Euclidean Distance

Definition

Definition

The Euclidean Distance Algorithm is a mathematical method used to calculate the distance between two points in Euclidean space

Explanation

The Euclidean Distance Algorithm computes the straight-line distance between two points in a multi-dimensional space. It utilizes the Pythagorean theorem, treating each dimension as a separate axis. By finding the square root of the sum of the squared differences between corresponding coordinates, the algorithm determines the distance

Guidance

• Identify the Dimensionality
  • determine the number of dimensions (features) in your space. Each dimension corresponds to a specific attribute or variable
• Retrieve the Coordinates
  • obtain the coordinates of the two points for which you want to calculate the distance. These coordinates represent the values of each dimension for each point
• Calculate the Squared Differences
  • for each dimension, subtract the corresponding coordinates of the two points and square the result. Repeat this process for all dimensions
• Sum the Squared Differences
  • add up all the squared differences obtained in the previous step. This yields the sum of squared differences
• Take the Square Root
  • compute the square root of the sum obtained in previous step. This is the Euclidean distance between the two points

Tips

• ensure consistency in dimensionality between the points being compared
• utilize vectorized operations for efficient computation, especially when dealing with large datasets
• normalize the data if the scales of different dimensions vary significantly

Practice

Practice

euclidean_distance(point1, point2):
  sum_of_squared_differences = 0
  for each dimension d in point1 and point2:
    difference = point1[d] - point2[d]
    squared_difference = difference * difference
    sum_of_squared_differences += squared_difference
  distance = square_root(sum_of_squared_differences)
  return distance

Solution

package main

import (
    "math"
)

func euclideanDistance(x1, y1, x2, y2 float64) float64 {
    return math.Sqrt(math.Pow(x2-x1, 2) + math.Pow(y2-y1, 2))
}

import java.lang.Math;

public class Main {

  public static double euclideanDistance(double x1, double y1, double x2, double y2) {
    return Math.sqrt(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2));
  }
}

function euclideanDistance(x1, y1, x2, y2) {
  return Math.sqrt(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2));
}

import kotlin.math.pow
import kotlin.math.sqrt

fun euclideanDistance(x1: Double, y1: Double, x2: Double, y2: Double): Double {
    return sqrt((x2 - x1).pow(2) + (y2 - y1).pow(2))
}

import math

def euclidean_distance(x1, y1, x2, y2):
    return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)

fn euclidean_distance(x1: f64, y1: f64, x2: f64, y2: f64) -> f64 {
    ((x2 - x1).powi(2) + (y2 - y1).powi(2)).sqrt()
}

function euclideanDistance(
  x1: number,
  y1: number,
  x2: number,
  y2: number,
): number {
  return Math.sqrt(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2));
}