Java Coding Test Course, Understanding Trees

The tree is a data structure frequently used in programming, consisting of nodes and edges in a connected structure. Each node contains data and connection information and has one root node connected to child nodes. In this article, we will learn about the basic concepts of trees and how to solve problems related to trees.

Basic Concepts of Trees

A tree consists of the following terms:

  • Node: A structure that contains data and the information connecting that data.
  • Root Node: The topmost node of the tree.
  • Parent Node: A node that has child nodes.
  • Child Node: A node connected to a parent node.
  • Leaf Node: A node that has no child nodes.
  • Depth: The length of the path from the root node to a specific node.
  • Height: The length of the path from a specific node to the deepest leaf node.

Problem Definition

Let’s solve a tree-related problem using Java. The problem is to find the depth of a given binary tree.

Problem: Finding the Depth of a Binary Tree

public class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;

    TreeNode(int x) {
        val = x;
    }
}

public class Solution {
    public int maxDepth(TreeNode root) {
        if (root == null) {
            return 0;
        } else {
            int leftDepth = maxDepth(root.left);
            int rightDepth = maxDepth(root.right);
            return Math.max(leftDepth, rightDepth) + 1;
        }
    }
}

Problem Solving Process

1. Understanding the Problem

The goal of this problem is to traverse the given binary tree and calculate the depth of each node. The depth is defined as the number of edges from the root node to a specific node.

2. Choosing a Solution Method

We will use a recursive approach to explore the tree to solve this problem. When the current node is null, it indicates a depth of 0. Otherwise, we will recursively find the depth of the left and right subtrees, choose the larger value, and add 1.

3. Writing the Code

We will write the code based on the above approach.

public class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;

    TreeNode(int x) {
        val = x;
    }
}

public class Solution {
    public int maxDepth(TreeNode root) {
        // Base case: when the node is empty
        if (root == null) {
            return 0;
        }

        // Recursively find the depth of the left and right subtrees
        int leftDepth = maxDepth(root.left);
        int rightDepth = maxDepth(root.right);

        // Return the greater value plus 1
        return Math.max(leftDepth, rightDepth) + 1;
    }
}

4. Time Complexity Analysis

The time complexity of this algorithm is O(n), where n is the number of nodes in the tree. This is because we need to visit all the nodes once.

5. Final Code and Testing

Now let’s test the completed code to see if it works correctly.

public class Main {
    public static void main(String[] args) {
        TreeNode root = new TreeNode(1);
        root.left = new TreeNode(2);
        root.right = new TreeNode(3);
        root.left.left = new TreeNode(4);
        root.left.right = new TreeNode(5);

        Solution solution = new Solution();
        System.out.println("The depth of the tree is: " + solution.maxDepth(root)); // Output: 3
    }
}

6. Conclusion

In this lecture, we covered the basic concepts of trees and the algorithmic problem of finding the depth of a binary tree. We found that the recursive approach can effectively solve this problem. Understanding these foundational concepts is very important for solving various tree problems and will be helpful for tackling more complex problems.

Note: To enhance your understanding of trees, please practice with various types of tree problems. It would be beneficial to study binary search trees, balanced binary trees, and tree traversal methods.

Additional Resources