Bi-directional search

 Bi-directional search is a search algorithm that works by simultaneously performing two separate searches, one forward from the starting state and one backward from the goal state, until they meet in the middle. The algorithm is used to find the shortest path between two nodes in a graph or tree.

The idea behind bi-directional search is that searching from both the start and goal states can reduce the search space and speed up the search process. Instead of searching the entire graph or tree, the algorithm searches from both ends simultaneously and stops when the two searches meet in the middle. The search space is reduced since the two searches are approaching each other and the algorithm does not need to explore the entire graph.

Bi-directional search is typically used in large, complex search problems where a traditional search algorithm would be too slow or inefficient. For example, it is commonly used in route-planning applications, such as finding the shortest path between two cities or locations on a map.

The main advantage of bi-directional search is that it can be faster than traditional search algorithms, especially in large search spaces. However, it may not always be possible to use bi-directional search, especially in cases where the graph is too complex or the goal state is not known in advance.

In summary, bi-directional search is a search algorithm that performs two separate searches from the start and goal states simultaneously until they meet in the middle. It is typically used in large search problems where a traditional search algorithm would be too slow or inefficient.