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Optimised Search Techniques: BFS vs A* Algorithm Comparison

Explore the basic idea of BFS and A* algorithm. BFS branches out to all surrounding nodes without direction discrimination. Best-First Search branches out to the closest nodes using heuristics. A* algorithm improves Best-First Search by assigning node weights based on cost and estimated distances. Learn about Manhattan Distance as an heuristic and see A* algorithm implementation examples. Compare BFS and A* algorithms along with their special cases like Dijkstra's Algorithm.

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Optimised Search Techniques: BFS vs A* Algorithm Comparison

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  1. Optimised Search Techniques

  2. Basic Idea BFS brances out to all surrounding nodes No discrimination based on direction of target node

  3. BFS example S E

  4. BFS example S E

  5. BFS example S E

  6. BFS example S E

  7. BFS example S Large area needlessly explored E

  8. Alternatives Best-First Search: Branch out to nodes which intuitively seem to be the closest to the destination Use heuristics to estimate distances to destination node Greedy algorithm However, a better solution exists

  9. A* algorithm A* is an improvement over Best-First Search Nodes are given weights based on: Cost to reach the node Estimated cost to reach the end node

  10. Manhattan Distance Manhattan distance - sum of the absolute distances between coordinates M(x1,y1,x2,y2) = |x1-x2| + |y1-y2| Reflection of distance between points if travel only parallel to axes

  11. Implementation of A* Using Manhattan distance as an heuristic to estimate distance to end point w(x,y) = c(x,y) + M(x,y,xE,yE) Item in priority queue with lowest weight popped off Surrounding nodes added with calculated weights

  12. A* example S E

  13. A* example S 9 7 E

  14. A* example S 9 7 9 7 E

  15. A* example S 9 7 9 7 7 E

  16. A* example S 9 7 9 7 7 7 7 E

  17. A* example 11 S 9 11 11 9 7 9 11 9 7 7 7 9 7 7 9 9 E

  18. Comparison: BFS vs A* BFS A* S S E E

  19. Special cases of A* Dijkstra's Algorithm is a case of A* with the weighting based solely on cost: w(x,y) = c(x,y) Breadth-First Search is just A* with all nodes have a weight of 0: w(x,y) = 0

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