Z-Normalized Shape Distance

Problem

Compute the Euclidean distance between two series after z-normalizing each: subtract the mean and divide by the population standard deviation (a constant series becomes all zeros).

Return None if the series have different lengths or are empty.

Hint

Z-normalization removes level and scale, leaving only shape.

Test cases

case 1

in: [[1,2,3],[2,4,6]]

expected: 0

case 2

in: [[1,2,3,4],[1,4,9,16]]

expected: 0.35356426632003163

case 3

in: [[1,1,1],[1,2,3]]

expected: 1.7320508075688772

case 4

in: [[1,2,3],[3,2,1]]

expected: 3.4641016151377544

Starter codePython

def z_normalized_distance(x, y):
    # Your code here
    pass

4 test cases · run your code against them in the editor