Author: root

Hello! In this blog post, we will discuss the Making Maximum Value by Pairing Numbers problem that can be presented in coding tests with JavaScript. This problem requires various algorithmic thinking and provides an opportunity to deepen understanding of optimization problems. The goal is to combine the given numbers to create the largest possible number.

Problem Definition

You need to repeatedly combine two given numbers and multiply them to create the maximum value. The detailed problem definition is as follows:

Problem: Given an array of N natural numbers, write a program that pairs all the numbers two by two to maximize the sum of their products.

Input:
- The first line contains a natural number N (1 ≤ N ≤ 1000).
- The second line contains N natural numbers a1, a2, ..., aN (1 ≤ ai ≤ 1000).

Output:
- Print the maximum value.

Example of the Problem

Input:
5
1 2 3 4 5

Output:
43

Approach to the Problem

To solve this problem, several key steps are needed.

• Sorting: Sort the given numbers in descending order. This is a preparatory step to keep the largest number and create a large multiplication result.
• Pairing: Pair and multiply the numbers two by two from the array, and accumulate all the results. When pairing, pair the two largest numbers first and then proceed with the next two largest numbers.
• Exception Handling: If an odd number of numbers are inputted, the remaining last number must be handled separately and included in the result.

Implementation

Let’s write the code to solve this problem with JavaScript. Below is the implemented code.

function maxSumFromPairs(numbers) {
    // Sort the array in descending order
    numbers.sort((a, b) => b - a);
    
    let maxSum = 0;

    // Pair two and multiply, then sum
    for (let i = 0; i < numbers.length; i += 2) {
        // If the last element is odd, add the remaining element alone
        if (i === numbers.length - 1) {
            maxSum += numbers[i];
        } else {
            maxSum += numbers[i] * numbers[i + 1];
        }
    }
    return maxSum;
}

// Example usage
const numbers = [1, 2, 3, 4, 5];
console.log(maxSumFromPairs(numbers)); // 43

Code Analysis

Let’s analyze each part of the code.

1. Sorting

First, we sort the array in descending order. This allows larger numbers to come first, and we calculate the product based on this. Sorting the array in JavaScript can be easily accomplished using the sort method.

2. Pairing and Summing

Through a loop, we read the elements of the array two by two and accumulate their product in maxSum. If the length of the array is odd, the last remaining element is simply added as it is.

3. Returning the Result

Finally, we return maxSum. The code is simple, but it allows us to efficiently obtain the maximum value.

Complexity Analysis

The time complexity of this algorithm is O(N log N). This is due to the time required to sort the array. The subsequent loop operates at O(N), making the overall operations linear, excluding sorting. The space complexity is O(1), as no additional space is used, making it memory efficient.

Test Cases

Let’s add a few test cases to verify the accuracy of the code.

console.log(maxSumFromPairs([3, 5, 1, 2, 4])); // 47
console.log(maxSumFromPairs([1])); // 1
console.log(maxSumFromPairs([9, 7, 5, 3])); // 64
console.log(maxSumFromPairs([1, 1, 1, 1, 1])); // 5

Conclusion

In this article, we discussed the problem of making maximum value by pairing numbers. We implemented the algorithm by sorting the array and calculating the maximum value. I hope this has been a valuable experience in considering how to efficiently handle immediate processing of arrays.

In coding tests using JavaScript, such optimization problems are often presented, so consistent practice is required. Additionally, I encourage you to challenge yourself with various problems to develop your algorithmic thinking!

Problem Description

Write a program to sort N given numbers in non-decreasing order. Non-decreasing order means that in the sorted sequence, a number can be equal to or greater than the preceding number.

Input

The first line contains the number of integers N (1 ≤ N ≤ 1,000,000). From the second line, N lines follow, each containing one integer. Each integer is a whole number and its absolute value does not exceed 1,000,000.

Output

Print the sorted numbers in ascending order, one per line, starting from the first line.

Problem Solving Process

Step 1: Problem Analysis

To understand the given problem, we need to clarify the structure of the input data and the required output.
– Input: Number N and the next N integers
– Output: The N integers sorted in non-decreasing order

The key to the problem is using an efficient sorting algorithm.
Since the size of the array can be up to 1,000,000, we cannot use common O(N^2) algorithms (like bubble sort, selection sort, etc.).
Therefore, we need to use sorting algorithms with a complexity of O(N log N), such as quicksort or mergesort.

