Author: root

Problem Description

There is a problem of finding the index of a specific permutation among the permutations that can be made from the given numbers.

For example, when the numbers 1, 2, and 3 are given, all the possible permutations are as follows:

• 123
• 132
• 213
• 231
• 312
• 321

The question is to find out the index of a specific number’s permutation. In the above example, 231 corresponds to the 4th position.

Input Format

The first line contains the number of digits n (1 ≤ n ≤ 10).

The second line contains n natural numbers. (Each number is a different natural number from 1 to n.)

The third line contains the desired permutation index k (1 ≤ k ≤ n!).

Output Format

Print the desired permutation.

Problem Solving

Approach

To solve this problem, we define the following steps:

1. Generate all combinations of the numbers to create a list of permutations.
2. Find the desired permutation in the list of permutations.

Permutation Generation Algorithm

Here, we will describe the process of generating permutations and finding a specific order using JavaScript. We will use the DFS (Depth-First Search) method to generate permutations.

JavaScript Code

        
function getPermutations(arr) {
    const result = [];
    
    const backtrack = (current, remaining) => {
        if (remaining.length === 0) {
            result.push(current);
            return;
        }
        
        for (let i = 0; i < remaining.length; i++) {
            const newCurrent = [...current, remaining[i]];
            const newRemaining = [...remaining.slice(0, i), ...remaining.slice(i + 1)];
            backtrack(newCurrent, newRemaining);
        }
    };
    
    backtrack([], arr);
    return result;
}

function findPermutation(n, nums, k) {
    const permutations = getPermutations(nums);
    return permutations[k - 1].join('');
}

// Example input
const n = 3;
const nums = [1, 2, 3];
const k = 4;

// Output
console.log(findPermutation(n, nums, k)); // 231
        
    

Code Explanation

The above code consists of two functions:

• getPermutations: Generates all permutations of the given array.
• findPermutation: Returns the permutation corresponding to the desired index.

Detailed Explanation of getPermutations Function

This function generates permutations recursively:

• Select one of the elements from the current array and add it to the current combination.
• Create a new array with the remaining elements, excluding the selected element, and proceed with the recursive call.
• Repeat this process until all elements are selected, and add the completed permutation to the result.

Detailed Explanation of findPermutation Function

This function goes through the following steps:

1. Generates all permutations for the given number array.
2. Finds the permutation corresponding to the k-1 index in the generated permutation array and returns it as a string.

Time Complexity

The time complexity of this algorithm is O(n!). Since it generates all permutations, the calculation time can become very long as the number of digits increases. However, since the value of n is limited to 10 or less, the problem can be solved at a practical level.

Conclusion

Now you have learned how to create permutations and find a specific ordered permutation. This is one of the types of problems that frequently appear in coding tests, so practice until you are fully proficient.

In the next session, I will return with another algorithm problem. Thank you!

Coding tests are a challenging process that many developers face. Especially when solving problems in JavaScript, one must have a good understanding of the language’s characteristics. In this course, we will explore the characteristics of JavaScript and algorithmic approaches through a problem titled ‘I Don’t Want to be a Liar.’

Problem Description

Imagine the following situation. You are going camping with several friends. Some of your friends are quirky and have decided to lie about a certain incident. Here is what each friend has claimed.

The given input is represented as an array, where each array value is the number of friends that a friend claims. Your goal is to determine that if the number of friends stated in the claims is a majority, then those friends are considered to be lying.

Example Input

    const statements = [
        [0, 1], // Friend 0 claims friend 1
        [1, 2], // Friend 1 claims friend 2
        [2, 0], // Friend 2 claims friend 0
        [3, 2], // Friend 3 claims friend 2 (here, friend 3 is a liar)
    ];
    

Example Output

Number of lying friends: 1

Problem Solving Process

The first step in approaching this problem is to understand the relationships in which each friend claims someone. We can use a directed graph to represent each friend as a node and the claiming relationship as edges.

1. Data Structure Design

First, we need to define a data structure that can store the claims made by each friend. To do this, we can use an object to map each friend’s ID to a list of IDs of the friends they claim.

    const graph = {};
    statements.forEach(([speaker, listener]) => {
        if (!graph[speaker]) {
            graph[speaker] = [];
        }
        graph[speaker].push(listener);
    });
    

2. Exploration through DFS/BFS

To explore the relationships between claims, we can use either DFS (Depth-First Search) or BFS (Breadth-First Search). This will allow us to verify the validity of each friend’s claims.

    function hasContradictions(speaker) {
        const visited = new Set();
        const stack = [speaker];

        while (stack.length) {
            const curr = stack.pop();
            if (visited.has(curr)) {
                return true; // A contradiction occurs when visiting a node that has already been visited
            }
            visited.add(curr);

            if (graph[curr]) {
                graph[curr].forEach(listener => {
                    stack.push(listener);
                });
            }
        }
        return false;
    }
    

3. Check all friends

We count the number of friends who have invalid claims by checking all friends. This is the process of identifying how many among the total friends are creating contradictions.

    let liarsCount = 0;
    for (let i = 0; i < statements.length; i++) {
        if (hasContradictions(i)) {
            liarsCount++;
        }
    }
    return liarsCount;
    

