1. A Series of Slides in 5 Parts Movement 2. BFS
Maze Running in C Minor
A Series of Slides in 5 Parts
Movement 2. BFS

2. AT: AA
QUEUE: AB
We will mark the nodes as visited in order to be compliant with how the visualizer code works. No visit information is actually being stored..
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

3. AT: AB
QUEUE: AA AC BB
Note that we added AA to the queue. We could choose not to add the node we came from, but we are doing so anyhow to show that it will only slowdown the search.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

4. AT: AA
QUEUE: AC BB AB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

5. AT: AC
QUEUE: BB AB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

6. AT: BB
QUEUE: AB AB BA CB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

7. AT: AB
QUEUE: AB BA AB CB AA AC BB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

8. AT: AB
QUEUE: BA AB CB AA AC BB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

9. AT: BA
QUEUE: AB CB AA AC BB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

10. AT: AB
QUEUE: CB AA AC BB CB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

11. AT: CB
QUEUE: AA AC BB AA CB DB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

12. AT: AA
QUEUE: AC BB AA AC CB DB AB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

13. AT: AC
QUEUE: BB AA AC BB CB DB AB BA DA
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

14. At this point, you should realize how inefficient BFS is without keeping visit information.
However, you should also see that it would eventually reach the exit due to the queue data structure.
We will now start over.

15. AT: AA
QUEUE: AB
For each node, we will keep track of the node that we first came from to reach that node.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

16. AT: AB
QUEUE: AC BB
Note that we did not add AA to the queue. This time, we do not add the node we came from.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

17. AT: AC
QUEUE: BB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

18. AT: BB
QUEUE: BA CB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

19. AT: BA
QUEUE: CB CA
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

20. AT: CB
QUEUE: CA DB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

21. AT: CA
QUEUE: DB DA
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

22. AT: DB
QUEUE: DA DA DC EB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

23. AT: DA
QUEUE: DA DC EB DB
This is an interesting situation. We add DB and not CA to the code since we know that we reached DB through CA.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

24. AT: DA
QUEUE: DC EB DB
This is an interesting situation. We add DB and not CA to the code since we know that we reached DB through CA.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

25. AT: DC
QUEUE: EB DB CC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

26. AT: EB
QUEUE: DB DB CC EA EC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

27. AT: DB
QUEUE: DB CC EA EC DA DC EB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

28. AT: DB
QUEUE: CC EA EC DA DC EB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

29. AT: CC
QUEUE: EA EC DA DC EB BC CD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

30. AT: EA
QUEUE: EC DA DC EB BC CD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

31. AT: EC
QUEUE: DA DC EB DA BC CD ED
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

32. AT: DA
QUEUE: DC EB DA DC BC CD ED DB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

33. AT: DC
QUEUE: EB DA DC EB BC CD ED DB CC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

34. AT: EB
QUEUE: DA DC EB BC CD ED DB CC EA EC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

35. AT: DA
QUEUE: DC EB BC CD ED DB CC EA EC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

36. AT: DC
QUEUE: EB BC CD ED DB CC EA EC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

37. AT: EB
QUEUE: BC CD ED DB CC EA EC
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

38. AT: BC
QUEUE: CD ED DB CC EA EC BD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

39. AT: CD
QUEUE: ED DB CC EA EC BD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

40. AT: ED
QUEUE: DB CC EA EC DB BD DD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

41. AT: DB
QUEUE: CC EA EC DB CC BD DD DA DC EB
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

42. AT: CC
QUEUE: EA EC DB CC EA BD DD DA DC EB BC CD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

43. AT: EA
QUEUE: EC DB CC EA EC BD DD DA DC EB BC CD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

44. AT: EC
QUEUE: DB CC EA EC BD DD DA DC EB BC CD ED
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

45. AT: DB
QUEUE: CC EA EC BD DD DA DC EB BC CD ED
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

46. AT: CC
QUEUE: EA EC BD DD DA DC EB BC CD ED
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

47. AT: EA
QUEUE: EC BD DD DA DC EB BC CD ED
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

48. AT: EC
QUEUE: BD DD DA DC EB BC CD ED
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

49. AT: BD
QUEUE: DD DA DC EB BC CD ED AD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

50. AT: DD
QUEUE: DA DC EB BC CD ED DA AD
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT
KEY: GREEN – Start
RED – Exit
YELLOW – Visited

51. Wow, that was still really inefficient.
What would happen if we kept track of the nodes we visited?

52. AT: AA
QUEUE: AB
For each node, we will keep track of the node that we first came from to reach that node.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

53. AT: AB
QUEUE: AC BB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

54. AT: AC
QUEUE: BB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

55. AT: BB
QUEUE: BA CB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

56. AT: BA
QUEUE: CB CA
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

57. AT: CB
QUEUE: CA DB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

58. AT: CA
QUEUE: DB DA
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

59. AT: DB
QUEUE: DA DA DC EB
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

60. AT: DA
QUEUE: DA DC EB
We still have the double DA effect occurring, but this time, we add no nodes to the queue since both neighbors of DA have already been visited.
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

61. AT: DA
QUEUE: DC EB
Ever have a feeling of déjà vu?
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

62. AT: DC
QUEUE: EB CC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

63. AT: EB
QUEUE: CC EA EC
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

64. AT: CC
QUEUE: EA EC BC CD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

65. AT: EA
QUEUE: EC BC CD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

66. AT: EC
QUEUE: BC CD ED
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

67. AT: BC
QUEUE: CD ED BD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

68. AT: CD
QUEUE: ED BD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

69. AT: ED
QUEUE: BD DD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

70. AT: BD
QUEUE: DD AD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

71. AT: DD
QUEUE: AD
KEY: GREEN – Start
RED – Exit
YELLOW – Visited
Nodes are taken in the order: UP, LEFT, DOWN, RIGHT

72. That was better, wasn’t it
That was better, wasn’t it? We still explored the same number of nodes in the maze but with less repetition.
However, did we change the principle that BFS always finds the optimal path?
The answer is no. Convince yourself as to why this is true.