Introduction to Trees

Trees are hierarchical data structures made up of nodes. Each node has a value and can have zero or more child nodes. The topmost node is called the root node, and it does not have a parent node.

Trees have various properties that make them useful for organizing and structuring data:

1. Hierarchical Structure: Trees are organized in a hierarchical structure, where each node can have child nodes.

2. Root Node: The topmost node in a tree is called the root node. It is the starting point of the tree and does not have a parent node.

3. Parent Node: A node that has child nodes is called a parent node. It is located above its child nodes in the hierarchy.

4. Child Node: A node that is below another node in the hierarchy is called a child node.

5. Leaf Node: A node that does not have any child nodes is called a leaf node or a terminal node. It is located at the bottom of the tree.

6. Depth: The depth of a node is the number of edges between the node and the root node. The depth of the root node is 0.

7. Height: The height of a node is the number of edges in the longest path from the node to a leaf node.

Trees have various applications in computer science, such as representing hierarchical relationships, organizing data in a hierarchical manner, searching and sorting, and implementing data structures like binary search trees.

Let's take a look at an example of a binary tree:

1        1
2      /   \
3     2     3
4    / \   / \
5   4   5 6   7

In this binary tree:

• Node 1 is the root node
• Node 2 is the left child of node 1
• Node 3 is the right child of node 1
• Node 4 is the left child of node 2
• Node 5 is the right child of node 2
• Node 6 is the left child of node 3
• Node 7 is the right child of node 3

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#include <iostream>

using namespace std;

int main() {

  // Trees are hierarchical data structures made up of nodes.

  // Each node has a value and can have zero or more child nodes.

  // The topmost node is called the root node,

  // and it does not have a parent node.

​

  // Trees have various properties that make them useful

  // for organizing and structuring data:

​

  // 1. Hierarchical Structure: Trees are organized in a

  //    hierarchical structure, where each node can have

  //    child nodes.

​

  // 2. Root Node: The topmost node in a tree is called

  //    the root node. It is the starting point of the tree

  //    and does not have a parent node.

​

  // 3. Parent Node: A node that has child nodes is called

  //    a parent node. It is located above its child nodes

  //    in the hierarchy.

​

  // 4. Child Node: A node that is below another node in the

  //    hierarchy is called a child node.

​

  // 5. Leaf Node: A node that does not have any child nodes

  //    is called a leaf node or a terminal node. It is located

  //    at the bottom of the tree.