Final Code

    function findLiars(statements) {
        const graph = {};
        statements.forEach(([speaker, listener]) => {
            if (!graph[speaker]) {
                graph[speaker] = [];
            }
            graph[speaker].push(listener);
        });

        function hasContradictions(speaker) {
            const visited = new Set();
            const stack = [speaker];

            while (stack.length) {
                const curr = stack.pop();
                if (visited.has(curr)) {
                    return true; 
                }
                visited.add(curr);

                if (graph[curr]) {
                    graph[curr].forEach(listener => {
                        stack.push(listener);
                    });
                }
            }
            return false;
        }

        let liarsCount = 0;
        for (let i = 0; i < statements.length; i++) {
            if (hasContradictions(i)) {
                liarsCount++;
            }
        }
        return liarsCount;
    }

    console.log(findLiars(statements)); // Output: 1
    

Conclusion

Through problems like the one described above, we learned how to apply basic syntax in JavaScript, utilize data structures, and implement DFS/BFS algorithms. It is important to practice such problems while preparing for coding tests to enhance algorithmic thinking.

Problem Description

Write a function that calculates the average of an array of given numbers.
The average is the sum of all numbers divided by the count of numbers.
If the array is empty, appropriate exception handling should return a suitable message.

Problem Example

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

        Input: []
        Output: "The array is empty."
    

Algorithm Approach

To solve this problem, we follow these steps:

1. Check if the input array is empty.
2. Iterate through each element of the array and calculate the sum.
3. Determine the length of the array to calculate the average.
4. Return the final calculated average value.

JavaScript Code Implementation

Now let’s implement each step in JavaScript.

function calculateAverage(numbers) {
    // Check if the input array is empty
    if (numbers.length === 0) {
        return "The array is empty.";
    }
    
    // Variable to store the sum
    let sum = 0;
    
    // Iterate through each element of the array and calculate the sum
    for (let i = 0; i < numbers.length; i++) {
        sum += numbers[i];
    }
    
    // Calculate the average
    const average = sum / numbers.length;
    
    // Return the average
    return average;
}

// Example test
console.log(calculateAverage([1, 2, 3, 4, 5])); // Output: 3
console.log(calculateAverage([])); // Output: "The array is empty."
    

Detailed Explanation of the Problem Solving Process

Step 1: Check the Input Array

In the first step, we check if the given array is empty.
If the length of the array is 0, the function immediately returns the string "The array is empty."
This is exception handling for cases where the user has incorrectly specified the input array.

Step 2: Calculate the Sum

If the array is not empty, we proceed to the next step to calculate the sum.
Here, we initialize a variable called sum to 0 and then iterate through each element of the array,
adding its value to the sum. The length of the array can be checked with numbers.length.

Step 3: Calculate the Average

Once the summation is complete, we divide the sum by the length of the array to calculate the average value.
In this process, we can write the calculation like const average = sum / numbers.length;.
Since the average may include decimal parts, there is no need to separately adjust the number of decimal places if not required.

Step 4: Return the Result

In the final step, we return the calculated average value.
This value can be utilized by the caller to print it out using console.log or other methods.

Results and Review

Thus, the algorithm for calculating the average is implemented through exception handling that checks if the array length is 0
and a simple method of summation through iteration.

To review, the process of calculating the average involves summing all the numbers in parentheses and dividing that value
by the count of numbers.
Handling exception situations in this process is crucial in actual coding tests, so it is always important to remain vigilant.

Overcoming Challenges

Here are some points to consider while solving this problem.

• Need to check if the input array always contains numbers
• Define the messages or values to be returned consistently when handling exceptions
• Consider the method of handling if non-number elements are included

When conducting coding tests, always keep the above exception situations in mind
to reduce the likelihood of problems arising.

Conclusion

The problem of finding the average is simple, but requires careful consideration of various exception situations and conditions.
With practice, you will be able to implement algorithms more effectively.

If you have any more questions or concerns, please leave a comment!
Next time, we'll return with another algorithm problem.

Problem Definition

Write a function that meets the following conditions:

Given an integer array, write a function that returns the indices of the two numbers that add up to a specific target value. Assume that there is always a solution, and you may not use the same element twice.

function twoSum(nums, target) {
    // Write your code here.
}

Input Example

Input:

twoSum([2, 7, 11, 15], 9)

Output Example

Output:

0, 1

Solution Process

To solve this problem, we can use two approaches. The first is to use a double loop, and the second is to use a hash map. Considering efficiency, we will choose to use a hash map.

1. Problem Analysis

What we need to do is look at each element of the array and find the value that, when subtracted from the target, gives us that element. When we find this value, we can return the index of that element.

