Binary Trees

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child.

struct node { int data; struct node* left; struct node* right; }

Tree Traversal

• Inorder Traversal• Preorder Traversal• Postorder Traversal• Level order Traversal

Postorder TraversalAlgorithm

1. Traverse the left subtree2. Traverse the right subtree3. Visit the root.

void printPostorder (struct node* node) { if (node == NULL) return; // first recur on both subtrees printTree(node->left); printTree(node->right); // then deal with the node printf("%d ", node->data); }

Inorder Traversal

Algorithm1. Traverse the left subtree2. Visit the root.3. Traverse the right subtree

void printPostorder (struct node* node) { if (node == NULL) return; printTree(node->left); printf("%d ", node->data); printTree(node->right); }

Preorder Traversal

Algorithm1. Visit the root.2. Traverse the left subtree3. Traverse the right subtree

void printPostorder (struct node* node) { if (node == NULL) return; printf("%d ", node->data); printTree(node->left); printTree(node->right); }

Level order Traversal

Level Order:

1, 2, 3, 4, 5

Use Queue

Binary Search Tree

The common properties of binary search trees are as follows:1. The left subtree of a node contains only nodes with keys less than the node's key.2. The right subtree of a node contains only nodes with keys greater than the node's key.3. The left and right subtree each must also be a binary search tree.4. Each node can have up to two successor nodes.5. There must be no duplicate nodes.6. A unique path exists from the root to every other node.

Binary Search Tree