Javascript Coding Test Course, Combine Numbers to Maximize Value

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!