Trees: Unlike Arrays, Linked Lists, Stack and queues, which are linear data structures, trees are hierarchical data structures.
Tree Vocabulary: The topmost node is called root of the tree. The elements that are directly under an element are called its children. The element directly above something is called its parent. For example, ‘a’ is a child of ‘f’, and ‘f’ is the parent of ‘a’. Finally, elements with no children are called leaves.
tree ---- j <-- root / \ f k / \ \ a h z <-- leaves
1. One reason to use trees might be because you want to store information that naturally forms a hierarchy. For example, the file system on a computer:
file system ----------- / <-- root / \ ... home / \ ugrad course / / | \ ... cs101 cs112 cs113
2. Trees (with some ordering e.g., BST) provide moderate access/search (quicker than Linked List and slower than arrays).
3. Trees provide moderate insertion/deletion (quicker than Arrays and slower than Unordered Linked Lists).
4. Like Linked Lists and unlike Arrays, Trees don’t have an upper limit on number of nodes as nodes are linked using pointers.
Main applications of trees include:
1. Manipulate hierarchical data.
2. Make information easy to search (see tree traversal).
3. Manipulate sorted lists of data.
4. As a workflow for compositing digital images for visual effects.
5. Router algorithms
6. Form of a multi-stage decision-making (see business chess).
Binary Tree: A tree whose elements have at most 2 children is called a binary tree. Since each element in a binary tree can have only 2 children, we typically name them the left and right child.
Binary Tree Representation in C: A tree is represented by a pointer to the topmost node in tree. If the tree is empty, then value of root is NULL.
A Tree node contains following parts.
2. Pointer to left child
3. Pointer to right child
In C, we can represent a tree node using structures. Below is an example of a tree node with an integer data.
First Simple Tree in C
Let us create a simple tree with 4 nodes in C. The created tree would be as following.
tree ---- 1 <-- root / \ 2 3 / 4
Summary: Tree is a hierarchical data structure. Main uses of trees include maintaining hierarchical data, providing moderate access and insert/delete operations. Binary trees are special cases of tree where every node has at most two children.
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- Tree Traversals (Inorder, Preorder and Postorder)
- Find the node with minimum value in a Binary Search Tree
- Write a program to Calculate Size of a tree | Recursion
- Write a Program to Find the Maximum Depth or Height of a Tree
- Write a program to Delete a Tree
- If you are given two traversal sequences, can you construct the binary tree?
- Convert a Binary Tree into its Mirror Tree
- Given a binary tree, print out all of its root-to-leaf paths one per line.
- Lowest Common Ancestor in a Binary Search Tree.
- The Great Tree-List Recursion Problem.
- Check sum of Covered and Uncovered nodes of Binary Tree
- Level Order Tree Traversal
- Program to count leaf nodes in a binary tree
- A program to check if a binary tree is BST or not
- Check for Children Sum Property in a Binary Tree