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Artificial Intelligence for Games Depth limited search

Artificial Intelligence for Games Depth limited search. Patrick Olivier p.l.olivier@ncl.ac.uk. Recap: Breadth-first search. Roadmap of Romania…. Class Exercise – Uniform-Cost. Uniform-cost search Cost to get to a node g(n) Expand the least-cost unexpanded node

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Artificial Intelligence for Games Depth limited search

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  1. Artificial Intelligence for GamesDepth limited search Patrick Olivier p.l.olivier@ncl.ac.uk

  2. Recap: Breadth-first search

  3. Roadmap of Romania…

  4. Class Exercise – Uniform-Cost • Uniform-cost search • Cost to get to a node g(n) • Expand the least-cost unexpanded node • Implement with fringe ordered by path cost • Romanian holiday: • Initial state: Arad • Goal state: Bucharest • Do a uniform cost search by hand

  5. Recap: Depth-first search

  6. Depth-limited search • depth-first search with depth limit L • nodes at depth L have no successors

  7. Iterative deepening • search to a depth limit L • if no solution research to limit L+1 • previous search repeated

  8. Iterative deepening search: L = 0

  9. Iterative deepening search: L = 1

  10. Iterative deepening search: L = 2

  11. Iterative deepening search: L = 3

  12. Iterative deepening search • Number of nodes generated in a depth-limited search to depth d with branching factor b: • NDLS = b0 + b1 + b2 + … + bd-2 + bd-1 + bd • Number of nodes generated in an iterative deepening search to depth d with branching factor b: • NIDS = (d+1)b0 + d.b1 + (d-1)b2 + … + 3bd-2 +2bd-1 + 1bd • For b=10, d=5: • NDLS= 1 + 10 + 100 + 1,000 + 10,000 + 100,000 = 111,111 • NIDS = 6 + 50 + 400 + 3,000 + 20,000 + 100,000 = 123,456 • Overhead = (123,456 - 111,111)/111,111 = 11%

  13. Properties of iterative deepening • Complete? • Yes • Time: • (d+1)b0 + d b1 + (d-1)b2 + … + bd = O(bd) • Space: • O(bd) • Optimal? • If the cost is the same per step

  14. Summary of uninformed search

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