A graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). A move on a graph is a move from one node to another along a single edge. Find the probability of going from Start to Finish in a sequence of two random moves in the graph shown.
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A graph consists of a collection of nodes (the
dots in the figure) connected by edges...
ignore red marks. Thanks 10. (16) You will compute the strongly connected components of this graph...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
Have the explaination please. 4 Graph Application: Network Connectivity (Adapted from Problem 9, Chapter 3 of...
Have the explaination please.
4 Graph Application: Network Connectivity (Adapted from Problem 9, Chapter 3 of K&T) Think of a communications network as a connected, undi rected graph, where messages from one node s to another node t are sent along paths from s to t. Nodes can sometimes fail. If a node v fails then no messages can be sent along edges incident on v. A network is particularly vulnerable if failure of a single node v can cause...
A graph with n nodes is connected, undirected, and acyclic. How many edges must it have? (Select ...
A graph with n nodes is connected, undirected, and acyclic. How many edges must it have? (Select the answer from the following options and prove your choice): a) n b) n*(n-1) c) n- 1 d) n/2 - 1
(b) A source in a directed graph is a node with no incoming edges. A sink...
(b) A source in a directed graph is a node with no incoming edges. A sink is a node with no outgoing edges. Assume that we know that every DAG has at least one sink. Use this fact to explain why every DAG must have at least one source. (c) Consider the following graph algorithm which takes a DAG G as input. function COMPUTESOMETHING(DAG G) Lempty linked list S stack of all source nodes in G while S is non-empty...
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...
PROMPT: Consider a graph G. A connected component is a maximal subset of nodes that induces a connected sub graph. It’s maximal in the sense that you cannot add a node with the resulting induced sub g...
PROMPT:
Consider a graph G. A connected component is a maximal subset of
nodes that induces a connected sub graph. It’s maximal in the sense
that you cannot add a node with the resulting induced sub graph
remaining connected.The following function
numComponents returns the number of connected
components in an undirected graph.
QUESTION:
What is the time complexity for this function? The time
complexity should be a function of the number of nodes |V| and the
number of edges |E|....
2 Super Mario Run A Mario World M consists of a k xk grid. Each field...
2 Super Mario Run A Mario World M consists of a k xk grid. Each field in the grid is either empty or brick. Two empty fields are marked as start and goal (see Fig. 2(a)). The goal of the game is to move the player, called Mario, from the start field to the goal field. When Mario is in field (x,y) he has the following options: Forward Mario moves to the field (x + 1,y). This move is possible...
NAME . You are given a strongly connected directed graph G (V, E) with positive edge...
NAME . You are given a strongly connected directed graph G (V, E) with positive edge weights along with a particular node vo E V. Give an efficient algorithm for finding shortest paths between all pairs of nodes, with the one restriction that these paths must all pass through v (8 points)
2 Super Mario Run A Mario World M consists of a k xk grid. Each field...
2 Super Mario Run A Mario World M consists of a k xk grid. Each field in the grid is either empty or brick. Two empty fields are marked as start and goal (see Fig. 2(a)). The goal of the game is to move the player, called Mario, from the start field to the goal field. When Mario is in field (x,y) he has the following options: Forward Mario moves to the field (x+1, y). This move is possible if...
Exercise 1 Adjacency Matrix In this part, you will implement the data model to represent a graph. Implement the followi...
Exercise 1 Adjacency Matrix In this part, you will implement the data model to represent a graph. Implement the following classes Node.java: This class represents a vertex in the graph. It has only a single instance variable of type int which is set in the constructor. Implement hashCode() and equals(..) methods which are both based on the number instance variable Node - int number +Node(int number); +int getNumberO; +int hashCode() +boolean equals(Object o) +String toString0) Edge.java: This class represents a...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
Have the explaination please.
4 Graph Application: Network Connectivity (Adapted from Problem 9, Chapter 3 of K&T) Think of a communications network as a connected, undi rected graph, where messages from one node s to another node t are sent along paths from s to t. Nodes can sometimes fail. If a node v fails then no messages can be sent along edges incident on v. A network is particularly vulnerable if failure of a single node v can cause...
(b) A source in a directed graph is a node with no incoming edges. A sink is a node with no outgoing edges. Assume that we know that every DAG has at least one sink. Use this fact to explain why every DAG must have at least one source. (c) Consider the following graph algorithm which takes a DAG G as input. function COMPUTESOMETHING(DAG G) Lempty linked list S stack of all source nodes in G while S is non-empty...
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...
PROMPT:
Consider a graph G. A connected component is a maximal subset of
nodes that induces a connected sub graph. It’s maximal in the sense
that you cannot add a node with the resulting induced sub graph
remaining connected.The following function
numComponents returns the number of connected
components in an undirected graph.
QUESTION:
What is the time complexity for this function? The time
complexity should be a function of the number of nodes |V| and the
number of edges |E|....
2 Super Mario Run A Mario World M consists of a k xk grid. Each field in the grid is either empty or brick. Two empty fields are marked as start and goal (see Fig. 2(a)). The goal of the game is to move the player, called Mario, from the start field to the goal field. When Mario is in field (x,y) he has the following options: Forward Mario moves to the field (x + 1,y). This move is possible...
NAME . You are given a strongly connected directed graph G (V, E) with positive edge weights along with a particular node vo E V. Give an efficient algorithm for finding shortest paths between all pairs of nodes, with the one restriction that these paths must all pass through v (8 points)
2 Super Mario Run A Mario World M consists of a k xk grid. Each field in the grid is either empty or brick. Two empty fields are marked as start and goal (see Fig. 2(a)). The goal of the game is to move the player, called Mario, from the start field to the goal field. When Mario is in field (x,y) he has the following options: Forward Mario moves to the field (x+1, y). This move is possible if...
Exercise 1 Adjacency Matrix In this part, you will implement the data model to represent a graph. Implement the following classes Node.java: This class represents a vertex in the graph. It has only a single instance variable of type int which is set in the constructor. Implement hashCode() and equals(..) methods which are both based on the number instance variable Node - int number +Node(int number); +int getNumberO; +int hashCode() +boolean equals(Object o) +String toString0) Edge.java: This class represents a...
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