Weighted Graph:
A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.
Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.
Example of storing edge in a weighted graph:
Object[][] edges =
{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };
Prim’s
Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.
Time Complexity of Prim’s algorithm:
Prim’s Algorithm Steps using adjacency matrix to store the weighted edges:
Step 1: Select a random vertex v, add v to S, assign an array A where A[i] = d{v, i}
Step 2: While there are vertices that belong to G and not to S do:
2.1. Iterate through A, select the minimum value A[i], add vertex i to S
2.2. for each edge e={i, j} connected to vertex i do:
2.2.1. if d{i, j} < A[j] then A[j] = d{i ,j}
Given Graph:
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Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
- Find the minimum spanning treearrow_forwardUse Prim's algorith to find a minimum spanning tree for the following weighted graph starting from vertex A. Draw the spanning tree.arrow_forwardDraw the minimum spanning tree for the following graph. Use induction to prove your result is a minimum spanning tree.arrow_forward
- Find the minimum spanning tree of the weighted grapharrow_forwardDesign an algorithm for finding a maximum spanning tree—a spanning tree with the largest possible edge weight—of a weighted connected graph. (Look at Kruskal’s Algorithm for supplemental information)arrow_forwardUse Kruskal’s Algorithm, determine a minimum spanning tree for the graph below.arrow_forward
- Find the minimum spanning tree of the weighted graph. (Show step by step)arrow_forwardCompute a minimum spanning of the following graph by using the Jarnık-Prim algorithm. Show the status of your partial minimum spanning tree after each edge insertion.arrow_forwardDesign an algorithm for finding a maximum spanning tree (a spanning tree with the largest possible edge weight) of a weighted connected graph. OR Write the algorithm for maximum spanning tree.arrow_forward
- Consider the following graph: Draw the DFS and BFS spanning trees for the above graph starting from vertex A.arrow_forwardFor the given graph draw the adjacency matrix & find the minimum spanning treearrow_forwardUse the high-level version of Kruskal's algorithm to find a minimum spanning tree for the following graph, showing the actions step-by-step.arrow_forward
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