Author: root

Hello! In this lecture, we will cover one of the JavaScript coding test problems for employment, ‘Finding the Shortest Path.’ This problem will be very helpful in understanding and utilizing the basic principles of algorithms and data structures. It is a common topic in coding interviews, and understanding priority queues and graph theory is essential.

Problem Description

We assume that we can represent the relationship between several cities and roads as a graph. Each city is represented as a node, and roads are represented as edges between nodes. We need to find the shortest path from one city to another.

Problem Definition

Given the number of cities n and the number of roads m, find the shortest path from a specific city k to all other cities. The information about the roads is given as a weight w connecting u and v. The weight represents the length of the road.

Input Format

n, m, k
u1, v1, w1
u2, v2, w2
...
um, vm, wm

Output Format

Array of the lengths of the shortest paths

For example, let’s assume the following input is given:

5 6 1
1 2 2
1 3 3
2 3 1
2 4 2
3 4 4
4 5 1

In the above example, the lengths of the shortest paths from city 1 to the other cities are as follows:

0
2
3
4
5

Since we start from city 1, the length of the shortest path includes 0 for itself and the shortest distances to the other cities.

Solution Approach

To solve this problem, we can use the Dijkstra Algorithm. The Dijkstra algorithm is used to find the shortest path from a specific starting node to all other nodes in a graph, utilizing a priority queue.

Description of the Dijkstra Algorithm

1) Initialization: Set the distance of the starting city to 0 and the distances of the remaining cities to infinity.
2) Storing visited cities: Keep track of visited cities separately to prevent duplicate calculations.
3) Using a priority queue: Select the city with the shortest distance to proceed. Update the distances of the neighboring cities.
4) Repeat: Continue the above process until all cities are visited.

JavaScript Implementation Example

Now, let’s implement the above algorithm in JavaScript.

function dijkstra(n, edges, start) {
    const INF = Infinity;
    const graph = Array.from({ length: n + 1 }, () => []);
    const dist = Array(n + 1).fill(INF);
    dist[start] = 0;
    const pq = new MinPriorityQueue();

    edges.forEach(([u, v, w]) => {
        graph[u].push([v, w]);
        graph[v].push([u, w]); // For undirected graphs
    });

    pq.enqueue(start, 0);

    while (!pq.isEmpty()) {
        const { element: current, priority: currentDist } = pq.dequeue();
        
        if (currentDist > dist[current]) continue; // If already visited with the shortest distance
        
        for (const [neighbor, weight] of graph[current]) {
            const newDist = currentDist + weight;
            if (newDist < dist[neighbor]) {
                dist[neighbor] = newDist;
                pq.enqueue(neighbor, newDist);
            }
        }
    }
    return dist.slice(1); // Exclude index 0
}

class MinPriorityQueue {
    constructor() {
        this.items = [];
    }

    enqueue(element, priority) {
        this.items.push({ element, priority });
        this.items.sort((a, b) => a.priority - b.priority);
    }

    dequeue() {
        return this.items.shift(); // Returns the one with the lowest priority
    }

    isEmpty() {
        return this.items.length === 0;
    }
}

// Example usage
const n = 5;
const edges = [
    [1, 2, 2],
    [1, 3, 3],
    [2, 3, 1],
    [2, 4, 2],
    [3, 4, 4],
    [4, 5, 1]
];
const start = 1;
console.log(dijkstra(n, edges, start)); // [0, 2, 3, 4, 5]

Summary of the Problem Solving Process

1) Initialize the number of nodes and edges.
2) Represent the roads (edges) between cities as a graph.
3) Use the Dijkstra algorithm to calculate the shortest paths.
4) Output the results of the shortest paths.

Conclusion

In this lecture, we learned how to implement graph algorithms in JavaScript through the ‘Finding the Shortest Path’ problem. The Dijkstra algorithm is simple to implement and can be applied to various problems, making it very useful. It often appears not only in coding tests but also in algorithm competitions, so be sure to master it.

Additionally, in order to gain a deeper understanding of algorithms, it is good to study various variations of the shortest path algorithms (such as the Bellman-Ford algorithm, Floyd-Warshall algorithm, etc.). By understanding the differences and use cases of these algorithms, you will gain a broader perspective.

I hope this is helpful, and I look forward to meeting you with more interesting topics in the next lecture. Thank you!

A tree is one of the data structures used to store data hierarchically. In this course, we will explore the basic concepts of trees and learn how to solve tree-related algorithm problems using JavaScript.

What is a Tree?

