Trees

1. Trees

2. What is a tree? • You know… • tall • green • leafy • possibly fruit • branches • roots • I’m sure you’veseen them

3. In the context of C (and CS in general) • Trees are a Data Structure (Like a linked list) • They • Are upside-down • Have one root • Have branches • Have leaves • (No fruit)

4. A Tree (In general)

5. Nodes

6. Edges (Links (Pointers))

7. The Root

8. Leaves

9. Branches (A.K.A. Sub-Trees)

10. Branches (A.K.A. Sub-Trees)

11. Branches (A.K.A. Sub-Trees)

12. Parent / Children

13. Some info • The root has no parent • The leaves have no children • The interior nodes have at least one child, and a parent

14. Types of trees • Binary trees • Every node has (at most) two childen • Trinary trees • Every node has (at most) three childen • N-ary trees • Every node has as many children as it wants/needs

15. We care about binary trees

16. Binary search trees 55 24 83 18 48 65 97 7 31 51 58 70 26 37 68 79 34 42

17. Binary Trees typedef struct S_tree { int value; // For example struct S_tree *left, *right; } tree; • Just like a linked list, but instead of one pointer, it has two! (left and right)

18. In Order Traversal • Printing an entire binary search tree. void print_tree(tree *t) { if (t == NULL) return; print_tree(t->left); printf(“%d\n”,t->val); print_tree(t->right); } Recursion!

19. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42

20. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42

21. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7

22. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18

23. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24

24. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26

25. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31

26. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31 34

27. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31 34 37

28. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31 34 37 42

29. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31 34 37 42 48

30. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31 34 37 42 48 51

31. Traversing a Tree Start with the root. Traverse Left Subtree Print Node Value Traverse Right Subtree 24 18 48 7 31 51 26 37 34 42 7 18 24 26 31 34 37 42 48 51