Knowee
Questions
Features
Study Tools

Write an algorithm to find single source shortest path for a graph G whose edge weights arepositive

Question

Write an algorithm to find single source shortest path for a graph G whose edge weights are positive.

🧐 Not the exact question you are looking for?Go ask a question

Solution

Sure, here is a simple algorithm known as Dijkstra's algorithm to find the shortest path from a single source in a graph with positive edge weights:

  1. Initialize a list or array distances where distances[i] is the shortest known distance from the source to vertex i. Set distances[source] = 0 and for all other vertices, set distances[i] = infinity.

  2. Initialize an empty priority queue Q. This queue will keep track of vertices to be examined. Insert the source vertex into Q.

  3. While Q is not empty, perform the following steps:

    • Dequeue the vertex u with the smallest distance from Q.
    • For each neighbor v of u, calculate the alternative path distance alt = distances[u] + weight(u, v).
    • If alt < distances[v], then we've found a shorter path to v. Update distances[v] = alt and enqueue v into Q.
  4. Once Q is empty, the algorithm is done. The shortest path from the source to any other vertex can be found in distances.

This algorithm works by iteratively improving the distances estimate until it contains the shortest possible distances. The priority queue ensures that vertices are examined in increasing order of their distance from the source.

This problem has been solved

Similar Questions

From a given vertex in a weighted connected graph, find shortest paths to other vertices using Dijkstra’s algorithm.

Solve the following instance of single source shortest paths problem with vertex 'a' as the source usingsuitable method.

The shortest path in a graph with weighted edges can be found using:A. Depth-first searchB. Breadth-first searchC. Dijkstra's algorithmD. Kruskal's algorithm

The shortest path problem can be solved using:A. Depth-first searchB. Breadth-first searchC. Dijkstra's algorithmD. Floyd-Warshall algorithm

What is the best time complexity we can achieve to precompute all-pairs shortest paths in a weighted graph?

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.