Kotlin Coding Test Course, Understanding Trees

1. Tree (Introduction)

A tree is a data structure used to represent hierarchical structures, where each node can have multiple children. A tree consists of nodes and edges, where the top node is called the root node, and the nodes at the ends of the tree are called leaf nodes. Trees are essential concepts for solving various problems and implementing algorithms.

1.1. Properties of Trees

  • A tree with n nodes always has n-1 edges.
  • The root node is unique, and each node has only one parent.
  • Not all leaf nodes are located at the same depth.

2. Algorithm Problem

Problem: Calculate the maximum depth of a binary tree

Write a function to calculate the maximum depth of a given binary tree. The depth of a binary tree is the number of nodes along the path from the root node to the deepest leaf node.

Input

  • A binary tree is defined with node types, and each node contains an integer value.
  • A node can have child nodes, and it can have up to two children.

Output

  • Returns the maximum depth as an integer.

3. Problem-Solving Process

3.1. Understanding the Problem

To understand the problem, examine the characteristics of the given binary tree. The depth refers to the longest path from the root to a leaf node, which can be obtained through exploration. A common method is depth-first search (DFS).

3.2. Defining the Tree Node Class

First, we will define a class to represent a node of the tree. It can be implemented in Kotlin as follows:

data class TreeNode(val value: Int, var left: TreeNode? = null, var right: TreeNode? = null)

3.3. Implementing the Algorithm to Find Maximum Depth

The maximum depth can be calculated recursively. Below is an example implemented using DFS.

fun maxDepth(node: TreeNode?): Int {
        if (node == null) return 0
        val leftDepth = maxDepth(node.left)
        val rightDepth = maxDepth(node.right)
        return Math.max(leftDepth, rightDepth) + 1
    }

The above function works as follows:

  • If the tree node is null, the depth is 0.
  • Recursively call the depths of the left and right child nodes and choose the deeper of the two.
  • Add 1 to return the maximum depth.

3.4. Complete Example Implementation

Let’s implement the entire code to find the maximum depth:

fun main() {
        val root = TreeNode(1)
        root.left = TreeNode(2)
        root.right = TreeNode(3)
        root.left!!.left = TreeNode(4)
        root.left!!.right = TreeNode(5)

        val depth = maxDepth(root)
        println("The maximum depth is: $depth")  // Output: The maximum depth is: 3
    }

4. Conclusion

The binary tree is an important topic for solving algorithm problems. By solving the problem, one can understand the structure of trees and practice recursive thinking, which is a useful skill in coding tests. It is recommended to try various tree-related problems in the future.

5. Additional Practice Problems

  • Finding a specific value in a binary search tree
  • Printing all paths in a binary tree
  • Checking the balance of a binary tree

6. References

To enhance your understanding of trees, please refer to the following resources: