1. Binary Tree Traversals
Lecture 38
Fri, Apr 28, 2006
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2. Topics Binary tree traversals Binary tree iterators
Pre-order traversals
In-order traversals
Post-order traversals
Level-order traversals
Binary tree iterators
Pre-order iterators
In-order iterators
Post-order iterators
Level-order iterators
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3. Binary Tree Traversals
Four Standard Traversals
Pre-order Traversal.
In-order Traversal.
Post-order Traversal.
Level-order Traversal.
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4. Pre-order Traversal At each node, Also called an VLR traversal.
First visit the node,
Then perform a pre-order traversal of the left subtree,
Then perform a pre-order traversal of the right subtree.
Also called an VLR traversal.
Visit - Left - Right.
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5. Pre-Order Traversal 10 20 30 40 50 60 70
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6. Pre-Order Traversal 10 20 30 40 50 60 70 10
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7. Pre-Order Traversal 10 20 30 40 50 60 70 10 20
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8. Pre-Order Traversal 10 20 30 40 50 60 70 10 20 40 1/16/2019
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9. Pre-Order Traversal 10 20 30 40 50 60 70 10 20 40 50 1/16/2019
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10. Pre-Order Traversal 10 20 30 40 50 60 70 10 20 30 40 50 1/16/2019
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11. Pre-Order Traversal 10 20 30 40 50 60 70 10 20 30 40 50 60 1/16/2019
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12. Pre-Order Traversal 10 20 30 40 50 60 70 10 20 30 40 50 60 70
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13. Pre-Order Traversal Order: 10, 20, 40, 50, 30, 60, 70 10 20 30 40 50
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14. In-order Traversal At each node, Also called an LVR traversal.
First, perform an in-order traversal of the left subtree,
Then visit the node,
Then perform an in-order traversal of the right subtree.
Also called an LVR traversal.
Left - Visit - Right.
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15. In-Order Traversal 10 20 30 40 50 60 70
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16. In-Order Traversal 10 20 30 40 50 60 70 40
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17. In-Order Traversal 10 20 30 40 50 60 70 20 40
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18. In-Order Traversal 10 20 30 40 50 60 70 20 40 50
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19. In-Order Traversal 10 20 30 40 50 60 70 10 20 40 50
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20. In-Order Traversal 10 20 30 40 50 60 70 10 20 40 50 60
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21. In-Order Traversal 10 20 30 40 50 60 70 10 20 30 40 50 60
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22. In-Order Traversal 10 20 30 40 50 60 70 10 20 30 40 50 60 70
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23. In-Order Traversal Order: 40, 20, 50, 10, 60, 30, 70 10 20 30 40 50 60
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24. Post-order Traversal At each node, Also called an LRV traversal.
First perform a post-order traversal of the left subtree,
Then perform a post-order traversal of the right subtree,
Then visit the node.
Also called an LRV traversal.
Left - Right - Visit.
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25. Post-Order Traversal 10 20 30 40 50 60 70
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26. Post-Order Traversal 10 20 30 40 50 60 70 40
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27. Post-Order Traversal 10 20 30 40 50 60 70 40 50
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28. Post-Order Traversal 10 20 30 40 50 60 70 20 40 50 1/16/2019
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29. Post-Order Traversal 10 20 30 40 50 60 70 20 40 50 60 1/16/2019
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30. Post-Order Traversal 10 20 30 40 50 60 70 20 40 50 60 70 1/16/2019
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31. Post-Order Traversal 10 20 30 40 50 60 70 20 30 40 50 60 70 1/16/2019
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32. Post-Order Traversal 10 20 30 40 50 60 70 10 20 30 40 50 60 70
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33. Post-Order Traversal Order: 40, 50, 20, 60, 70, 30, 10 10 20 30 40 50
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34. Level-order Traversal
Traverse the levels of the tree from top to bottom.
Within each level, visit the nodes from left to right.
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35. Level-Order Traversal10 20 30 40 50 60 70
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36. Level-Order Traversal10 20 30 40 50 60 70 10
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37. Level-Order Traversal10 20 30 40 50 60 70 10 20
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38. Level-Order Traversal10 20 30 40 50 60 70 10 20 30
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39. Level-Order Traversal10 20 30 40 50 60 70 10 20 30 40
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40. Level-Order Traversal10 20 30 40 50 60 70 10 20 30 40 50
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41. Level-Order Traversal10 20 30 40 50 60 70 10 20 30 40 50 60
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42. Level-Order Traversal10 20 30 40 50 60 70 10 20 30 40 50 60 70
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43. Level-Order Traversal10 20 30 40 50 60 70 10 20 30 40 50 60 70
Order: 10, 20, 30, 40, 50, 60, 70
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44. Binary Tree Iterators
A binary tree iterator systematically visits each node of a binary tree.
The four standard iterators correspond to the four standard traversal methods.
Pre-order iterator
In-order iterator
Post-order iterator
Level-order iterator
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45. Pre-order Iterator Visit the nodes in a pre-order traversal.
Use a stack to store unvisited nodes.
Begin with the root node.
Visit the node.
If there is a right subtree, push the pointer to it.
If there is a left subtree, move to the left subtree and continue recursively.
If there is no left subtree, pop a node and continue recursively.
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46. Pre-order Iterator 10 20 30 40 50 60 70 10 10 10 20 20 20 30 30 30 40 50 60 70
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47. In-order Iterator Visit the nodes in an in-order traversal.
Use a stack to store unvisited nodes.
Move from the root to the “leftmost” node, pushing nodes along the way, etc.
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48. In-order Iterator 10 20 30 40 50 60 70 10 10 20 20 30 30 40 50 60 70
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49. Post-order Iterator Visit the nodes in a post-order traversal.
Use a stack to store unvisited nodes.
Move to the “leftmost” leaf, pushing nodes along the way, etc.
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50. Post-order Iterator 10 20 30 40 50 60 70 10 10 20 20 30 30 40 50 60 70
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51. Level-order Iterator Visit the nodes in a level-order traversal.
Use a queue to store unvisited nodes.
Begin with the root node.
Enqueue the node’s children, left first.
Visit the node.
Dequeue a node and continue recursively until the queue is empty.
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52. Level-order Iterator 10 20 30 40 50 60 70 10 20 20 30 30 40 40 50 50 60 60 70 70
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