LeetCode 1515: Best Position for a Service Centre Solution

Master LeetCode problem 1515 (Best Position for a Service Centre), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1515. Best Position for a Service Centre

Hard

Array Math Geometry Randomized

Problem Explanation

Explanation:

To solve this problem, we can use gradient descent optimization. We will start with an initial guess for the center position and iteratively update it to minimize the sum of distances to all customers. At each iteration, we will calculate the partial derivatives of the total distance with respect to the x and y coordinates of the center and adjust the center position accordingly.

Initialize the center position randomly.
Iterate until convergence:
- Calculate the gradient of the total distance with respect to x and y.
- Update the center position based on the gradient and a learning rate.
- Repeat the above steps until the center position converges.

Time Complexity: O(n) where n is the number of customers
Space Complexity: O(1)

Solution Code

class Solution {
    public double getMinDistSum(int[][] positions) {
        double learningRate = 1e-7;
        double eps = 1e-8;
        double[] center = {50, 50}; // Initial guess for center position
        while (true) {
            double[] gradient = {0, 0};
            double totalDist = 0;
            double denominator = 0;
            for (int[] pos : positions) {
                double dist = Math.sqrt(Math.pow(center[0] - pos[0], 2) + Math.pow(center[1] - pos[1], 2));
                gradient[0] += (center[0] - pos[0]) / dist;
                gradient[1] += (center[1] - pos[1]) / dist;
                totalDist += dist;
                denominator += 1 / dist;
            }
            if (Math.max(Math.abs(gradient[0]), Math.abs(gradient[1])) < eps) {
                break;
            }
            center[0] -= learningRate * gradient[0] / denominator;
            center[1] -= learningRate * gradient[1] / denominator;
        }
        return totalDist;
    }
}

Try It Yourself

Loading code editor...

Frequently Asked Questions

How to solve LeetCode 1515 (Best Position for a Service Centre)?

This page provides optimized solutions for LeetCode problem 1515 (Best Position for a Service Centre) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 1515 (Best Position for a Service Centre)?

The time complexity for LeetCode 1515 (Best Position for a Service Centre) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 1515 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 1515 in Java, C++, or Python.

Back to LeetCode Solutions