_023_BinaryTree.java Documentation#

Java Binary Tree Implementation and Traversal#

This Java code implements a binary tree data structure and provides methods for two specific tree traversals: level order traversal (with alternating direction) and finding all paths with a given sum.

1. Overview#

The code defines a Node class representing a node in the binary tree, containing an integer value, and left and right child nodes. Two primary functionalities are implemented:

• levelOrderTraversalII(Node root): Performs a level order traversal of the binary tree, alternating the traversal direction (left-to-right, then right-to-left, and so on) for each level. It returns a list of lists, where each inner list represents a level in the tree.

• pathSum(Node root, int targetSum): Finds all root-to-leaf paths in the binary tree that sum up to a given targetSum. It returns a list of lists, where each inner list represents a path.

2. Detailed Explanation of Key Methods and Classes#

2.1 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. It contains:

• left: A reference to the left child node.
• value: An integer value stored in the node.
• right: A reference to the right child node.
• Node(int value): Constructor to create a new node with a given value.

2.2 heightOfTree(Node root)#

static int heightOfTree(Node root){
    if (root==null)return 0;
    return 1+Math.max(heightOfTree(root.left),heightOfTree(root.right));
}

This method recursively calculates the height of the binary tree. The height is the number of edges on the longest path from the root to a leaf node. An empty tree has a height of 0.

2.3 levelOrderTraversalII(Node root)#

static List<List<Integer>> levelOrderTraversalII(Node root){
    int height = heightOfTree(root);
    List<List<Integer>> ans = new ArrayList<>();
    for (int i = height; i > 0 ; i--) {
        boolean leftToRight = (height - i) % 2 == 0;
        ans.add(traversal(root, i, leftToRight));
    }
    return ans;
}

This method performs a level order traversal with alternating directions. It first determines the height of the tree. Then, it iterates through each level from the bottom up, calling the traversal helper method to get the nodes at that level. The leftToRight boolean variable controls the traversal direction.

2.4 traversal(Node root, int level, boolean leftToRight)#

private static List<Integer> traversal(Node root,int level,boolean leftToRight){
    if (root == null) return new ArrayList<>();
    List<Integer> arr = new ArrayList<>();
    if (level == 1){
        arr.add(Integer.valueOf(root.value));
        return arr;
    }
    if (leftToRight){
        arr.addAll(traversal(root.left,level-1,leftToRight));
        arr.addAll(traversal(root.right,level-1,leftToRight));
    }else{
        arr.addAll(traversal(root.right,level-1,leftToRight));
        arr.addAll(traversal(root.left,level-1,leftToRight));
    }
    return arr;
}

This recursive helper method retrieves the nodes at a given level. If leftToRight is true, it traverses left then right; otherwise, it traverses right then left.

2.5 pathSum(Node root, int targetSum)#

public static List<List<Integer>> pathSum(Node root, int targetSum) {
    List<List<Integer>> allPaths = new ArrayList<>();
    dfs(root, new ArrayList<>(),0,targetSum ,allPaths);
    return allPaths;
}

This method initiates the Depth-First Search (DFS) to find all paths that sum to targetSum.

2.6 dfs(Node root, List<Integer> path, int currentSum, int targetSum, List<List<Integer>> allPaths)#

private static void dfs(Node root, List<Integer> path,int currentSum ,int targetSum,List<List<Integer>> allPaths) {
    if (root == null) return;
    path.add(Integer.valueOf(root.value));
    currentSum+=root.value;
    if (root.left == null && root.right == null && currentSum == targetSum) {
        allPaths.add(new ArrayList<>(path));
    } else {
        dfs(root.left, path,currentSum, targetSum, allPaths);
        dfs(root.right, path,currentSum, targetSum, allPaths);
    }
    path.remove(path.size() - 1);
}

This recursive helper method performs a Depth-First Search (DFS) to find all paths. It adds the current node’s value to the path and currentSum. If a leaf node is reached and the currentSum equals the targetSum, the path is added to allPaths. The backtracking step (path.remove(path.size() - 1)) is crucial for exploring other paths.

3. Code Workflow and Logic Flow#

The main method creates a sample binary tree and then calls levelOrderTraversalII to perform the alternating level order traversal and pathSum to find paths summing to 22. Both methods use recursion to traverse the tree. levelOrderTraversalII uses a helper function to traverse each level in a specified order, while pathSum uses DFS to explore all paths from the root to leaves.

4. Use Cases and Examples#

• Level Order Traversal: Useful for visualizing the tree structure level by level, and for algorithms that process nodes level by level (e.g., breadth-first search). The alternating direction adds a variation to the standard level order traversal.

• Path Sum: Useful in problems where you need to find combinations of node values that add up to a specific target. For instance, finding combinations of expenses that equal a budget.

The main method demonstrates both use cases with a sample tree. The output of levelOrderTraversalII will be a list of lists representing the tree levels, traversed alternately left-to-right and right-to-left. The pathSum method, when called with targetSum = 22, will identify and print paths in the tree that sum to 22.

5. Important Notes and Considerations#

• Error Handling: The code lacks explicit error handling (e.g., for null root). Production-ready code should include checks for null inputs.

• Efficiency: The levelOrderTraversalII method has a time complexity of O(N), where N is the number of nodes, due to visiting each node once. The pathSum method also has a time complexity of O(N) in the worst case (when all paths need to be explored). Space complexity for both methods is O(W) where W is the maximum width of the tree for levelOrderTraversalII and O(H) where H is the height of the tree for pathSum, due to the recursive calls.

• Generics: The Node class could be made more generic by using a type parameter <T> for the value field to allow storing different data types.

This detailed explanation should provide a comprehensive understanding of the provided Java code. Remember to handle edge cases and consider efficiency improvements for production environments.

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This documentation was automatically generated from the source code.