Sure, here is a step-by-step guide on how to find the shortest paths to other vertices from a given vertex in a weighted connected graph using Dijkstra’s algorithm:

1. Initialize the shortest paths: Start by setting the distance from the source vertex to itself as 0 and to all other vertices as infinity (∞). This is because we don't know any paths to other vertices yet, so we assume they are infinitely far away.

2. Set of visited vertices: Create a set of all visited vertices. Initially, this set is empty.

3. For the current vertex, consider all its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current vertex A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, the current value will be kept.

4. When we are done considering all of the neighbors of the current vertex, mark the current node as visited. A visited node will not be checked ever again; its distance recorded now is final and minimal.

5. Select the unvisited node that is marked with the smallest tentative distance, and set it as the new "current node" then go back to step 3.

6. If all the nodes have been visited, then we have the shortest path to all other vertices from our initial vertex. If not, repeat steps 3-5 until all vertices have been visited.

This algorithm is called Dijkstra's algorithm and it is used to find the shortest paths from one node to all other nodes in a graph. It is a greedy algorithm as it picks the node with the smallest distance at each step.

Question

Sure, here is a step-by-step guide on how to find the shortest paths to other vertices from a given vertex in a weighted connected graph using Dijkstra’s algorithm:

1. Initialize the shortest paths: Start by setting the distance from the source vertex to itself as 0 and to all other vertices as infinity (∞). This is because we don't know any paths to other vertices yet, so we assume they are infinitely far away.

2. Set of visited vertices: Create a set of all visited vertices. Initially, this set is empty.

3. For the current vertex, consider all its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current vertex A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, the current value will be kept.

4. When we are done considering all of the neighbors of the current vertex, mark the current node as visited. A visited node will not be checked ever again; its distance recorded now is final and minimal.

5. Select the unvisited node that is marked with the smallest tentative distance, and set it as the new "current node" then go back to step 3.

6. If all the nodes have been visited, then we have the shortest path to all other vertices from our initial vertex. If not, repeat steps 3-5 until all vertices have been visited.

This algorithm is called Dijkstra's algorithm and it is used to find the shortest paths from one node to all other nodes in a graph. It is a greedy algorithm as it picks the node with the smallest distance at each step.

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