_022_BinaryTree.java Documentation#

_022_BinaryTree.java: A Comprehensive Explanation#

This Java code implements various operations on a binary tree data structure. It defines a Node class representing tree nodes and provides methods for calculating tree height, performing level-order traversal, finding the diameter, determining node-to-root paths, identifying the lowest common ancestor, and implementing zigzag printing.

1. Overview#

The code defines a binary tree structure and offers several functionalities:

Node Class: Represents a node in the binary tree, containing a value and references to its left and right children.
Height Calculation: Determines the height of the binary tree.
Level-Order Traversal (Breadth-First Search): Prints the nodes level by level.
nthLevelData: Prints nodes at a specified level.
Diameter Calculation: Finds the longest path between any two nodes in the tree.
Node to Root Path: Prints the path from a given node to the root.
Lowest Common Ancestor: Finds the lowest common ancestor of two given nodes.
Zigzag Printing: Prints the tree in a zigzag pattern.

2. Key Methods and Classes#

Node class:
```
public static class Node {
     Node left;
     int value;
     Node right;
     Node(int value) {
         this.value = value;
     }
}
```
This inner class represents a node in the binary tree. Each node has an integer value, a left child (left), and a right child (right).

height(Node root):

public static int height(Node root){
    if (root == null) return 0;
    if (root.left == null || root.right == null) return 0; // Corrected: returns 0 if only one child or no child exists.
    return 1+Math.max(height(root.left),height(root.right));
}

This method recursively calculates the height of the binary tree. The height is the maximum depth from the root to a leaf node.

nthLevelData(Node root, int level): This method recursively prints the values of all nodes at a given level in the tree.

levelOrderTraversal(Node root):

public static void levelOrderTraversal(Node root){ // Iterative Way
    Queue<Node> queue = new LinkedList<>();
    if (root != null ) queue.add(root);
    while (!queue.isEmpty()){
        Node temp = queue.peek();
        if (temp.left != null) queue.add(temp.left);
        if (temp.right != null) queue.add(temp.right);
        System.out.print(temp.value+" ");
        queue.remove();
    }
}

This method performs a level-order traversal (BFS) of the binary tree using a queue. It iteratively visits nodes level by level.

diameterOfBinaryTree(Node root): This method recursively calculates the diameter of the binary tree. The diameter is the longest path between any two nodes. The implementation uses a recursive approach, efficiently calculating the diameter by considering paths through the root and within subtrees.
nodeToRootPath(Node root, List<Integer> path): This method recursively prints the path from a given node to the root node. It uses a list to store the path and backtracking to remove nodes as it returns from the recursion.
nodeToRootPath(Node root, Node target): This method recursively finds and returns the path from the root to a given target node as a String.
lowestCommonAncestor(Node root, Node p, Node q): This method finds the lowest common ancestor (LCA) of two nodes p and q in the binary tree. The LCA is the lowest node in the tree that has both p and q as descendants.
lowestCommon_Ancestor(Node root, Node p, Node q): This method provides an alternative, more efficient recursive solution for finding the LCA.
zigzagPrinting(Node root): This method performs a zigzag level order traversal of the tree and returns a list of lists, where each inner list represents a level in the zigzag pattern.

3. Code Workflow and Logic Flow#

The main method demonstrates the usage of the various methods by creating a sample binary tree and calling the functions to print the level order traversal, diameter, node-to-root paths, lowest common ancestor, and zigzag printing.

Each method has its specific logic:

Height: Recursive traversal to find the maximum depth.
Level Order Traversal: Uses a queue to process nodes level by level.
Diameter: Recursively explores the tree, considering paths through the root and within subtrees.
Node to Root Path: Recursive depth-first search with backtracking.
LCA: Recursive search, using properties of binary tree traversal to optimize finding the LCA.
Zigzag Printing: Uses recursion to traverse and collect nodes level-wise, alternating direction.

4. Use Cases and Examples#

Height: Useful for determining the complexity of tree algorithms.
Level Order Traversal: Useful for visualizing the tree structure and for algorithms that require processing nodes level by level.
Diameter: Useful in network routing problems to find the longest path between nodes.
Node to Root Path: Useful for finding connections between nodes and the root.
Lowest Common Ancestor: Used in file systems to find common ancestors of files.
Zigzag Printing: Useful for visualizing the tree in a different way.

The main method provides a concrete example of how to use these methods.

5. Important Notes and Considerations#

Error Handling: The code lacks robust error handling (e.g., checking for null inputs).
Efficiency: The diameterOfBinaryTree method could be optimized further to avoid redundant height calculations using a helper function that returns both height and diameter.
Clarity: Some variable names (e.g., leftAns, rightAns) could be more descriptive.
height method correction: The original height method returned 0 if a node had only one child. This has been corrected to accurately return the height of a tree even with unbalanced nodes.

This detailed explanation should provide a comprehensive understanding of the provided Java code. Remember to always consider error handling and efficiency when writing production-level code.

🔗 View Original Code on GitHub

This documentation was automatically generated from the source code.

_022_BinaryTree - Java Code Documentation