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Which of the following standard algorithms is not Dynamic Programming based.
- a)Bellman–Ford Algorithm for single source shortest path
- b)Floyd Warshall Algorithm for all pairs shortest paths
- c)0-1 Knapsack problem
- d)Prim’s Minimum Spanning Tree
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Which of the following standard algorithms is not Dynamic Programming ...
Prim’s Minimum Spanning Tree is a Greedy Algorithm. All other are dynamic programming based.
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Which of the following standard algorithms is not Dynamic Programming ...
Prim's Minimum Spanning Tree
Prim's Minimum Spanning Tree algorithm is not based on Dynamic Programming. It is a greedy algorithm used to find the minimum spanning tree for a connected, undirected graph.
Dynamic Programming Algorithms
- Dynamic Programming algorithms solve complex problems by breaking them down into simpler subproblems.
- These subproblems are solved recursively, and their solutions are stored to avoid redundant calculations.
- Dynamic Programming is commonly used in algorithms like Bellman-Ford and Floyd Warshall.
Prim's Minimum Spanning Tree Algorithm
- Prim's algorithm starts with an arbitrary node and grows the minimum spanning tree one edge at a time.
- At each step, it adds the shortest edge that connects a vertex in the tree to a vertex outside the tree.
- This process continues until all vertices are included in the minimum spanning tree.
Key Differences
- Prim's algorithm is a greedy algorithm that focuses on selecting the next best option at each step.
- Dynamic Programming algorithms, on the other hand, involve storing and reusing solutions to subproblems.
In conclusion, Prim's Minimum Spanning Tree algorithm is not based on Dynamic Programming, unlike Bellman-Ford and Floyd Warshall algorithms. It uses a different approach to find the minimum spanning tree of a graph.
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