Javascript Coding Test Course, Arrays and Lists

Problem Description

You are required to return a new array that represents the differences of each element from an input array consisting of integers. The i-th element of the new array corresponds to the difference between the i-th element and the next element of the input array. The last element requires special handling since there is no subsequent element.

Input

• Integer array nums (size n, 1 ≤ n ≤ 1000, -1000 ≤ nums[i] ≤ 1000)

Output

• Integer array diff representing the differences (size n-1)

Example

                
                Input: [3, 7, 1, 8, -4]
                Output: [4, -6, 7, -12]
                
            

Solution Process

To solve this problem, the following steps are followed:

1. Problem Analysis: The goal is to calculate the differences of each element. It can be simplified by only dealing with the differences between adjacent elements.
2. Input Verification: The input array should not be empty and must contain at least two elements.
3. New Array Initialization: Declare a new array to store the differences. The size of this array is one less than the size of the input array.
4. Difference Calculation Using a Loop: Traverse the array and calculate the differences between the current element and the next element.
5. Return Result: Return the calculated array to solve the problem.

Implementation Code

                
                function calculateDifferences(nums) {
                    if (nums.length < 2) {
                        throw new Error("The input array must contain at least two elements.");
                    }
                    const diff = [];
                    for (let i = 0; i < nums.length - 1; i++) {
                        diff.push(nums[i + 1] - nums[i]);
                    }
                    return diff;
                }

                // Example execution
                const input = [3, 7, 1, 8, -4];
                const output = calculateDifferences(input);
                console.log(output); // [4, -6, 7, -12]
                
            

Code Explanation

The code above works in the following way:

• The function calculateDifferences takes an integer array nums as a parameter.
• First, it throws an error if the length of the array is less than 2.
• An empty array diff is declared to prepare for storing the results.
• A for loop is used to calculate the differences of each element and add it to the diff array.
• Finally, the calculated diff array is returned.

Complexity Analysis

The time complexity of this algorithm is O(n) because it traverses the array once. The space complexity is also O(n) as it uses extra space to store the new array.

Additional Problems

Variations of this basic problem can be proposed as follows:

1. How can we handle the case when the input array is empty?
2. What considerations should be made when calculating differences in an array with mixed positive and negative numbers?
3. What issues might arise when the elements of the array are very large (e.g., above 10^9) during the calculation of differences?

Conclusion

This concludes the solution to a basic algorithm problem using arrays and lists in JavaScript. Although it was a simple problem of calculating differences between arrays, tackling such problems can enhance your ability to work with arrays. In the next lecture, we will cover more complex data structures and algorithms. If you have any questions, please leave a comment!