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Which of the following standard algorithms is not a Greedy algorithm?
- a)Dijkstra's shortest path algorithm
- b)Prim's algorithm
- c)Kruskal algorithm
- d)Huffman Coding
- e)Bellmen Ford Shortest path algorithm
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
Which of the following standard algorithms is not a Greedy algorithm?a...
The Bellman-Ford algorithm is a graph search algorithm that finds the shortest path between a given source vertex and all other vertices in the graph. This algorithm can be used on both weighted and unweighted graphs.
Like Dijkstra's shortest path algorithm, the Bellman-Ford algorithm is guaranteed to find the shortest path in a graph. Though it is slower than Dijkstra's algorithm, Bellman-Ford is capable of handling graphs that contain negative edge weights, so it is more versatile. It is worth noting that if there exists a negative cycle in the graph, then there is no shortest path. Going around the negative cycle an infinite number of times would continue to decrease the cost of the path (even though the path length is increasing). Because of this, Bellman-Ford can also detect negative cycles which is a useful feature.
Most Upvoted Answer
Which of the following standard algorithms is not a Greedy algorithm?a...
Explanation:
A greedy algorithm is an algorithmic paradigm that follows the problem-solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum. In other words, the algorithm makes the best possible decision at each step, without considering the overall effect on the problem.
Among the given options, the Bellman-Ford Shortest path algorithm is not a Greedy algorithm. Here's why:
1. Dijkstra's shortest path algorithm:
● It is a Greedy algorithm.
● It works by selecting the vertex with the smallest distance from the source vertex at each step.
● It does not consider the possibility that a longer path may lead to a shorter overall distance.
2. Prim's algorithm:
● It is a Greedy algorithm.
● It works by starting with a single vertex and adding the closest vertex to the existing tree at each step.
● It does not consider the possibility that a longer edge may lead to a shorter overall distance.
3. Kruskal's algorithm:
● It is a Greedy algorithm.
● It works by sorting all the edges by weight and selecting the edges in ascending order while avoiding cycles.
● It does not consider the possibility that selecting a heavier edge may lead to a better solution overall.
4. Huffman coding:
● It is a Greedy algorithm.
● It works by assigning variable-length codes to input characters based on their frequency of occurrence.
● It does not consider the possibility that a different code assignment may lead to a better overall compression.
5. Bellman-Ford Shortest path algorithm:
● It is not a Greedy algorithm.
● It works by relaxing all the edges in the graph repeatedly, and keeping track of the distance from the source vertex to each vertex.
● It considers all possible paths, even those that do not lead to an immediate improvement in distance, and avoids negative cycles.
In conclusion, while all the other given algorithms are Greedy algorithms, the Bellman-Ford Shortest path algorithm is not.
A greedy algorithm is an algorithmic paradigm that follows the problem-solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum. In other words, the algorithm makes the best possible decision at each step, without considering the overall effect on the problem.
Among the given options, the Bellman-Ford Shortest path algorithm is not a Greedy algorithm. Here's why:
1. Dijkstra's shortest path algorithm:
● It is a Greedy algorithm.
● It works by selecting the vertex with the smallest distance from the source vertex at each step.
● It does not consider the possibility that a longer path may lead to a shorter overall distance.
2. Prim's algorithm:
● It is a Greedy algorithm.
● It works by starting with a single vertex and adding the closest vertex to the existing tree at each step.
● It does not consider the possibility that a longer edge may lead to a shorter overall distance.
3. Kruskal's algorithm:
● It is a Greedy algorithm.
● It works by sorting all the edges by weight and selecting the edges in ascending order while avoiding cycles.
● It does not consider the possibility that selecting a heavier edge may lead to a better solution overall.
4. Huffman coding:
● It is a Greedy algorithm.
● It works by assigning variable-length codes to input characters based on their frequency of occurrence.
● It does not consider the possibility that a different code assignment may lead to a better overall compression.
5. Bellman-Ford Shortest path algorithm:
● It is not a Greedy algorithm.
● It works by relaxing all the edges in the graph repeatedly, and keeping track of the distance from the source vertex to each vertex.
● It considers all possible paths, even those that do not lead to an immediate improvement in distance, and avoids negative cycles.
In conclusion, while all the other given algorithms are Greedy algorithms, the Bellman-Ford Shortest path algorithm is not.
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Community Answer
Which of the following standard algorithms is not a Greedy algorithm?a...
Greedy is an algorithmic paradigm that builds up a solution piece by piece,
always choosing the next piece that offers the most obvious and immediate benefit. So the problems where choosing locally optimal also leads to global solution are best fit for Greedy.
- Standard Greedy Algorithms :
- Activity Selection Problem
- Egyptian Fraction Job
- Sequencing Problem Job
- Sequencing Problem (Using Disjoint Set) Job
- Sequencing Problem – Loss Minimization Job
- Selection Problem – Loss Minimization Strategy
- Huffman Coding
- Efficient Huffman Coding for sorted input
- Huffman Decoding
- Water Connection Problem
- Policemen catch thieves
- Minimum Swaps for Bracket Balancing
- Fitting Shelves Problem
- Assign Mice to Holes
For a perfect guide to C++ and greedy algos surf through the link below:
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