Informed search algorithms are particularly advantageous for exploring extensive search spaces. Leveraging heuristic principles, these algorithms are also referred to as Heuristic search algorithms.

### Heuristic function

One crucial component of informed search algorithms is the heuristic function, which estimates the cost from any given state to the goal state. While the heuristic method may not always yield the best solution, it ensures finding a good solution within a reasonable timeframe. The heuristic function, denoted as h(n), assesses the cost of an optimal path between state pairs, always producing a positive value.### Best-first search algorithm

One type of informed search algorithm is the Best-first search algorithm, also known as Greedy search. In this algorithm, nodes are expanded based on their heuristic value, prioritizing nodes that are closest to the goal state according to the heuristic function. Greedy search tends to be very efficient in terms of memory usage and computational resources. However, it may not always find the optimal solution, as it focuses solely on the heuristic value without considering the actual path cost.#### Advantages:

- Best-first search combines the benefits of both breadth-first search (BFS) and depth-first search (DFS).
- It offers improved efficiency compared to BFS and DFS.

#### Disadvantages:

- In the worst-case scenario, it may operate similarly to an unguided depth-first search.
- It is prone to getting trapped in loops like DFS.

### A* search algorithm.

A* search is the widely recognized variant of best-first search. A* combines the benefits of both uniform cost search and greedy search by considering both the actual cost of reaching a state and the heuristic estimate of the remaining cost to reach the goal. The A* algorithm evaluates nodes based on a combination of the actual cost of reaching the node from the start state and the heuristic estimate of the cost from that node to the goal. This combination ensures that A* finds the optimal solution while also being efficient in terms of computational resources.

A* search algorithm guarantees both completeness and optimality under certain conditions, specifically when the heuristic function is admissible. However, the efficiency and effectiveness of A* heavily depend on the quality of the heuristic function. If the heuristic function is not admissible or consistent, A* may fail to find the optimal solution or may require significantly more computational resources.

#### Advantages:

1. A* is considered superior to other search algorithms.

2. A* algorithm guarantees finding the optimal solution if a heuristic function satisfies certain conditions.

3. A* excels at solving intricate and challenging problems.

#### Disadvantages:

1. Heuristic Dependency: The effectiveness of A* heavily relies on the quality of the heuristic function, which may not always be available or easy to define.

2. Memory Intensive: In large search spaces, A* may require significant memory resources to store and evaluate nodes, impacting scalability.

3. Complexity: Implementing and understanding A* algorithm can be complex, especially for beginners, due to its intricate mechanics and heuristics.

In summary, informed search algorithms leverage heuristic information to guide the search process efficiently towards the goal state. The heuristic function estimates the cost from a given state to the goal state, allowing the algorithm to prioritize nodes for expansion based on their estimated cost. Best-first search and A* search are two prominent examples of informed search algorithms, with A* being particularly notable for its optimality and efficiency when the heuristic function is admissible.