Category: Javascript Coding Test

Hello! In this article, we will take a detailed look at the algorithm problem of finding the parent of a tree using JavaScript. We will emphasize the importance of understanding tree structures and their application in coding tests, and we will systematically organize how to solve related problems step by step. In particular, we will discuss what it means to understand the definition of a tree and the parent-finding algorithm in coding tests.

What is a Tree Structure?

A tree is one of the data structures that has a hierarchical structure. It is a type of graph made up of nodes and the connections between those nodes. A tree has the following characteristics:

• A tree is a non-linear structure.
• A tree consists of one or more child nodes (Child Node) and a root node (Root Node).
• Each node can have one parent node (Parent Node), and the root node has no parent.
• A tree does not contain cycles.

Problem Description

In this problem, we need to implement an algorithm to find the parent node of a specific node in a given tree structure. It has the following input format:

    Example input:
    {
        "1": [2, 3],
        "2": [4, 5],
        "3": [],
        "4": [],
        "5": []
    }
    

In the example above, each key represents a node, and the value is an array of child nodes of that node. For example, node 1 has 2 and 3 as children.

Requirements

• Create a function to find the parent node of a specific node.
• It should be able to parse the tree structure through the input format.
• If there is no parent node, it should return null.

Problem Solving Process

Now, let’s look step-by-step at how to parse the tree structure and find the parent node to solve the problem.

Step 1: Parsing the Tree Structure

First, we need to parse the tree structure based on the given input. The example tree we will deal with is transmitted in object form, and we need a structure that can store parent information based on child nodes and their relationships in order to find the parents.

    const tree = {
        "1": [2, 3],
        "2": [4, 5],
        "3": [],
        "4": [],
        "5": []
    };
    

Each node of the tree can be accessed in adjacency list form. However, to find parent information, we must explicitly store the parents of each node. To do this, we will create a new object and update the parent information while traversing the child nodes.

Step 2: Implementing the Parent Finding Logic

Finding a parent involves checking which parent each node has in the tree structure. The function can be implemented in the following steps:

    const findParent = (tree, child) => {
        let parentNode = null;
        
        for (const key in tree) {
            if (tree[key].includes(child)) {
                parentNode = key;
                break;
            }
        }
        
        return parentNode ? parentNode : null;
    };
    

The above `findParent` function accepts the tree object and the child node as input and searches for the parent node of that child. It checks each node for the child node and returns the parent node found in the node that includes the child. If there is no parent, it returns null.

Step 3: Implementing the Full Code

Now, let’s integrate the parts we have written above to complete the full code.

    const tree = {
        "1": [2, 3],
        "2": [4, 5],
        "3": [],
        "4": [],
        "5": []
    };

    const findParent = (tree, child) => {
        let parentNode = null;
        
        for (const key in tree) {
            if (tree[key].includes(child)) {
                parentNode = key;
                break;
            }
        }
        
        return parentNode ? parentNode : null;
    };

    // Example usage
    console.log(findParent(tree, 4)); // Output: "2"
    console.log(findParent(tree, 5)); // Output: "2"
    console.log(findParent(tree, 1)); // Output: null
    

Conclusion

In this lecture, we explored the process of solving the algorithm problem of finding the parent of a child node in a tree structure using JavaScript. Understanding tree structures and solving algorithm problems using them is an important skill for developers. As we become more familiar with various tree structures, we can effectively solve many problems through tree traversal techniques.

In the future, we will cover a wider range of algorithms and data structures. Thank you!

Graph problems frequently appear in coding tests. A bipartite graph refers to a graph that can be divided into two sets, where adjacent vertices belong to different sets. In this lecture, we will learn about the algorithm to determine whether a graph is bipartite.

Problem Definition

Write a function to determine whether the given undirected graph is bipartite. A bipartite graph must divide the vertices into two groups, with no edges existing between vertices in the same group.

Input

• Number of vertices n (1 ≤ n ≤ 1000)
• Number of edges m (0 ≤ m ≤ 1000)
• Information on m edges (pairs of integers u, v indicating that vertex u is connected to vertex v)

Output

If the graph is a bipartite graph, print true, otherwise print false.

Approach to the Problem

To determine if a graph is bipartite, we can use a graph coloring technique. We color each vertex with two colors, such as ‘0’ and ‘1’, and if adjacent vertices are colored the same, the graph is not bipartite.

The implementation method is as follows:

• Represent the graph as an adjacency list
• Create an array to store the color of each vertex
• Use breadth-first search (BFS) or depth-first search (DFS) to visit and color the vertices
• If adjacent vertices have the same color, return that it is not a bipartite graph

Code Implementation

Let’s implement a function to determine whether a graph is bipartite according to the steps above using JavaScript.

function isBipartiteGraph(n, edges) {
    // Represent the graph as an adjacency list
    const graph = Array.from({length: n}, () => []);
    edges.forEach(([u, v]) => {
        graph[u].push(v);
        graph[v].push(u); // Since it is an undirected graph, add in both directions
    });

    const colors = Array(n).fill(-1); // Store the color of each vertex (-1: unvisited, 0: first color, 1: second color)

    const bfs = (start) => {
        const queue = [start];
        colors[start] = 0; // Color the starting vertex with the first color

        while (queue.length) {
            const node = queue.shift();

            for (const neighbor of graph[node]) {
                if (colors[neighbor] === -1) {
                    // If the adjacent vertex is unvisited, color it and add to the queue
                    colors[neighbor] = 1 - colors[node];
                    queue.push(neighbor);
                } else if (colors[neighbor] === colors[node]) {
                    // If the adjacent vertex's color is the same as the current node, it is not a bipartite graph
                    return false;
                }
            }
        }
        return true;
    };

    // Check all vertices and perform BFS if there are connected components
    for (let i = 0; i < n; i++) {
        if (colors[i] === -1) {
            if (!bfs(i)) return false;
        }
    }
    
    return true;
}

// Test case
const n = 4;
const edges = [[0, 1], [0, 2], [1, 3], [2, 3]];
console.log(isBipartiteGraph(n, edges)); // false
    

Algorithm Analysis

The above algorithm uses breadth-first search (BFS) to traverse all the vertices of the graph. Consequently, the time complexity is O(n + m) where n is the number of vertices and m is the number of edges. This is because we visit each vertex and edge once.

The space complexity is also O(n + m) required to store the adjacency list and color array.

Conclusion

In this lecture, we learned about the algorithm to determine whether a graph is bipartite. With this algorithm, we can ascertain if a graph problem involves a bipartite graph. Given its applicability to various problems, a thorough understanding is beneficial.

Furthermore, the solution to this problem can also be implemented similarly using DFS in addition to BFS. Understand the unique characteristics of the algorithm and try solving various derivative problems based on that.

Additional Practice Problems

To help your understanding, try solving the following problems:

• Symmetric Bipartite Graph Determination: Determine whether the given edge information constitutes a bipartite graph when provided symmetrically.
• Maximum Matching in Bipartite Graph: Implement an algorithm to find the maximum matching in a given bipartite graph.

References

For a detailed explanation of bipartite graphs, please refer to the Bipartite Graph article on Wikipedia.