How to calculate Euclidean Distance? How to measure the distance between two points?
What is Euclidean Distance?
In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.wikipedia
One Dimensional
To calcualte the distance between two points in one dimensional is that substract one point from another point. For example, we have two points which are 8 and 2; by subtracting 8 from 2 equals 6. So the distance between these two points are 6. The order of the substraction doesn't matter. If we substract 3 from 8 equals -6. To get the absolute value, we can square the number (-62 , Math.pow(-6, 2)) which equals to 36. And then we square root of that number (Math.sqrt(36)) equals to 6.
/**
* Calculate the distance between two points in one dimensional space
* @param {number} a first point
* @param {number} b second point
* @return {number}
* @time complexity: O(1)
* @space complexity: O(1)
*/
function oneDimensional(a, b) {
let dist = a - b;
if (dist < 0) {
dist = Math.sqrt(Math.pow(dist, 2));
}
return dist;
// Or
// return Math.abs(a - b);
};
Two Dimensional
This is the Euclidean Distance formula for two dimensional.
Subtract the x coordinate of the second point from the x coordinate of the first point, and then square that number. Do the same for y coordinates. After that square root the sum of those two number.
For example, we have two points (2, 4) and (-3, 8). First, substract -3 from 2 (-3 - 2) equals -5, and then square -5 equals 25. Second, substract 8 from 4 (8 - 4) equals 4, and then square 4 equals 16. Finally, square root the sum of 25 and 16 (25 + 16), equals 6.403.
/**
* Calculate the distance between two points in two dimensional space
* @param {number[]} a first point, Ex. [2, 4]
* @param {number[]} b second point, Ex. [-3, 8]
* @return {number}
* @time complexity: O(1)
* @space complexity: O(1)
*/
function twoDimensional(a, b) {
return Math.sqrt(Math.pow(b[0] - a[0], 2) + Math.pow(b[1] - a[1], 2));
}
Three Dimensional
To calculate the Euclidean Distance in three dimensional is similar to two dimensional. The formula as following.
