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893416. Minimum Distance between Two Points

Minimum Distance between Two Points

Summary

Given two points (x1, y1) and (x2, y2), find the minimum distance between them. This problem can be approached by using the Euclidean distance formula.

Detailed Explanation

The minimum distance between two points in a 2D space is calculated using the Euclidean distance formula, which is given as:

√((x2 - x1)^2 + (y2 - y1)^2)

To find this distance, we first calculate the differences in x and y coordinates. Then, we square these differences and add them together. Finally, we take the square root of the sum to get the Euclidean distance.

Here is a step-by-step breakdown:

  1. Calculate the difference in x-coordinates: dx = x2 - x1
  2. Calculate the difference in y-coordinates: dy = y2 - y1
  3. Square these differences: dx^2 = dx * dx and dy^2 = dy * dy
  4. Add the squares of the differences: distance_squared = dx^2 + dy^2
  5. Calculate the square root of the sum: distance = √distance_squared

The time complexity for this solution is O(1), as we are only performing a few constant operations. The space complexity is also O(1), as we are not using any extra space that scales with the input size.

Optimized Solutions

Java

View GeeksforGeeks Problem
public class Main {
    public static void main(String[] args) {
        double x1 = 1;
        double y1 = 2;
        double x2 = 4;
        double y2 = 6;

        double dx = x2 - x1;
        double dy = y2 - y1;
        double distanceSquared = Math.pow(dx, 2) + Math.pow(dy, 2);
        double distance = Math.sqrt(distanceSquared);

        System.out.println("The minimum distance is: " + distance);
    }
}

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