Data structures and algorithms lab9
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This document summarizes a lab assignment on data structures and algorithms focusing on binary trees and binary search trees. It includes objectives, definitions of key concepts, examples of traversals and operations on binary trees and binary search trees, and exercises involving writing functions to find the maximum height of a tree, compare heights of subtrees, find the lowest value in a BST, display values between limits, and rotate a BST.
Data structures and algorithms lab9
- 1. DATA STRUCTURES AND ALGORITHMS LAB 9 Bianca Tesila FILS, April 2014
- 2. OBJECTIVES Binary Trees Binary Search Trees
- 3. BINARY TREES & BINARY SEARCH TREES What is a tree? How can we check if a graph is a tree? What binary tree traversals do you know? How do they work? What’s the difference between a binary tree and a binary search tree? What traversal should we use in order to get the values of the nodes in ascending order? What happens when we delete a node from a binary search tree?
- 4. BINARY TREES APPLICATIONS !! Exercise: Write a function that displays the values of the nodes located on a given level (sent as a parameter). Hint: What happens when the given level greater than the tree’s height? Make a recursive function in which you decrement level by 1 as you advance to the next level. When level equals 0, you’ve reached the given level. Display (T,level): if(level==0) then print(T.data) else Display (T.left, level-1); Display (T.right, level-1);
- 5. BINARY TREES APPLICATIONS !! Exercise: Given a binary tree, compute its "maximumHeight" -- the number of nodes along the longest path from the root node down to the farthest leaf node. Hint: The maximum height of a tree is the maximum of the heights of its children
- 6. BINARY TREES APPLICATIONS !! Exercise: Write a function that returns, for the root node, the difference between the height of the left sub-tree and the height of the right sub-tree. Hint: you should take into consideration the maximum heights of the sub-trees. use the previous exercise int difHeight() { if(this == NULL) { return - 1;} return abs(left_son->maxHeight()-right_son- >maxHeight()); }
- 7. BINARY SEARCH TREES APPLICATIONS !! Exercise: Write a function which finds the lowest value in a binary search tree. Hint: traverse the node from root to left, recursively, until left is NULL the node whose left is NULL is the node with minimum value
- 8. BINARY SEARCH TREES APPLICATIONS !! Exercise: Write a function that displays the nodes which have values greater than x and smaller than y, where x and y are given as parameters. Hint: Take the value of the root into account in order to decide on which way to go to find the corresponding nodes.
- 9. BINARY SEARCH TREES APPLICATIONS
- 10. BINARY SEARCH TREES APPLICATIONS !! Exercise: Write a function that rotates a binary search tree that is given as a parameter. It shouldn’t change the results of the inorder traversal.
- 11. BINARY SEARCH TREES APPLICATIONS Hint: if the height of the right subtree is smaller than the height of the left subtree, it should be right- rotated. if the height of the left subtree is smaller than the height of the right subtree, it should be left- rotated. if the tree is balanced, nothing happens
- 12. HOMEWORK Finish all the lab assignments.