Explanation Given: Prism algorithm Concept used: Prism algorithm: It is a greedy algorithm which traverse each edge of the graph only keeping the smallest connection to each node. Calculation: Algorithm to find minimum spanning tree using prism’s algorithm is as follows: Program: Import java. util. * ; Import java. lang. * ; Import java.io. * ; Class MST { Private static final int V = 5 ; int min Key ( int key [ ] , Boolean mstSet [ ] ) { / / Initialize min value int min = lnteger . MAX _ VALUE , min _ index = − 1 ; For ( int v = O ; v < V ; v ÷ ÷ ) If ( mstSet [ v ] = = false & & key [ v ] < mm ) { min = key [ v ] ; min _ index = v ; } Return min _index; / / A utility operate to print the made MST stored in / / parent [ ] Void printMST ( int parent [ ] , int n , int graph [ ] [ ] ) { System .out .println ( " Edge Weight" ) ; for ( int i = 1 ; i < V ; i ÷ ÷ ) System .out .println ( parent [ i ] + " − " + i + " " + graph [ i ] ( Parent [ i ] ) ) / / Function to construct and print MST for a graph diagrammatically / / Using adjacency matrix representation Void primMST ( int graph [ ] [ ] ) { / / Array to store constructed MST int parent [ ] = new int [ V ] ; / / Key values used to pick the least weight edge in cut int key [ ] = new int [ V ] ; / / To represent set of vertices nonetheless enclosed in MST Boolean mstSet [ ] = new Boolean [ V ] ; / / Initialize all keys as INFINITE For ( int i = O ; i < V ; k + + ) { key [ i ] = Integer

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ISBN: 9781264309689

Author: ROSEN

Publisher: MCG

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Chapter 11, Problem 17CP

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Given tile list of edges and their weights of a weighted undirected connected graph, use Prim’s algorithm to find a minimum spanning tree of this graph.

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Chapter 11, Problem 16CP

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Chapter 11 Solutions

DISCRETE MATHEMATICS LOOSELEAF

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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Given tile list of edges and their weights of a weighted undirected connected graph, use Prim’s algorithm to find a minimum spanning tree of this graph.

Solution Summary: The author explains Prim's algorithm to find a minimum spanning tree of the weighted undirected connected graph.

Given tile list of edges and their weights of a weighted undirected connected graph, use Prim’s algorithm to find a minimum spanning tree of this graph.

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Chapter 11 Solutions