Solving Ricochet Robots

Ricochet Robots is a puzzle board game for any number of players. While being a very fun game to play with some fascinating properties, it is also interesting to think about writing a program to play the game.

Let’s discuss a computerized player for Ricochet Robots that finds the optimal solution to any board in a reasonable amount of time. Along the way, we’ll learn about graph search techniques, data representation, algorithms, heuristics, pruning, and optimization.

Transcript

1. www .codingzeal.com @codingzeal Randy Coulman Solving Ricochet Robots Senior Software Engineer @randycoulman
2. Why Graphs, Trees & Algorithms? Hierarchical structures: Organization charts
3. Why Graphs, Trees & Algorithms? Relationship Maps: Social Networks like LinkedIn & Facebook
4. Why Graphs, Trees & Algorithms? Trip Planning
5. Why Graphs, Trees & Algorithms? Network Routing
6. What is Ricochet Robots?
7. Moves to get to
8. 1 1. Blue Right Moves to get to
9. 1 2 1. Blue Right 2. Blue Down Moves to get to
10. 1 2 3 1. Blue Right 2. Blue Down 3. Blue Left Moves to get to
11. 1 2 3 4 1. Blue Right 2. Blue Down 3. Blue Left 4. Green Right Moves to get to
12. 1 2 3 4 5 1. Blue Right 2. Blue Down 3. Blue Left 4. Green Right 5. Green Down Moves to get to
13. 1 2 3 4 5 6 1. Blue Right 2. Blue Down 3. Blue Left 4. Green Right 5. Green Down 6. Green Left Moves to get to
14. 1 2 3 4 5 6 7 1. Blue Right 2. Blue Down 3. Blue Left 4. Green Right 5. Green Down 6. Green Left 7. Green Down Moves to get to
15. Characterizing the Problem Possible Board States (size of state space): 252 * 251 * 250 * 249 * 248 = 976,484,376,000
16. Characterizing the Problem Branching Factor: 9 - 20 possible moves from each state
17. Representing the Board • Board (Static: 16 x 16)
18. Representing the Board • Board (Static: 16 x 16) • Walls & Targets (changes each game)
19. Representing the Board • Board (Static: 16 x 16) • Walls & Targets (changes each game) • Goal (changes each turn)
20. Representing the Board • Board (Static: 16 x 16) • Walls & Targets (changes each game) • Goal (changes each turn) • Robot Positions (changes each move)
21. Representing Robot Movement 1 2 1 2 1
22. Trees
23. Search Algorithms See Jamis Buck’s book Basil & Fabian: Three Ways Through
24. Depth-First Search
25. Depth-First Search 1
26. Depth-First Search 1 2
27. Depth-First Search 1 2 3
28. Depth-First Search 1 2 3 4
29. Depth-First Search 1 2 3 4 5
30. Depth-First Search 1 2 3 4 5 6
31. Depth-First Search 1 2 3 4 5 6 7
32. Depth-First Search 1 2 3 4 5 6 7 8
33. Depth-First Search 1 2 3 4 5 6 7 8 9
34. Depth-First Search 1 2 3 4 5 6 7 8 9 10
35. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11
36. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11 12
37. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13
38. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14
39. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
40. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
41. Depth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
42. Depth-First Search def solve solve_recursively(Path.initial(state)) candidates.min_by(&:length) || Outcome.no_solution(state) end def solve_recursively(path) return candidates << path.to_outcome if path.solved? path.allowable_successors.each do |successor| solve_recursively(successor) end end
43. Depth-First Search: Cycles
44. Depth-First Search: Cycles
45. Depth-First Search: Cycles
46. Depth-First Search: Cycles
47. Depth-First Search: Cycles
48. Depth-First Search: Cycles
49. Depth-First Search: Cycles
50. Depth-First Search: Cycles
51. Depth-First Search: Cycles
52. Depth-First Search: Cycles 3 1 1 2 3 2 4
53. Depth-First Search: Cycles
54. Depth-First Search: Cycles
55. Depth-First Search: Cycles
56. Depth-First Search: Cycles
57. 1 Depth-First Search: Cycles
58. 1 2 Depth-First Search: Cycles
59. 1 2 3 Depth-First Search: Cycles
60. 1 2 3 4 Depth-First Search: Cycles
61. 1 2 3 4 5 Depth-First Search: Cycles
62. Breadth-First Search
63. Breadth-First Search 1
64. Breadth-First Search 1 2
65. Breadth-First Search 1 2 3
66. Breadth-First Search 1 2 3 4
67. Breadth-First Search 1 2 3 4 5
68. Breadth-First Search 1 2 3 4 5 6
69. Breadth-First Search 1 2 3 4 5 6 7
70. Breadth-First Search 1 2 3 4 5 6 7 8
71. Breadth-First Search 1 2 3 4 5 6 7 8 9
72. Breadth-First Search 1 2 3 4 5 6 7 8 9 10
73. Breadth-First Search 1 2 3 4 5 6 7 8 9 10 11
74. Breadth-First Search 1 2 3 4 5 6 7 8 9 10 11 12
75. Breadth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13
76. Breadth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14
77. Breadth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
