Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph? ans. topological sort binary search radix sort hash tab
Question
Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph? ans. topological sort
binary search
radix sort
hash tab
Solution
The algorithm that efficiently calculates the single source shortest paths in a Directed Acyclic Graph is the Topological Sort.
Here's a step-by-step explanation:
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Topological Sort is used to find the shortest path in a Directed Acyclic Graph (DAG). It uses a stack to keep track of the vertices in the graph.
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The algorithm starts by calling the recursive helper function for all vertices that have not been visited. In the recursive function, for every adjacent and unvisited vertex, it calls the recursive function for those vertices.
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If the vertex has no adjacent vertices or all adjacent vertices have been visited, the vertex is pushed to the stack.
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Once the recursive function has been called for all vertices and the stack is complete, the vertices are popped from the stack and printed, giving the Topological sorting of the graph.
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The Topological Sort algorithm can then be used to find the shortest path in the DAG. The algorithm initializes distances to all vertices as infinite and distance to source as 0, then it finds a topological sorting of the graph.
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Topological Sorting of a graph represents a linear ordering of the graph (Each directed edge uv from vertex u to vertex v, u comes before v in the ordering).
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Once a topological order is established, the algorithm processes all vertices in topological order. For every vertex processed, it updates distances of its adjacent using distance of current vertex.
This way, the Topological Sort algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph.
Similar Questions
Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph
Which algorithm is used to find the shortest path in a graph?Question 16Select one:Bellman-Ford algorithmTopological SortFloyd-Warshall algorithmDijkstra's Algorithm
Describe, in plain English, an algorithm that given a weighted, directed, acyclic graph G=(V,E,w) (with integer weights) and a vertex s in V calculates the length of the longest path from s to every other vertex v (if a vertex is unreachable from s, then the length of the longest path for that vertex should be infinity). Your algorithm should run in O( |V| + |E| ) time in total, assuming that G is implemented with an adjacency list, as usual. Explain why your algorithm has this running time.[Hint: you might want to consider a new graph G', more or less similar to G, and reduce the problem for G to a problem for G' that we have solved in the lectures]
Let G be a directed acyclic graph. If we have the topological ordering of G, we can modify the Bellman's Ford algorithm to be a one-pass Bellman's Ford algorithm. It works as follow:For each vertex u of G in topological order, we relax the cost of u's outgoing edges. for each vertex u in topological order for each edge e // e = (u -> v) relax(e)Since the shortest path to vertex u is already found, we can subsequently update the shortest path of its adjacent vertices when we follow the topological order.What is the time complexity for the algorithm above?
Which graph theory algorithm is used to find the shortest path from a source vertex to all other vertices in a graph?A. Kruskal's algorithmB. Prim's algorithmC. Dijkstra's algorithmD. Floyd-Warshall algorithm
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