A tree is a non-linear data structure composed of nodes. Each node contains data and connections (edges) to child nodes. It starts from a single root node and can have several child nodes below it, and each child node can also have its own child nodes. The main uses of trees are as follows:

• Hierarchical data representation (e.g., family trees, organizational charts)
• Data searching (e.g., binary search trees)
• Solving various problems (e.g., shortest path problems)

Components of a Tree

• Root Node: The topmost node of the tree, it is the ancestor of all other nodes.
• Edge: A line that connects nodes, linking parent nodes to child nodes.
• Leaf Node: A node that has no child nodes; it is a node that cannot be expanded further.
• Subtree: A tree consisting of the child nodes of a specific node.

Tree Problem: Calculate the Depth of a Given Binary Tree

Let’s solve the following problem. Write a function that calculates the depth of a given binary tree.

Problem Description

Given a binary tree, write a function that returns the maximum depth of the binary tree. The depth is defined as the distance from the root node to the deepest leaf node.

Example Input

Input: 
       3
      / \
     9  20
        /  \
       15   7

Example Output

Output: 3

Solution Approach

This problem can be solved using Depth First Search (DFS) or Breadth First Search (BFS) methods. Here, we will explain the approach using DFS.

1. Recursive Approach

We can visit the left and right child nodes recursively at each node to calculate the depth. The basic idea is as follows:

1. If the node is null, return 0.
2. Calculate the depth of the current node’s left and right children.
3. Return the maximum of the left and right depths plus 1 for the parent node’s depth.

2. Code Implementation

Below is the code implemented in JavaScript.

class TreeNode {
    constructor(val) {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

function maxDepth(root) {
    if (root === null) {
        return 0;
    }
    const leftDepth = maxDepth(root.left);
    const rightDepth = maxDepth(root.right);
    return Math.max(leftDepth, rightDepth) + 1;
}

3. Code Explanation

• TreeNode: This class defines the nodes of a tree. Each node has a value and possesses left and right children.
• maxDepth: This function recursively calculates the depth. It returns 0 if root is null and otherwise calculates and returns the larger value from the left and right child depths.

4. Testing

Let’s test the `maxDepth` function using the provided example. You can add the following code.

// Create a binary tree
const root = new TreeNode(3);
root.left = new TreeNode(9);
root.right = new TreeNode(20);
root.right.left = new TreeNode(15);
root.right.right = new TreeNode(7);

// Calculate depth
console.log(maxDepth(root)); // Output: 3

Conclusion

We have explored how to calculate the maximum depth of a tree using JavaScript and the process of solving algorithm problems. Understanding trees will help solve many programming challenges. Practice various tree problems to build a deep understanding of tree structures.

Hello, everyone! In this blog post, we will take an in-depth look at the coding test algorithm problem “Taking Out Pebbles” using JavaScript. This problem will greatly help in understanding data structures and algorithms. Now, let’s define the problem.

Problem Definition

There is a bag containing several pebbles. Each pebble is numbered, and you need to extract pebbles that satisfy specific conditions. The pebbles are represented by n numbers, each of which represents the unique ID of that pebble.

Your task is to return the number of pebbles that are smaller than the given integer k when provided with the pebble array rocks and the integer k. The length of the array is from 1 to 1000, and each pebble’s ID is between 1 and 10,000.

For example:

• Input: rocks = [5, 2, 8, 3, 6], k = 4
• Output: 2 (Pebble IDs: 2, 3)

Problem-Solving Strategy

To solve this problem, we will use a basic array search technique. We will follow these steps to arrive at a solution.

1. Array Search

We will traverse the given array rocks and check if each pebble’s ID is smaller than k. If this condition is met, we will increase the count.

2. Return Count

After reviewing all the pebbles, we will finally return the count.

JavaScript Code Implementation

Now, let’s write a JavaScript function based on the above plan:

function countRocks(rocks, k) {
    let count = 0;
    for (let i = 0; i < rocks.length; i++) {
        if (rocks[i] < k) {
            count++;
        }
    }
    return count;
}

// Example usage
const rocks = [5, 2, 8, 3, 6];
const k = 4;
console.log(countRocks(rocks, k)); // Output: 2

Code Analysis

In the above code, the countRocks function takes two parameters: the rocks array and the k value. We initialize the count with let count = 0; and traverse the array using a for loop. If each pebble’s ID is smaller than k, we increase the count. Finally, we return the count.

Time Complexity Analysis

The time complexity for this problem is O(n). Since we check each element in the array only once, it has a linear time complexity.

