Shortest Path Algorithm
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The document summarizes information about shortest path algorithms. It discusses what shortest path algorithms are, the main types including Bellman-Ford, Dijkstra's, and Floyd-Warshall algorithms, and their applications. Bellman-Ford finds shortest paths from a source to all other vertices in a weighted graph. Dijkstra's algorithm finds shortest paths from a source to all vertices. Floyd-Warshall finds shortest paths between all pairs of vertices, handling negative edge weights. Shortest path algorithms are used for routing, social networks, mapping, and more. They are simple to implement and understand, and widely used by companies.
![Floyd-
warshall’s
AlgorithmAlgorithm Steps:
1. Initialize the shortest paths between any 2 vertices with Infinity.
2. Find all pair shortest paths that use 0 intermediate vertices, then find the shortest path
s that use 1intermediate vertex and so on.. until using all N vertices as intermediate no
des.
3. Minimize the shortest paths between any 2 pairs in the previous operation.
4. For any 2 vertices (i,j) , one should actually minimize the distances between this pair u
sing the first Knodes, so the shortest path will be: min(dist[i][k]+dist[k][j],dist[i][j]).
Floyd Warshall’s Ford Algorithms](https://image.slidesharecdn.com/shortestpathalgorithm-190327150241/85/Shortest-Path-Algorithm-7-320.jpg)
Shortest Path Algorithm
- 1. WELCOME TO OPEN DAY ORGANIZED BY SAMBHARAM INSTITUTE OF TECHNOLOGY
- 2. What we’re going to discuss? 01 02 03 Shortest Path Algorithms What is Shortest Path Algorithm? . Types of Shortest Path Algorithm How many types of Shortest Path algorithm is there? Applications and usage Where it is used and what are some real life examples? Features What are the features of Shortest Path Algorithm. 04
- 3. What is Shortest Path Algorithm 1. The shortest path Algorithm is about finding a path between two vertices in a graph such that the total sum of the edges weights is minimum. 2. Shortest path Algorithm is used to find a path between two vertices(or nodes) in a graph such that the sum of weights of its constituent edge is minimized. Shortest Path Algorithms Shortest path (A, C, E, D, F) bet ween vertices A and F in the wei ghted directed graph
- 4. Types of Shortest path Algorithm Below are the types Bellman Ford’s Algorithm is used to find the shortest paths from the source vertex to all other vertices in a weighted graph. Bellman Ford’s Algorithm Dijkstra’s algorithm has many variants but the most common one is to find the shortest path from source vertex to all other vertices in the graph. Dijkstra’s Algorithm Floyd-Warshall’s Algorithm is used to find the shortest paths between all pairs of vertices in a graph. Where each edge In the graph has a weight either negative or positive. The biggest advantage of using this algorithm is that all the shortest distance between in any vertices can be calculated. Floyd-Warshall’s Algorithm 01 02 03
- 5. Bellman- Ford Algorithm Algorithm Steps: 1. The outer loop traverses from 0 : n−1. 2. Loop over all edges, check if the next node distance > current node distance + edge weight, in this case update the next node distance to "current node distance + edge weight". Bellman Ford Algorithms
- 6. Dijkstra’s Algorithm Algorithm Steps: 1. Set all vertices distances = infinity except for the source vertex, set the source distance = 0. 2. Push the source vertex in a min-priority queue in the form (distance , vertex), as the co mparison in the min-priority queue will be according to vertices distances. 3. Pop the vertex with the minimum distance from the priority queue (at first the popped ve rtex = source). 4. Update the distances of the connected vertices to the popped vertex in case of "current vertex distance + edge weight < next vertex distance", then push the vertex with the new distance to the priority queue. 5. If the popped vertex is visited before, just continue without using it. 6. Apply the same algorithm again until the priority queue is empty. Dijkstra’s Algorithms
- 7. Floyd- warshall’s AlgorithmAlgorithm Steps: 1. Initialize the shortest paths between any 2 vertices with Infinity. 2. Find all pair shortest paths that use 0 intermediate vertices, then find the shortest path s that use 1intermediate vertex and so on.. until using all N vertices as intermediate no des. 3. Minimize the shortest paths between any 2 pairs in the previous operation. 4. For any 2 vertices (i,j) , one should actually minimize the distances between this pair u sing the first Knodes, so the shortest path will be: min(dist[i][k]+dist[k][j],dist[i][j]). Floyd Warshall’s Ford Algorithms
- 8. Application and usage Of Shortest Path Algorithm Networking protocols Social Media Dynamic Programming's Google Maps IP Routing Telephone networks For routing purpose and efficient delivery of packet Finding shortest path between two persons. To implement the routing. Google map uses these to find shortest routes Many routers used algorithm to deliver packet For routing connections in communication.
- 9. Features Of shortest path algorithms Simple to understand and work on it. Easy to use It is very easy to implement using many high level programing languages. Can be Implemented easily Companies like google uses it for Maps Used by my big companies 01 02 03 It is simple yet best algorithms to finding shortest path. Best for finding shortest path 04
- 10. Thank you