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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- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Check if a binary tree is subtree of another binary tree | Set 1
- Check if a binary tree is subtree of another binary tree | Set 2
- Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)
- Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)
- Binary Tree to Binary Search Tree Conversion using STL set
- Binary Tree | Set 3 (Types of Binary Tree)
- Maximum sub-tree sum in a Binary Tree such that the sub-tree is also a BST
- Binary Tree to Binary Search Tree Conversion
- Check whether a binary tree is a full binary tree or not
- Minimum swap required to convert binary tree to binary search tree
- Check whether a binary tree is a full binary tree or not | Iterative Approach
- Check whether a given binary tree is skewed binary tree or not?
- Difference between Binary Tree and Binary Search Tree
- Check if a binary tree is subtree of another binary tree using preorder traversal : Iterative
- Check whether a binary tree is a complete tree or not | Set 2 (Recursive Solution)
- Print Binary Tree levels in sorted order | Set 3 (Tree given as array)
- Check if the given binary tree has a sub-tree with equal no of 1's and 0's | Set 2
- ScapeGoat Tree | Set 1 (Introduction and Insertion)
- Persistent Segment Tree | Set 1 (Introduction)