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Minimum Spanning Tree Using Prism's Algorithm
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- 2. Design & Analysis ofAlgorithm Greedy Technique Algorithm Design Technique : Problem : Prim's Algorithm Name: Mrunal Sanjay Patil Roll No: 64 Year: FYMCA
- 3. Greedy Method •Greedy Method finds out of many options, but you have to choose the best option. • In this method we focused on the first stage and decide the output.
- 4. Minimum SpanningTree A connected subgraph ‘M’ of graph G(V,E) is said to be spanning Iff, ‘M’ should contain all vertices of ‘G’. ‘M’ should contain (|V|-1) edges. 𝑉1 𝑉2 𝑉3 𝑉4 𝐸1 𝐸2 𝐸4 𝐸3
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- 6. Minimum CostSpanning Tree • The cost of the spanning tree is the sum of the weights of all the edges in the tree. • Minimum spanning tree is the spanning tree where the cost is minimum among all the spanning trees. Undirected Graph 4 1 3 2 5 A B C D Spanning Tree Cost = 4+5+2 = 11 4 1 3 2 5 A B C D Minimum Cost Spanning Tree Cost = 4+1+2 = 7 1 4 3 2 5 A B C D
- 7. We canfind the minimum cost spanning tree using 2 methods: Prim’s Algorithms Kruskal’s Algorithms
- 8. Prim’s Algorithms •Prim’s algorithm is a famous greedy algorithm. • It is used for finding the Minimum Spanning Tree of a given graph. • To apply prims algorithm, the given graph must be weighted, connected and undirected.
- 9. Explanation : B A C G F H I D 1 E 510 6 7 6 3 2 8 12 3 7 8
- 10. B A D 1 5 C F 3 2 E 7 H 8 G 7 I 3 Minimum CostSpanning Tree
- 11. = Sum ofall edge weight Cost of Minimum Spanning Tree = 1 + 5 + 2 + 3 + 7 + 8 + 7 + 3 = 36
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- 14. If the inputgraph is presented using adjacency list , then the time complexity of Prim’s algorithm can be reduced to O(E log V) with the help of binary heap. Time Complexity of the above program is O( ) 𝑉2
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