Lecture 12 - Binary Trees, Binary Search Trees

Lecture 12 - Binary Trees, Binary Search Trees - Wednesday...

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Unformatted text preview: Wednesday, Feb 29th • Binary Tree Traversals • Using Binary Trees to Evaluate Expressions • Binary Search Trees • Binary Search Tree Operations – Searching for an item – Inserting a new item – Finding the minimum and maximum items – Printing out the items in order – Deleting the whole tree CONSIDER REVAMPING SIMPLIFY INSERTION PSEUDOCODE SHOW TREE BEING HALVED DURING EACH SEARCH STEP Binary Tree Traversals When we process all the nodes in a tree, it’s called a traversal. There are four common ways to traverse a tree. 1. Pre-order traversal 2. In-order traversal 3. Post-order traversal 4. Level-order traversal Let’s see a pre-order traversal first! The Preorder Traversal Preorder : 1. Process the current node. 2. Process the nodes in the left sub-tree. 3. Process the nodes in the right sub-tree. By “ process the current node ” we typically mean one of the following: 1. Print the current node’s value out. 2. Search the current node to see if its value matches the one you’re searching for. 3. Add the current node’s value to a total for the tree 4. Etc… NULL “a” “b” “c” NULL “d” NULL NULL NULL “e” NULL root void PreOrder(Node *cur) { if (cur == NULL) // if empty, return… return; cout << cur->value; // Process the current node. PreOrder(cur->left); // Process nodes in left sub-tree . PreOrder(cur-> right); // Process nodes in left sub-tree . } main() { Node *root; … PreOrder(root); } NULL “a” “b” “c” NULL “d” NULL NULL NULL “e” NULL root cur Output: a b The Pre-order Traversal d void PreOrder(Node *cur) { if (cur == NULL) // if empty, return… return; cout << cur->value; // Process the current node. PreOrder(cur->left); // Process nodes in left sub-tree . PreOrder(cur-> right); // Process nodes in left sub-tree . } cur void PreOrder(Node *cur) { if (cur == NULL) // if empty, return… return; cout << cur->value; // Process the current node. PreOrder(cur->left); // Process nodes in left sub-tree . PreOrder(cur-> right); // Process nodes in left sub-tree . } cur void PreOrder(Node *cur) { if (cur == NULL) // if empty, return… return; cout << cur->value; // Process the current node....
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Lecture 12 - Binary Trees, Binary Search Trees - Wednesday...

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