**Shortest Path Problem-**

In data structures,

- Shortest path problem is a problem of finding the shortest path(s) between vertices of a given graph.
- Shortest path between two vertices is a path that has the least cost as compared to all other existing paths.

**Shortest Path Algorithms-**

Shortest path algorithms are a family of algorithms used for solving the shortest path problem.

**Applications-**

Shortest path algorithms have a wide range of applications such as in-

- Google Maps
- Road Networks
- Logistics Research

**Types of Shortest Path Problem-**

Various types of shortest path problem are-

- Single-pair shortest path problem
- Single-source shortest path problem
- Single-destination shortest path problem
- All pairs shortest path problem

**Single-Pair Shortest Path Problem-**

- It is a shortest path problem where the shortest path between a given pair of vertices is computed.
- A* Search Algorithm is a famous algorithm used for solving single-pair shortest path problem.

**Single-Source Shortest Path Problem-**

- It is a shortest path problem where the shortest path from a given source vertex to all other remaining vertices is computed.
- Dijkstra’s Algorithm and Bellman Ford Algorithm are the famous algorithms used for solving single-source shortest path problem.

**Single-Destination Shortest Path Problem-**

- It is a shortest path problem where the shortest path from all the vertices to a single destination vertex is computed.
- By reversing the direction of each edge in the graph, this problem reduces to single-source shortest path problem.
- Dijkstra’s Algorithm is a famous algorithm adapted for solving single-destination shortest path problem.

**All Pairs Shortest Path Problem-**

- It is a shortest path problem where the shortest path between every pair of vertices is computed.
- Floyd-Warshall Algorithm and Johnson’s Algorithm are the famous algorithms used for solving All pairs shortest path problem.

**Also Read-** **Floyd-Warshall Algorithm**

**Next Article-** **Dijkstra’s Algorithm**

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Summary

Article Name

Shortest Path Problem | Shortest Path Algorithms | Examples

Description

Shortest Path Problem in Data Structure is a problem of finding the shortest path between vertices of a given graph. Shortest Path Algorithms are a family of algorithms used for solving Shortest Path Problem. Examples.

Author

Akshay Singhal

Publisher Name

Gate Vidyalay

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