JavaScript Coding Test Course, Understanding Time Complexity Notation

JavaScript is one of the most commonly used languages in web development and often appears in coding tests. In this article, we will cover algorithm problems that can be solved with JavaScript and learn more about time complexity notation. Through the process of solving algorithm problems, let’s understand the importance of time complexity and build a foundation for writing efficient code.

Problem Description

Given an integer array nums and an integer target, write a function that returns the indices of the two numbers that add up to target. It is assumed that there is exactly one solution for each input, and you may not use the same element twice.

For example:

  • Input: nums = [2, 7, 11, 15], target = 9
  • Output: [0, 1] (nums[0] + nums[1] = 2 + 7 = 9)

Solution Explanation

There are several ways to solve this problem, but the method using a hashmap is the most efficient. Using a hashmap allows for quick lookup of numbers and finding their indices. This problem can be solved in the following steps:

  1. Create a hashmap.
  2. Traverse the array and store each number in the hashmap.
  3. For each number, look for the value obtained by subtracting the current number from target in the hashmap.
  4. Return the index of the found value.

JavaScript Implementation


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);
    }
}

Time Complexity Analysis

Let’s analyze the time complexity of this algorithm:

  • The array is traversed once, so the time complexity is O(n).
  • Searching and inserting into the hashmap is O(1) on average.

Therefore, the overall time complexity is O(n). This is a very efficient algorithm that performs well compared to other methods.

Conclusion

In this article, we implemented an efficient algorithm using a hashmap through the problem of the sum of two numbers. Considering time complexity when solving algorithm problems is very important. While there can be multiple ways to solve a problem, choosing the optimal method is the first step to writing good code.

Understanding Time Complexity Notation

Time complexity is an important concept used to evaluate the performance of algorithms. The execution time of an algorithm varies depending on the input size, and time complexity is the numerical expression of this.

Types of Time Complexity

  • O(1): Takes a constant amount of time regardless of input size.
  • O(log n): The growth rate is slow as the input size increases. The binary search algorithm falls under this category.
  • O(n): Occurs when traversing an array or list once.
  • O(n log n): Advanced sorting algorithms such as merge sort and quicksort belong to this category.
  • O(n^2): Occurs in cases with nested loops. A typical bubble sort is an example of this.
  • O(2^n): Refers to recursive problems such as calculating the Fibonacci sequence.

The Importance of Time Complexity Analysis

Choosing efficient algorithms is crucial in software development. Understanding and optimizing time complexity is essential for improving program performance and providing a better experience for users.

Final Thoughts

In this article, we explored methods for solving algorithm problems using JavaScript and time complexity notation. In future coding tests, you will be able to solve more problems based on these algorithms and time complexities.