1979. Find Greatest Common Divisor of Array

 

Finding the Greatest Common Divisor (GCD) in JavaScript

When working with arrays of numbers, it's sometimes necessary to find the Greatest Common Divisor (GCD). The GCD of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. This concept is crucial in many areas, such as simplifying fractions, cryptography, and various algorithmic problems.

In this blog post, we will explore a practical approach to finding the GCD of an array of numbers using JavaScript. We'll walk through the intuition, the approach, and the implementation, ending with a discussion on the complexity of the solution.

Intuition

The GCD of a set of numbers is a measure of the common factors shared among those numbers. To find the GCD of an array, one efficient approach is to consider only the maximum and minimum values of the array. This works because the GCD of the entire array is a divisor of the GCD of its maximum and minimum values.

Approach

  1. Identify Maximum and Minimum Values: First, find the maximum and minimum values in the array. These values will be used to compute the GCD.

  2. Euclidean Algorithm: Use the Euclidean algorithm to compute the GCD. This algorithm is efficient and works by repeatedly replacing the pair of numbers with their remainder until one of them becomes zero.

  3. Return GCD: Compute and return the GCD of the maximum and minimum values.

Implementation

Here's the complete implementation in JavaScript:

javascript
/**
 * @param {number[]} nums
 * @return {number}
 */

var findGCD = function(nums) {
    let result = 1;
    let max = Math.max(...nums);
    let min = Math.min(...nums);
    if(max % min === 0) {
        result = min;
    }else {
        for(let i = 2; i < min ; i++) {
            if(max % i === 0 && min % i === 0) {
                result = i;
            }
        }
    }
    return result;
};

Complexity

  • Time Complexity: Finding the maximum and minimum values in the array takes O(n) time. The Euclidean algorithm for computing the GCD has a time complexity of O(log(min(a, b))). Therefore, the overall time complexity is O(n + log(min(a, b))).

  • Space Complexity: The space complexity is O(1) since the algorithm uses only a constant amount of extra space.

Conclusion

Finding the GCD of an array of numbers is a common problem in many mathematical and algorithmic contexts. By leveraging the properties of the GCD and using the efficient Euclidean algorithm, we can quickly and accurately compute the GCD in JavaScript. This method ensures that the solution is both optimal and easy to understand.

Check out my detailed solution on LeetCode here: Find Greatest Common Divisor of Array - LeetCode

We hope this guide helps you understand how to find the GCD of an array of numbers using JavaScript. Happy coding! šŸš€

If you have any questions or need further clarification, feel free to ask in the comments below! šŸ˜Š

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