Step 2: Algorithm Selection

We can use the built-in method of JavaScript Array.prototype.sort(), but since we need to guarantee the stability of the sort, we will implement quicksort or mergesort.

Step 3: Implementation

I will solve the problem using the Merge Sort algorithm.
Merge Sort works by dividing the list in half, recursively sorting each part, and then merging the two sorted parts.

Execution Process of Merge Sort

• Divide the array into two subarrays by splitting it in half.
• Recursively sort each subarray.
• Combine the two sorted subarrays to create one sorted array.

Implementation of Merge Sort

function mergeSort(arr) {
    if (arr.length <= 1) {
        return arr;
    }

    const mid = Math.floor(arr.length / 2);
    const left = mergeSort(arr.slice(0, mid));
    const right = mergeSort(arr.slice(mid));

    return merge(left, right);
}

function merge(left, right) {
    const result = [];
    let i = 0; 
    let j = 0;

    while (i < left.length && j < right.length) {
        if (left[i] < right[j]) {
            result.push(left[i]);
            i++;
        } else {
            result.push(right[j]);
            j++;
        }
    }

    return result.concat(left.slice(i)).concat(right.slice(j));
}
    

Step 4: Input and Output Processing

Now, I will write a function that takes input, sorts it using merge sort, and then outputs the results.
I will read the nodes, convert them to an array, and then call the merge sort function.

const fs = require('fs');

// Read input from the file.
let input = fs.readFileSync('/dev/stdin').toString().trim().split('\n').map(Number);
const n = input.shift(); // Remove the first line which indicates the number of integers.

const sortedArray = mergeSort(input);

console.log(sortedArray.join('\\n')); // Print the sorted result with line breaks.
    

Step 5: Testing and Result Verification

I have tested the implemented code using the sample input.
Using the following input:

5
5
2
3
1
4
    

The expected output is as follows.

1
2
3
4
5
    

Conclusion

Through this problem, I learned about the importance of sorting algorithms in JavaScript and how to implement Merge Sort.
Since this is a common topic in practical interviews and coding tests, it is important to practice and implement various cases.
Understanding the theory of algorithms, along with writing code to get hands-on experience, is a crucial method for improving skills.

Coding tests are an important means of validating programming skills, and companies use them to assess the candidate’s algorithmic thinking and problem-solving abilities. In this course, we will closely examine the process of solving the DNA Password problem using JavaScript.

Problem Description

The DNA Password problem is as follows:

Problem: Given a DNA string of length N, find the number of all possible substrings from the DNA string that can be a password. The conditions for a password are that it must contain exactly 1 or 2 of the characters ‘A’, ‘C’, ‘G’, ‘T’, and must contain at least 1.

Example Input and Output

Input: "ACGTACGTA"
Output: 16

Problem Solving Process

To solve this problem, we will follow these steps:

Step 1: Problem Analysis

We need to find all substrings from the given DNA string that satisfy the password conditions. A password must contain either 1 or 2 of the characters ‘A’, ‘C’, ‘G’, ‘T’. Therefore, we need to consider cases for substrings that include each character.

Step 2: Generate Substrings

To generate all substrings of the DNA string, we can use two pointers to define the startIndex and endIndex. This process generates O(N^2) cases.

Step 3: Check Password Conditions

For each substring, we need to check the counts of ‘A’, ‘C’, ‘G’, ‘T’. We can use regular expressions or a counting array for this.

Step 4: Implement Code

Now, let’s implement the JavaScript code to solve the problem:

function countDNAPasswords(dna) {
    const n = dna.length;
    let count = 0;

    // Generate all substrings
    for (let start = 0; start < n; start++) {
        const charCount = { 'A': 0, 'C': 0, 'G': 0, 'T': 0 };
        
        for (let end = start; end < n; end++) {
            // Current character count
            const char = dna[end];
            if (charCount[char] !== undefined) {
                charCount[char]++;
            }

            // Check password conditions
            const uniqueCount = Object.values(charCount).filter(x => x > 0).length;
            if (uniqueCount >= 1 && uniqueCount <= 2) {
                count++;
            }
        }
    }

    return count;
}

// Example usage
const dnaString = "ACGTACGTA";
console.log(countDNAPasswords(dnaString)); // Output: 16

Code Explanation

The main functions of the code written above are as follows:

• The countDNAPasswords function takes the DNA string as input and calculates the number of passwords.
• Two nested for loops are used to generate all substrings.
• For each substring, the charCount object is used to count the occurrences of ‘A’, ‘C’, ‘G’, ‘T’, and check the password conditions.
• It counts the cases that meet the conditions.

