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5. Consider the graph G and spanning tree T drawn below. Alice says that T is...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex A, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex A, and using the convention that nearby vertices should be...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex A, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex A, and using the convention that nearby vertices should be...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex E, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex E, and using the convention that nearby vertices should be...
Consider the following weighted graph G:
Consider the following weighted graph G: Use Prim's algorithm to find a minimal spanning tree T of this graph starting at the vertex s. You do not need to show every step of the algorithm, but to receive full credit you should: list the edges of T in the order in which they're added; redraw G and indicate which edges belong to T; compute the cost of T.
Consider the graph below. Use Prim's algorithm to find a minimal spanning tree of the graph rooted in vertex A.
Consider the graph below. Use Prim's algorithm to find a minimal spanning tree of the graph rooted in vertex A. Note: enter your answer as a set of edges [E1, E2, ...) and write each edge as a pair of nodes between parentheses separate by a comma and one blank space e.g. (A,B)
2. Consider the (undirected) graph G having the following vertex set Vand edge set E. V-0,1,2,3,4,5,6,7,8,9...
2. Consider the (undirected) graph G having the following vertex set Vand edge set E. V-0,1,2,3,4,5,6,7,8,9 E- 0,1,10,2), 11,2;, 12,4), 12,3), 13,4), (4,5), {5.6,, 14,6, 2,7) e) [8pts] Show the action of BFS starting at vertex 2. Show action of queue, parent array implementation of BFS spanning tree and display nodes in order they are traversed. Choose next node as it occurs in the adjacency list.
Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST)...
Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST) with node 1 as the "root". List the vertices in the order in which the algorithm adds them to the solution, along with the edge and its weight used to make the selection, one per line. Each line should look like this: add vertex y: edge = (x,y), weight = 5 When the algorithm ends there are, generally, edges left in the heap. List...
You are given an undirected graph G with weighted edges and a minimum spanning tree T of G.
You are given an undirected graph G with weighted edges and a minimum spanning tree T of G. Design an algorithm to update the minimum spanning tree when the weight of a single edge is increased. The input to your algorithm should be the edge e and its new weight: your algorithm should modify T so that it is still a MST. Analyze the running time of your algorithm and prove its correctness.
You are given an undirected graph G with weighted edges and a minimum spanning tree T of G.
You are given an undirected graph G with weighted edges and a minimum spanning tree T of G. Design an algorithm to update the minimum spanning tree when the weight of a single edge is decreased. The input to your algorithm should be the edge e and its new weight; your algorithm should modify T so that it is still a MST. Analyze the running time of your algorithm and prove its correctness.
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.
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex A, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex A, and using the convention that nearby vertices should be...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex A, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex A, and using the convention that nearby vertices should be...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex E, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex E, and using the convention that nearby vertices should be...
2. Consider the (undirected) graph G having the following vertex set Vand edge set E. V-0,1,2,3,4,5,6,7,8,9 E- 0,1,10,2), 11,2;, 12,4), 12,3), 13,4), (4,5), {5.6,, 14,6, 2,7) e) [8pts] Show the action of BFS starting at vertex 2. Show action of queue, parent array implementation of BFS spanning tree and display nodes in order they are traversed. Choose next node as it occurs in the adjacency list.
Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST) with node 1 as the "root". List the vertices in the order in which the algorithm adds them to the solution, along with the edge and its weight used to make the selection, one per line. Each line should look like this: add vertex y: edge = (x,y), weight = 5 When the algorithm ends there are, generally, edges left in the heap. List...
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.
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