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

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.