Time Complexity Analysis

The time complexity of this algorithm is O(N^2). It generates all substrings using two nested loops. However, this method may lead to performance issues as the length of the string increases. Therefore, it is worth considering optimized methods or applying other algorithms.

Conclusion

In this course, we learned how to solve the DNA Password problem using JavaScript. We started from an algorithmic problem, implemented the code, and examined the process of deriving results in detail. Such problems frequently appear in coding tests, so consistent practice is necessary.

Through this practice, you can repeatedly improve your problem-solving skills, so it is recommended to tackle various problems. Thank you!

Hello! In this post, we will learn how to solve algorithm problems using JavaScript. The topic is ‘Insertion Sort’. All algorithms are means to solve specific problems, and insertion sort is one of the most fundamental and important sorting algorithms. Through this article, we will understand the concept of insertion sort and explore in detail how to implement it in JavaScript.

1. What is Insertion Sort?

Insertion sort is a very efficient sorting algorithm when the data is nearly sorted. This algorithm basically divides the list into two parts and builds a sorted list by inserting new elements into their appropriate positions. It has a methodology of comparing each element one by one and inserting it into its rightful place.

1.1. How Insertion Sort Works

The basic process of insertion sort works as follows:

1. Compare the first two elements.
2. If the first element is greater than the second element, swap their positions.
3. Select the next element and appropriately insert it into the sorted list. Repeat this process until all elements are sorted.

2. Time Complexity of Insertion Sort

The average time complexity of insertion sort is O(n²). Even in the worst case, it remains O(n²), and it only shows O(n) performance in the best case. However, the best case occurs when the data is already sorted. For this reason, insertion sort is very efficient for cases with a small number of elements or nearly sorted data.

3. Problem Definition

3.1. Problem Statement

Given an integer array like the following, write a function to sort the array in ascending order using insertion sort.

Input: [5, 2, 9, 1, 5, 6]
Output: [1, 2, 5, 5, 6, 9]
    

4. Algorithm Implementation

Now let’s actually implement insertion sort in JavaScript. The code is simple and is as follows:

function insertionSort(arr) {
    for (let i = 1; i < arr.length; i++) {
        let key = arr[i];
        let j = i - 1;

        // Compare the current key with the sorted part to find position
        while (j >= 0 && arr[j] > key) {
            arr[j + 1] = arr[j];  // Move position
            j--;
        }
        arr[j + 1] = key;  // Insert position
    }
    return arr;
}

// Test
const input = [5, 2, 9, 1, 5, 6];
console.log(insertionSort(input));  // [1, 2, 5, 5, 6, 9]
    

4.1. Code Explanation

The above code is structured as follows:

• for loop: Starts from the second element of the array (index 1) and iterates to the last element of the array.
• key variable: This is the element that is currently used as a reference. This value will be inserted into the sorted array.
• while loop: Compares the current element (key) with the sorted part (left) to find its position. Moves larger elements to the right.
• Inserts each element into its appropriate position and ultimately returns the sorted array.

5. Performance Analysis

The performance of insertion sort depends on the composition of the input data, but it generally has an average speed of O(n²) for an array of length n. It is very simple, but it does not perform well on large datasets, so it is common to use it alongside other sorting algorithms in practical applications.

6. Advantages and Disadvantages of Insertion Sort

6.1. Advantages

• It can be easily implemented.
• It is very fast when the data is nearly sorted.
• It uses little memory and does not require additional space.
• It is a stable sorting algorithm.

6.2. Disadvantages

• It is inefficient for large datasets.
• With a time complexity of O(n²), it performs poorly in the worst case.

7. Conclusion

In this post, we learned about insertion sort. It is a simple sorting algorithm, but understanding and utilizing its structure and working mechanism is very useful. In particular, it is a fundamental algorithm you must know when writing advanced algorithms in JavaScript. In the next tutorial, we will compare it with other sorting algorithms to further expand your understanding of algorithms!

8. References

• Wikipedia – Insertion Sort
• MDN – JavaScript Guide