Checking and Printing Binary Tree

A binary tree is a fundamental data structure in computer science that hierarchically organizes elements. Each node in the tree can have at most two child nodes: a left child and a right child. This structure allows for efficient searching, sorting, and traversal operations.

Checking Properties of Binary Trees

There are various properties that binary trees can exhibit, and checking for these properties can be crucial for specific algorithms and applications. Here are some common checks:

• Is it a Binary Search Tree (BST)?
  • A BST has a specific ordering property: all nodes in the left subtree are less than the root node, and all nodes in the right subtree are greater than the root node. This ordering facilitates efficient searching. You can implement a recursive function that traverses the tree, comparing the values of nodes with their children to ensure adherence to this rule.
• Is it a Full Binary Tree?
  • A full binary tree has every level completely filled, except possibly the last level, which can be filled with all leaves on the left side. You can check for a full binary tree by comparing the number of nodes at each level with the expected number based on the tree's height.
• Is it a Complete Binary Tree?
  • A complete binary tree has all levels filled except possibly the last level, which must be filled from the left side as far right as possible. This property is often used for efficient heap implementations. Checking for completeness can involve similar calculations to full binary trees, but with stricter requirements for the last level.
• Balanced Binary Tree (for specific balancing criteria)
  • Balanced binary trees aim to maintain a roughly equal height for the left and right subtrees of each node. This can be achieved using techniques like AVL trees or red-black trees, which have specific balancing properties. Checking for balance often involves calculating the heights of subtrees and comparing them.

Printing Binary Trees

There are several ways to print a binary tree, depending on the desired output format:

• In-Order Traversal
  • This traversal visits the left subtree, then the root node, and then the right subtree. It's commonly used for printing BSTs in sorted order.
• Pre-Order Traversal
  • This traversal visits the root node first, followed by the left subtree and then the right subtree.
• Post-Order Traversal
  • This traversal visits the left subtree, then the right subtree, and finally the root node.
• Level-Order Traversal (Breadth-First Search)
  • This traversal visits all nodes at a given level before moving to the next level. It requires using a queue data structure to keep track of nodes to be visited.
• Printing as a Two-Dimensional Structure
  • This format visually represents the hierarchical structure of the tree, using indentation or special characters to indicate parent-child relationships. This can be achieved using recursive functions that track the current level and print nodes with appropriate spacing.

Practice problems on Checking and Printing Binary Tree:

• Check for Children Sum Property in a Binary Tree
• Check sum of Covered and Uncovered nodes of Binary Tree
• Check if two nodes are cousins in a Binary Tree
• Check if removing an edge can divide a Binary Tree in two halves
• Check if all leaves are at same level
• Check if a given Binary Tree is SumTree
• Check whether a given binary tree is perfect or not
• Check whether a binary tree is a full binary tree or not
• Check whether a binary tree is a full binary tree or not | Iterative Approach
• Check whether a given Binary Tree is Complete or not | Set 1 (Iterative Solution)
• Check if a given Binary Tree is height balanced like a Red-Black Tree
• Check if a binary tree is subtree of another binary tree | Set 2
• Iterative function to check if two trees are identical
• Check if a Binary Tree (not BST) has duplicate values
• Check if a Binary Tree contains duplicate subtrees of size 2 or more
• Print middle level of perfect binary tree without finding height
• Print cousins of a given node in Binary Tree
• Given a binary tree, print out all of its root-to-leaf paths one per line
• Check if there is a root to leaf path with given sequence
• Print the longest leaf to leaf path in a Binary tree.
• Print path from root to a given node in a binary tree
• Print root to leaf paths without using recursion
• Print all root to leaf paths with there relative positions
• Print the nodes at odd levels of a tree
• Print all full nodes in a Binary Tree
• Print nodes between two given level numbers of a binary tree
• Print nodes at k distance from root
• Print nodes at k distance from root | Iterative
• Print all leaf nodes of a Binary Tree from left to right
• Given a binary tree, print all root-to-leaf paths
• Print all nodes at distance k from a given node
• Print all nodes that don’t have sibling
• Print all nodes that are at distance k from a leaf node
• Print Levels of all nodes in a Binary Tree
• Print a Binary Tree in Vertical Order
• Print leftmost and rightmost nodes of a Binary Tree
• Print Binary Tree levels in sorted order
• Print Binary Tree in 2-Dimensions
• Print Left View of a Binary Tree
• Print Right View of a Binary Tree
• Right view of Binary Tree using Queue
• Print Nodes in Top View of Binary Tree

All articles on Binary Tree !

Quick Links :

• 'Practice Problems' on Trees
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