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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 ...
The correct answer is option 'D' – Prim's Minimum Spanning Tree algorithm.
Prim's algorithm is a greedy algorithm used to find the minimum spanning tree of a connected, weighted graph. It does not fall under the category of dynamic programming.
Let's briefly explain the other options to understand why they are dynamic programming-based algorithms:
a) Bellman-Ford Algorithm: This algorithm is used to find the shortest path from a single source vertex to all other vertices in a weighted directed graph. It employs dynamic programming by iteratively relaxing the edges of the graph to gradually find the shortest paths. It utilizes the principle of optimal substructure, which is a key characteristic of dynamic programming.
b) Floyd Warshall Algorithm: This algorithm is used to find the shortest paths between all pairs of vertices in a weighted directed graph. It relies on the concept of dynamic programming to iteratively update the shortest paths matrix based on intermediate vertices. The algorithm builds upon previously computed subproblems, making it a classic example of dynamic programming.
c) 0-1 Knapsack Problem: The 0-1 Knapsack problem is a classic optimization problem where a knapsack has a limited capacity, and there are items with different weights and values. The goal is to maximize the value of the items included in the knapsack while not exceeding its capacity. This problem is often solved using dynamic programming techniques, specifically the memoization or tabulation approach, to efficiently compute the optimal solution.
In summary, while options 'a', 'b', and 'c' involve dynamic programming approaches, option 'd' – Prim's Minimum Spanning Tree algorithm – does not fall into the category of dynamic programming.
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Community 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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