Conclusion

Through today’s problem, “Taking Out Pebbles,” we laid the foundation of array searching and learned how to design efficient algorithms. Such problems will frequently appear in coding tests, playing a crucial role in building your fundamentals. I hope you also gain experience by solving various problems!

Practice Problem

Now it’s your turn to test your skills. Try to solve the following modified problem.

• Modified Problem: Write a function to count the number of pebbles in the given rocks array that are greater than the value of k.

To solve this problem, you only need to change the condition. Think about what changes are needed in your code!

In this tutorial, we will take a detailed look at how to solve employment-related algorithm problems using JavaScript. This article will address the ‘Find Minimum 2’ problem, explaining the approach to problem-solving, step-by-step processes, and optimization methods.

Problem Description

The following problem involves finding the minimum value that satisfies specific conditions in an array. For the given array, the following conditions apply:

• An array consisting of positive integers is given.
• Only the elements at odd indices of the array should be considered to find the minimum value.
• If a minimum value cannot be found, it should return `null`.

Example of the Problem

            Input: [5, 3, 4, 1, 2, 7, 6]
            Output: 1

            Input: [2, 9, 6, 7, 10]
            Output: 9

            Input: [4, 4, 4, 4]
            Output: null
        

Approach to Solve the Problem

To solve this problem, we follow these steps:

1. Extract only the elements at odd indices from the input array.
2. Find the minimum value among the extracted elements.
3. If a minimum value exists, return it; otherwise, return `null`.

Step 1: Extract Odd Index Elements

To extract elements at odd indices, we can use the `filter` method. This method returns an array of elements that satisfy a given condition.

Step 2: Find the Minimum Value

There are several ways to find the minimum value from the array extracted from odd indices. Using the `Math.min` function allows for straightforward minimum value retrieval.

Step 3: Return the Result

After finding the minimum value, we add logic to return it or `null` based on the condition.

Code Implementation for Problem Solving

Now, based on these processes, let’s write JavaScript code to solve the problem. Below is the code that implements the algorithm described above:

            function findMinOddIndex(arr) {
                // Extracting odd index elements
                const oddIndexedElements = arr.filter((_, index) => index % 2 === 1);

                // Return null if there are no odd index elements
                if (oddIndexedElements.length === 0) {
                    return null;
                }

                // Return the minimum value
                return Math.min(...oddIndexedElements);
            }

            // Example tests
            console.log(findMinOddIndex([5, 3, 4, 1, 2, 7, 6])); // 1
            console.log(findMinOddIndex([2, 9, 6, 7, 10])); // 9
            console.log(findMinOddIndex([4, 4, 4, 4])); // null
        

Code Explanation

The above code works as follows:

• The function `findMinOddIndex` takes the input array and filters out the elements corresponding to odd indices.
• If the filtered result is an empty array, meaning there are no elements at odd indices, it returns `null`.
• If not, it calculates and returns the minimum value using `Math.min`.

Testing and Verifying Results

Let’s run various test cases with the code we wrote. We will check the execution results to ensure the correct outcomes are returned.

• Input: [5, 3, 4, 1, 2, 7, 6] → Output: 1
• Input: [2, 9, 6, 7, 10] → Output: 9
• Input: [4, 4, 4, 4] → Output: null
• Input: [] → Output: null
• Input: [0, -1, 3, -5, 4] → Output: -5 (the minimum value among -1 and -5 at odd indices)

Performance Optimization

The performance of the currently implemented code is good, with an average time complexity of O(n). However, if the array size is very large, we can further optimize performance. For example, we can use a single iteration to find the minimum value at odd indices. Below is an example of this implementation:

            function findMinOddIndexOptimized(arr) {
                let min = Infinity;

                for (let i = 1; i < arr.length; i += 2) {
                    if (arr[i] < min) {
                        min = arr[i];
                    }
                }

                return min === Infinity ? null : min;
            }

            // Example tests
            console.log(findMinOddIndexOptimized([5, 3, 4, 1, 2, 7, 6])); // 1
            console.log(findMinOddIndexOptimized([2, 9, 6, 7, 10])); // 9
            console.log(findMinOddIndexOptimized([4, 4, 4, 4])); // null
        

Conclusion

In this tutorial, we learned how to find the minimum value at odd indices in a given array using JavaScript. Clearly understanding the requirements of the problem, and deriving the optimal solution through an efficient algorithm is a crucial skill in coding tests. While filtering and mapping arrays can easily solve problems, optimization with performance in mind is also necessary.

In your practice for upcoming coding tests, I hope you get familiar with solving similar pattern problems repeatedly. Additionally, attempting various variations of problems can help enhance your problem-solving abilities.