![Expand the nodes of S and put in the CLOSED list
Initialization: Open [A, B], Closed [S]
Iteration 1: Open [A], Closed [S, B]
Iteration 2: Open [E, F, A], Closed [S, B]
: Open [E, A], Closed [S, B, F]
Iteration 3: Open [I, G, E, A], Closed [S, B, F]
: Open [I, E, A], Closed [S, B, F, G]
Hence the final solution path will be: S----> B----->F----> G](https://image.slidesharecdn.com/astaralgorithms-210921165841/85/A-star-algorithms-14-320.jpg)
A star algorithms
- 1. A* Algorithms Best First Algorithms
- 3. Start by setting the starting node (A) as the current node.
- 4. Check all the nodes connected to A and update their “Shortest Distance from A” and set their “previous node” to “A”.
- 5. Set the current node (A) to “visited” and use the unvisited node with the smallest total distance as the current node ( this case: Node C).
- 6. Check all unvisited nodes connected to the current node (B) and add the distance from A to B to all distances from the connected nodes. Replace their values only if the new distance is lower than the previous one.
- 7. Check all unvisited nodes connected to the current node (D) and add the distance from A to D to all distances from the connected nodes. Replace their values only if the new distance is lower than the previous one.
- 8. Check all unvisited nodes connected to the current node (E) and add the distance from A to E to all distances from the connected nodes. Replace their values only if the new distance is lower than the previous one.
- 9. We found the shortest path from A to Z. Read the path from Z to A using the previous node column: Z > E > D > C > A So the Shortest Path is: A – C – D – E – Z with a length of 17
- 10. Best-first Search Algorithm (Greedy Search) Greedy best-first search algorithm always selects the path which appears best at that moment. It is the combination of depth-first search and breadth- first search algorithms. It uses the heuristic function and search.With the help of best-first search, at each step, we can choose the most promising node. In the best first search algorithm, we expand the node which is closest to the goal node and the closest cost is estimated by heuristic function, i.e. f(n)= g(n). Where, h(n)= estimated cost from node n to the goal.
- 11. Best first search algorithm: Step 1: Place the starting node into the OPEN list. Step 2: If the OPEN list is empty, Stop and return failure. Step 3: Remove the node n, from the OPEN list which has the lowest value of h(n), and places it in the CLOSED list. Step 4: Expand the node n, and generate the successors of node n. Step 5: Check each successor of node n, and find whether any node is a goal node or not. If any successor node is goal node, then return success and terminate the search, else proceed to Step 6. Step 6: For each successor node, algorithm checks for evaluation function f(n), and then check if the node has been in either OPEN or CLOSED list. If the node has not been in both list, then add it to the OPEN list. Step 7: Return to Step 2.
- 12. Advantages: • Best first search can switch between BFS and DFS by gaining the advantages of both the algorithms. • This algorithm is more efficient than BFS and DFS algorithms. Disadvantages: • It can behave as an unguided depth-first search in the worst case scenario. • It can get stuck in a loop as DFS. • This algorithm is not optimal.
- 13. Consider the below search problem, and we will traverse it using greedy best-first search. At each iteration, each node is expanded using evaluation function f(n)=h(n) , which is given in the below table.
- 14. Expand the nodes of S and put in the CLOSED list Initialization: Open [A, B], Closed [S] Iteration 1: Open [A], Closed [S, B] Iteration 2: Open [E, F, A], Closed [S, B] : Open [E, A], Closed [S, B, F] Iteration 3: Open [I, G, E, A], Closed [S, B, F] : Open [I, E, A], Closed [S, B, F, G] Hence the final solution path will be: S----> B----->F----> G