ITEC2620 Introduction to Data Structures

Transcription

1 ITEC2620 Introduction to Data Structures Lecture 8b Search Trees Traversals Typical covered as graph traversals in data structures courses I ve never seen a graph traversal in practice! AI background Tree traversals Search trees Direct vs. Indirect Problems I Direct problems Can always make a step towards the solution Sorting Find next smallest value Direct vs. Indirect Problems II Indirect problems A step towards the final solution may not always be possible Mazes 1

2 Water Jug Problem We have two jugs 4L 3L How can we get exactly 2L? Basic AI Search Techniques Turn solutions into a decision tree Tree nodes are states Links are decisions (among states) Turn logic into brute force Computers have no intelligence, only raw computational power Represent knowledge in the tree, and exploit brute force to produce intelligence Tree-Based Search Depth-first Pick a path and follow it to the end Lots of solutions easy to find Breadth-first Follow all paths equally Not too many paths Best-first Add more insight to improve brute force Decision Trees I These are conceptual Decisions trees are not implemented using a tree-based data structure Like a complete binary tree stored in an array We visualize a tree from a linear data structure 2

3 Decision Trees II Tree-based search is really state generation and analysis Search depends on knowing how to generate all possible moves Analysis means knowing how to detect a goal state Decision Trees III Water Jug Problem All possible moves Fill a jug Empty a jug Transfer water from one job to the other Goal 2L of water in either jug Decision Trees IV We visualize the generation of the states in a tree structure initial state All possible moves state 1 state 2 state 3 Decision Trees V State Creation place initial state in a data structure while (goal not found && data structure not empty) { remove state (according to search strategy) expand generate new states from current state test states (for goal) add (unique) new states to data structure } 3

4 Depth-first Search (DFS) Like an in-order traversal of a binary tree Data structure is a stack Leaf nodes in decision tree are visited left to right If there are leaf nodes! Breadth-first Search (BFS) Like a level-order traversal of a binary tree Data structure is a queue Nodes are visited top to bottom, left to right Like how nodes are added to a complete binary tree Best-First Search (A*) Data structure is a heap Requires a heuristic to differentiate which nodes are better (e.g. closer to the final solution) than others Comparison of Tree Searches BFS finds minimum depth solution BFS finds minimum depth solution Good for low branching, few solutions DFS may find solutions faster Good for high branching, many solutions A* finds solutions faster Always better to use problem knowledge over brute force when available 4

5 DFS Example Water Jug I DFS Example Water Jug II DFS Example Water Jug III DFS Example Water Jug IV 5

6 DFS Example Water Jug V DFS Example Water Jug VI DFS Example Water Jug VII DFS Example Water Jug VIII

7 DFS Example Water Jug IX DFS Example Water Jug X DFS Example Water Jug XI DFS Example Water Jug XII

8 DFS Example Water Jug XIII DFS Example Water Jug XIV BFS Example Water Jug I BFS Example Water Jug II 8

9 BFS Example Water Jug III BFS Example Water Jug IV BFS Example Water Jug V BFS Example Water Jug VI

10 BFS Example Water Jug VII BFS Example Water Jug VIII BFS Example Water Jug IX BFS Example Water Jug X

11 BFS Example Water Jug XI BFS Example Water Jug XII BFS Example Water Jug XIII BFS Example Water Jug XIV

12 BFS Example Water Jug XV BFS Example Water Jug XVI , , Summary of State Space Search I Define a state space that contains all possible (and perhaps some impossible) configurations of the relevant objects Individual boards, board matrix Specify the initial state(s) Specify the goal state(s) Checkmate Summary of State Space Search II Specify the production rules that Specify the production rules that define general state transitions Valid moves, standard openings, famous end-games 12

13 Summary of State Space Search III Select a (systematic) control strategy (need global and local motion) Cannot fill one jug repeatedly (no local motion) Cannot fill, then empty one jug repeatedly (no global motion) Summary of State Space Search IV Apply intelligence (pruning, selectivity) if possible Alpha-beta pruning (game trees) The rest is more AI (fuzzy hand-waving stuff) than basic search... Readings and Assignments Suggested Readings from Shaffer (third Suggested Readings from Shaffer (third edition) 7.3.1,