1. Trees in C CSE 2541 Rong Shi

2. Tree definition Recursively defined data structure Tree (in general) – Empty – Data + a specific number of subtrees Binary tree – Empty – Data + left subtree + right subtree

3. C Binary Tree node struct btnode { int data; struct btnode *left; struct btnode *right; } ;

4. What is this? struct treenode { int data; struct treenode *mynode; } ; Equivalent to a linked list

5. Creating a tree struct btnode *root; struct btnode *mynode = (struct btnode *) malloc (sizeof(struct btnode)); root = mynode; // use root to access the tree, like head for a linked list

6. Visual example of a binary tree Each value corresponds to a node in the tree root is a struct btnode pointer that points at the node containing the 9

7. Tree traversal (preorder) PreOrderPrint(struct btnode *anode) { printf(“%i”, anode->data); PreOrderPrint(anode->left); PreOrderPrint(anode->right); } Any problems with this function?

8. Tree traversal (preorder corrected) PreOrderPrint(struct btnode *anode) { if(anode == NULL) return; printf(“%i ”, anode->data); PreOrderPrint(anode->left); PreOrderPrint(anode->right); } Output of PreOrderPrint(root) is: (po9  pt9  po6  pt6… see blackboard) 9 6 2 7 15 12 25

9. Tree traversal (inorder) InOrderPrint(struct btnode *anode) { if(anode == NULL) return; InOrderPrint(anode->left); printf(“%i ”, anode->data); InOrderPrint(anode->right); } Output of InOrderPrint(root) is: 2 6 7 9 12 15 25

10. Tree traversal (postorder) PostOrderPrint(struct btnode *anode) { if(anode == NULL) return; PostOrderPrint(anode->left); PostOrderPrint(anode->right); printf(“%i ”, anode->data); } Output of PostOrderPrint(root) is: 2 7 6 12 25 15 9

11. Tree termination NULL pointers NULL are not btnodes, but the value of their parent’s left and right pointers NULL data -1 are btnodes, whose left and right btnodes are uninitialized Assumption: -1 is never valid data in the tree

12. Creating nodes struct node * NewNode(int data) { struct node *mynode = (struct node *) malloc (sizeof(struct node)); mynode->data = data; mynode->left = NULL; mynode->right = NULL; return(node); }

13. Deallocating binary trees Three things to do – Free current node – Recursively free left subtree – Recursively free right subtree What is the order? void delete_tree(struct btnode *leaf) { if( leaf != NULL ) { delete_tree(leaf->left); delete_tree(leaf->right); free( leaf ); }

14. Trees and arrays Figure from http://scientopia.org/blogs/goodmath/2008/04/29/implementing-compact-binary-heaps/ Map current node, left child, and right child to array positions Order in the array by level in the tree

15. Trees and arrays Figure from http://scientopia.org/blogs/goodmath/2008/04/29/implementing-compact-binary-heaps/ Map current node, left child, and right child to array positions t[i], t[2i+1], t[2i+2] Order in the array by level in the tree

16. Additional Terminology Depth: number of edges from the root to the node (node ‘7’ has depth 2, etc) Height: number of edges from the node to the deepest leaf Height of Tree: height of the root (tree-height = 2)

17. Reference Wiki http://en.wikipedia.org/wiki/Binary_search_tree http://en.wikipedia.org/wiki/Tree_(data_structurehttp://en.wikipedia.org/wiki/Tree_(data_structure) Slides from CMU http://www.cs.cmu.edu/~adamchik/15- 121/lectures/Trees/trees.html