78. Breadth-First Search 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
79. Breadth-First Search 1 2 5 3 7 8 4 9 10 11 6 12 13 14 15 16
80. Breadth-First Search def solve paths = [Path.initial(initial_state)] until paths.empty? path = paths.shift return path.to_outcome if path.solved? paths += path.allowable_successors end Outcome.no_solution(initial_state) end
81. Breadth-First Search Global visited list works now
82. Optimization Do Less Things: Reduce the size of the state space by pruning branches from the graph
83. Optimization Do Things Faster: Less work per state
84. Optimization Heuristics: Rules of Thumb Less certain; may work in some circumstances, but not others
85. Heuristic: Move Active Robot First States Considered 0 350000 700000 1050000 1400000 Original Algorithm Active First
86. Do Less Things: Check for Solutions at Generation Time def solve paths = [Path.initial(initial_state)] until paths.empty? path = paths.shift return path.to_outcome if path.solved? paths += path.allowable_successors end Outcome.no_solution(initial_state) end
87. Do Less Things: Check for Solutions at Generation Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
88. Do Less Things: Check for Solutions at Generation Time def solve paths = [Path.initial(initial_state)] until paths.empty? path = paths.shift successors = path.allowable_successors solution = successors.find(&:solved?) return solution.to_outcome if solution paths += successors end Outcome.no_solution(initial_state) end
89. Do Less Things: Check for Solutions at Generation Time 1 2 3 4 5 6 X X X X X X X X X 16
90. Do Less Things: Check for Solutions at Generation Time 0 800,000 1,600,000 2,400,000 3,200,000 Original Algorithm Check at Generation Total States Considered
91. Do Things Faster: Precompute stopping cells
92. Do Things Faster: Precompute stopping cells States / second 0 675 1350 2025 2700 Original Algorithm Pre-compute Stops
93. Do Less Things / Do Things Faster: Treat non-active robots as equivalent
94. Do Less Things / Do Things Faster: Treat non-active robots as equivalent 0 1,000,000 2,000,000 3,000,000 4,000,000 Original Algorithm Check at Generation Robot Equivalence Total States Considered
95. Do Less Things / Do Things Faster: Treat non-active robots as equivalent States / second 0 750 1500 2250 3000 Original Algorithm Pre-compute Stops Robot Equiv.
96. Do Things Faster: Sorted Array vs Set States / second 0 800 1600 2400 3200 Original Algorithm Pre-compute Stops Robot Equiv. Arrays not Sets
97. Do Things Faster: Less Object Creation States / second 0 1250 2500 3750 5000 Original Algorithm Pre-compute Stops Robot Equiv. Arrays not Sets Less Objects
98. Do Things Faster: Use Object Identity Instead of Deep Equality States / second 0 1750 3500 5250 7000 Original Algorithm Pre-compute Stops Robot Equiv. Arrays not Sets Less Objects Object Identity
99. Final Results Solving time (seconds) 0 750 1500 2250 3000 Original Active First Check at Gen. Pre-compute Robot Equiv. Arrays not Sets Less Objects Robot Identity
100. Demo
101. Future Ideas: Better Algorithms A* Algorithm
102. A* Algorithm Next state to expand is one with minimum distance so far + estimated distance to goal
103. A* Algorithm 0
104. A* Algorithm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
105. A* Algorithm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0
106. A* Algorithm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0
107. A* Algorithm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0
108. A* Algorithm 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 0
109. Future Ideas: Better Algorithms Collision Detection
110. Future Ideas: Better Algorithms Work Backwards
111. Work Backwards
112. Future Ideas: Better Heuristics Move most-recently moved robots first (MRU)
113. Future Ideas: Better Heuristics Some combination of active robot and MRU robots
114. Future Ideas: Better Heuristics Sort movement directions intelligently
115. Future Ideas: More Optimizations Pre-compute per-robot stopping positions
116. Future Ideas: More Optimizations Use less objects and more primitive types
117. Future Ideas: More Optimizations Parallelism
118. Acknowledgements • Trever Yarrish of Zeal for the awesome graphics and visualizations • The Zealots of Zeal for ideas, feedback, and pairing on the solver • Michael Fogleman for some optimization ideas • Trevor Lalish-Menagh for introducing me to the game
119. Questions ? http://randycoulman.com http://speakerdeck.com/randycoulman http://speakerrate.com/randycoulman Code is on Github https://github.com/CodingZeal/robots
120. www .codingzeal.com @codingzeal Thank You! Randy Coulman @randycoulman