2. Using Hash Map

As a first step, we create an empty hash map (object). We traverse the array, adding each element to the hash map and also storing its index. Then, with each iteration, we check if the value that equals the target minus the current element exists in the hash map. If it does, we return that index.

function twoSum(nums, target) {
    const map = new Map();
    for (let i = 0; i < nums.length; i++) {
        const complement = target - nums[i];
        if (map.has(complement)) {
            return [map.get(complement), i];
        }
        map.set(nums[i], i);
    }
}

3. Debugging Cases

After writing the code, it is important to check for parts that may cause errors. Through debugging, you can verify whether the logic for ‘finding the value equal to the target minus the current element’ works as intended. You can also use console logs to check the status of variables at each step.

function twoSum(nums, target) {
    const map = new Map();
    for (let i = 0; i < nums.length; i++) {
        const complement = target - nums[i];
        console.log(`Current Number: ${nums[i]}, Complement: ${complement}`);
        if (map.has(complement)) {
            console.log(`Found complement: ${complement} at index ${map.get(complement)}`);
            return [map.get(complement), i];
        }
        map.set(nums[i], i);
    }
}

Conclusion

By solving the problem in the above manner, you can utilize the characteristics of JavaScript and conduct debugging more easily. After writing the code, it is always a good idea to use debugging tools (such as the developer tools in the browser) to test various cases and check the status of each variable, focusing on a deeper understanding of the problem.

In this lecture, we learned about algorithm problem-solving in JavaScript and the importance of debugging. We hope that this approach will help you in your coding test preparations.

In modern software development environments, algorithms play a crucial role. Let’s take a look at topological sorting,
which is one of the problems frequently encountered in coding tests. Topological sorting is a technique for
ordering all nodes in a directed graph by considering the direction of edges. It is primarily used to
express dependencies between tasks.

Problem Description

Let’s explore a problem that receives input as follows. Given the precedence between the tasks,
the problem is to output the order in which all tasks can be completed using topological sorting.

Example Problem:
There are N tasks, and each task is identified by a number from 1 to N.
M edges are given, which define the precedence between the tasks.
Check if the given tasks can be processed through topological sorting and output that order.

Input Example:
6 6
6 5
5 4
4 3
2 5
3 1
1 2

Output Example:
6 5 4 3 1 2

Problem Solving Process

1. Understanding the Problem

First, we need to understand what topological sorting is and what is required in this problem.
Topological sorting is the process of ordering each node in a directed graph while respecting the direction of all edges.
Based on the direction of the given edges, we can define the order in which each task should precede.
A graph that allows for topological sorting must be acyclic (Directed Acyclic Graph, DAG).

2. Approach to Solve the Problem

The basic approach to solving the problem is as follows:

1. Represent the precedence between the given tasks as a graph.
2. Calculate the indegree for each task.
3. Add tasks with an indegree of 0 to a queue.
4. Process tasks one by one from the queue and decrease the indegree of tasks connected to it.
   Tasks that become 0 indegree are added back to the queue.
5. Repeat until all tasks are processed.
6. Output the result of the topological sorting.

3. Implementation in JavaScript

Now, let’s implement the JavaScript code according to the above steps.
The code below performs topological sorting based on the given input.

        
        function topologicalSort(N, edges) {
            const graph = {};
            const indegree = new Array(N + 1).fill(0);
            const result = [];

            // Create graph and initialize indegree
            edges.forEach(([u, v]) => {
                if (!graph[u]) graph[u] = [];
                graph[u].push(v);
                indegree[v]++;
            });

            const queue = [];
            
            // Add tasks with indegree of 0
            for (let i = 1; i <= N; i++) {
                if (indegree[i] === 0) {
                    queue.push(i);
                }
            }

            while (queue.length > 0) {
                const node = queue.shift();
                result.push(node);
                
                // Decrease indegree of connected nodes
                if (graph[node]) {
                    graph[node].forEach(neighbor => {
                        indegree[neighbor]--;
                        if (indegree[neighbor] === 0) {
                            queue.push(neighbor);
                        }
                    });
                }
            }

            // Check if topological sorting was possible.
            if (result.length !== N) {
                return "A cycle exists.";
            }

            return result;
        }

        // Input Example
        const N = 6;
        const edges = [
            [6, 5],
            [5, 4],
            [4, 3],
            [2, 5],
            [3, 1],
            [1, 2],
        ];
        console.log(topologicalSort(N, edges));
        
    

4. Code Explanation

I will now explain how to implement topological sorting through the above code.

• Graph Construction:
  The graph is created in the form of an adjacency list based on the given list of edges.
  The indegree of each node is recorded, indicating how many edges depend on that node.
• Finding Nodes with Indegree of 0:
  Check all nodes and add those with an indegree of 0 to the queue.
• Processing via BFS:
  Process nodes one by one from the queue and reduce the indegree of connected nodes.
  If a node’s indegree becomes 0, add it to the queue.
• Check the Length of the Result:
  If all tasks are processed, the length of the result array should be the same as the number of nodes,
  indicating that topological sorting has been successfully performed.

5. Conclusion and Lessons Learned

Topological sorting is very useful when tasks need to be performed in a specific order based on dependencies.
Through this tutorial, we learned the fundamental idea of topological sorting and how to implement it in JavaScript.
Having opportunities to utilize various data structures and algorithms is essential for successful performance in coding tests.

Since there are many scenarios in real problems that require topological sorting,
it is important to understand the characteristics of each problem and solve it using the appropriate data structures and algorithms.
Keep practicing various problems to improve your skills!