Indicate the order nodes are added to cloud. Draw a Minimum Spanning Tree for the graph. You should label all nodes in the tree, but you do not need to indicate edge weights or total distance. 2 D C L 7 6 2 7 2 A K B 4 7 4 1...
Run Prim (starting from vertex "f") and Kruskal algorithms on the graph below: 3 2 9...
Run Prim (starting from vertex "f") and Kruskal algorithms on the graph below: 3 2 9 3 . (5 points) Prim's algorithm: draw a table that shows the vertices in the queue at each iteration, similar to example from the notes (2 points) Prim's algorithm: using the table from the first part, list the order in which edges are added to the tree (3 points) Kruskal's algorithm: list the order in which edges are added to the tree
Find the list of vertices following the breadth-first traversal of the graph below starting from vertex A.
Find the list of vertices following the breadth-first traversal of the graph below starting from vertex A. (Note: when two or more nodes are equally as likely to be selected, select the one that comes first alphabetically). Enter your answer as a list of nodes with no space (or any other separator) between them.
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:The Bellman-Ford algorithm makes |V|-1 = 7-1 = 6 passes through the edge list E. Each pass relaxes the edges in the order they appear in the edge list. As with Dijkstra's algorithm, we record the current best known cost D[V] to reach each vertex V from the start vertex S. Initially D[A]=0 and D[V]=+oo for all the other vertices...
3. Given a directed graph G < V E >, we define its transpose Gr < V.E1 > to be the graph such tha...
3. Given a directed graph G < V E >, we define its transpose Gr < V.E1 > to be the graph such that ET-{ < v, u >:< u, v >EE). In other words, GT has the same number of edges as in G, but the directions of the edges are reversed. Draw the transpose of the following graph: ta Perform DFS on the original graph G, and write down the start and finish times for each vertex in...
Draw the DFS search tree with starting vertex E and break ties alphabetically. Assuming unit edge length (i.e., ignore edge weight), draw the BFS search tree with starting vertex E and break ties alphabetically. Suppose the Dijkstras algorithm is run on the graph with starting vertex E: (i) draw a table showing the intermediate distance values of all vertices at each iteration of the algorithm; (ii) show the final shortest-path tree.
Algorithm Question
5. Below is a graph with edge lengths. Apply Dijkstra's algorithm to find the shortest paths, starting at vertex A, to all other vertices. Write down the sequence in which the edges are chosen, breaking ties by using vertices at the same length in alphabetic orde. 3 Ga 2
5. Below is a graph with edge lengths. Apply Dijkstra's algorithm to find the shortest paths, starting at vertex A, to all other vertices. Write down the sequence in...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in the order they were added to the minimum spanning tree. Demonstrate Dijkstra's algorithm on the graph, using vertex A as the source. Write the vertices in the order which they are marked and compute all distances at each step.
You're running Dijkstra's algorithm to find all shortest paths
starting with vertex A in the graph below, but you pause after
vertex E has been added to the solution (and the relaxation step
for vertex E has been performed). Annotate the graph as follows:
(1) label each node with its current dist value, (2)
darken the edges that are part of the current spanning tree (i.e.,
the parent links), (3) draw a dotted circle around the
"cloud'' of vertices that...
Using the following graph and Dijkstra's algorithm, calculate the shortest distance to each other vertex starting from vertex A. Label all vertices with the total distance (from A). Indicate the order nodes are added to cloud. Draw a Minimum Spanning Tree for the graph. You should label all nodes in the tree, but you do not need to indicate edge weights or total distance. 2 D C L 7 6 2 7 2 A K B 4 7 4 1...
Run Prim (starting from vertex "f") and Kruskal algorithms on the graph below: 3 2 9 3 . (5 points) Prim's algorithm: draw a table that shows the vertices in the queue at each iteration, similar to example from the notes (2 points) Prim's algorithm: using the table from the first part, list the order in which edges are added to the tree (3 points) Kruskal's algorithm: list the order in which edges are added to the tree
3. Given a directed graph G < V E >, we define its transpose Gr < V.E1 > to be the graph such that ET-{ < v, u >:< u, v >EE). In other words, GT has the same number of edges as in G, but the directions of the edges are reversed. Draw the transpose of the following graph: ta Perform DFS on the original graph G, and write down the start and finish times for each vertex in...
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