Artificial Intelligence# Is A* Algorithm a Quick Solution to Pathfinding Issues?

Many real-life problems of scientific importance involve finding a path with the minimum cost between two nodes (say source and destination) in a graph network. For example routing of network traffic, navigation through a maze, etc. A* algorithm is one of the best and most popular techniques used in path-finding and graph traversals.

Informally speaking, A* Search algorithms, unlike other traversal techniques, it has "brains". What it means is that it is really a smart algorithm that separates it from the other conventional algorithms. This fact is cleared in detail in the below sections. And it is also worth mentioning that many games and web-based maps use this algorithm to find the shortest path very efficiently (approximation).

A* algorithm has 3 parameters:

g : The cost of moving from the initial cell to the current cell. Basically, it is the sum of all the cells that have been visited since leaving the first cell.

h : Also known as the heuristic value, it is the estimated cost of moving from the current cell to the final cell. The actual cost cannot be calculated until the final cell is reached. Hence, h is the estimated cost. We must make sure that there is never an overestimation of the cost.

f : It is the sum of g and h. So, f = g + h

The way that the algorithm makes decisions by taking the f-value into account. The algorithm selects the smallest f-valued cell and moves to that cell. This process continues until the algorithm reaches its goal cell.

AI helps us solve problems of various complexities. Computational problems like path search problems can be solved using AI. Search problems where you need to find a path from one point to another, say, point A to point B. Sometimes you need to solve it by mapping those problems to graphs, where nodes represent all the possible outcomes. A* algorithm comes up as an answer to these problems.

A* search is the most commonly known form of best-first search. It uses heuristic function h(n), and cost to reach the node n from the start state g(n). It has combined features of UCS and greedy best-first search, by which it solves the problem efficiently. A* search algorithm finds the shortest path through the search space using the heuristic function. This search algorithm expands fewer search trees and provides optimal results faster. A* algorithm is similar to UCS except that it uses g(n)+h(n) instead of g(n).

In A* search algorithm, we use search heuristic as well as the cost to reach the node. Hence we can combine both costs as follows, and this sum is called a fitness number.

** **Search algorithms have the following main properties:

**Completeness**: A search algorithm can be said to be complete if it provides a solution for a given input when there exists at least one solution for this input.

**Optimality**: Search algorithms are also characterized by optimal solutions. These are the best solutions given by the search algorithms at the lowest path cost.

**Time Complexity**: These algorithms have a maximum time needed to accomplish a task or provide a solution. The time taken is usually based on the complexity of the task.

**Space Complexity**: They have a maximum memory or storage space needed when conducting a search operation. This memory is also based on the complexity of the task.

- A* search algorithm is the best algorithm than other search algorithms.
- A* search algorithm is optimal and complete.
- This algorithm can solve very complex problems.

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