Leetcode Problem 1515. Best Position for a Service Centre

1515. Best Position for a Service Centre

Leetcode Solutions

Simulated Annealing Approach

  1. Initialize the center point (x, y) with the centroid of the given positions.
  2. Set an initial step size, for example, 50, since the positions are within a 100x100 grid.
  3. Calculate the total distance from the current center to all positions.
  4. Iteratively adjust the center point by moving in the direction that decreases the total distance, using the step size for the magnitude of the move.
  5. If no improvement is found in all directions, reduce the step size (e.g., divide by 2).
  6. Repeat steps 3-5 until the step size is smaller than a predefined threshold (e.g., 1e-6).
  7. Return the minimum total distance found.
UML Thumbnail

Gradient Descent Approach

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