# What is shortest path in a graph?

## What is shortest path in a graph?

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

How do you find the shortest path in a directed graph?

Shortest Path in Directed Acyclic Graph

1. 1) Initialize dist[] = {INF, INF, ….} and dist[s] = 0 where s is the source vertex.
2. 2) Create a topological order of all vertices.
3. 3) Do following for every vertex u in topological order. ………..Do following for every adjacent vertex v of u.

How the shortest path is determined?

Dijkstra’s algorithm can be used to determine the shortest path from one node in a graph to every other node within the same graph data structure, provided that the nodes are reachable from the starting node. Dijkstra’s algorithm can be used to find the shortest path.

### How do you calculate shortest path in a graph with examples?

For a graph with vertices:

1. Initialize the shortest paths between any vertices with Infinity.
2. Find all pair shortest paths that use intermediate vertices, then find the shortest paths that use intermediate vertex and so on..
3. Minimize the shortest paths between any pairs in the previous operation.

How do you find the shortest path between two vertices on A graph?

Algorithm to find the shortest path between two vertices in an undirected graph

1. Input the graph.
2. Input the source and destination nodes.
3. Find the paths between the source and the destination nodes.
4. Find the number of edges in all the paths and return the path having the minimum number of edges.

How do you find the shortest path on A graph in C?

Step 1 : Create a set shortPath to store vertices that come in the way of the shortest path tree. Step 2 : Initialize all distance values as INFINITE and assign distance values as 0 for source vertex so that it is picked first. Step 3 : Loop until all vertices of the graph are in the shortPath.

#### How do you find the shortest path between two vertices?

How do you find the shortest path from the vertex?

Dijkstra’s Algorithm

1. Mark the ending vertex with a distance of zero. Designate this vertex as current.
2. Find all vertices leading to the current vertex. Calculate their distances to the end.
3. Mark the current vertex as visited.
4. Mark the vertex with the smallest distance as current, and repeat from step 2.

How do you find the path on a graph?

Find if there is a path between two vertices in a directed graph

1. Approach: Either Breadth First Search (BFS) or Depth First Search (DFS) can be used to find path between two vertices. Take the first vertex as source in BFS (or DFS), follow the standard BFS (or DFS).
2. BFS Algorithm: