Evaluating bounds using Manhattan and Euclidean distances

less than 1 minute read

The maximum and minimum bounds of Euclidean and Manhattan distances between n, d-dimensional arrays were calculated.

1. Data generation

Generate n, d-dimensional arrays using the following pseudo-code:

initialize empty array
for i in range(n):
  append into array(d-dimensional random array)

2. Euclidean distance

Computed the minimum and maximum Euclidean distance between points using the formula:

$Euclidean=\sqrt{d_{i}^{2}-d_{j}^{2}}$

3. Manhattan distance

Computed the minimum and maximum Manhattan distance between points using the formula:

$Manhattan=|d_{i}-d_{j}|$

Check out the code here.

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