Use itertools.groupby() to split a series of numbers into sub-itervals based on distance to the first element.

groupby_distance.py

#! /usr/bin/env python3

"""Use itertools.groupby() to split a series of numbers into sub-itervals.
For each interval, all its elements satisfy (x_{i} - x_{0}) < WINDOW.

Keys to this approach:
- We need a global variable to keep track of the current x_{0}.
- The key value of each element is x_{0} (so that all the elements fall into the same group).
"""

import itertools

_X0 = None
_WINDOW = 10

numbers = [1, 2, 4, 5, 15, 14, 18, 19, 20, 21, 23, 34, 38, 45]

def check_window(x):
    global _X0
    if _X0 is None:
        _X0 = x
    if abs(_X0 - x) >= _WINDOW:
        _X0 = x
    return _X0


for _, g in itertools.groupby(numbers, key=check_window):
    print(list(g))

"""
Mandatory improvement: use a callable class to keep state, instead of global variables.
"""

class WindowChecker:

    def __init__(self, window):
        self.window = window
        self.x0 = None

    def __call__(self, x):
        if self.x0 is None:
            self.x0 = x
        if abs(self.x0 - x) >= self.window:
            self.x0 = x
        return self.x0


for _, g in itertools.groupby(numbers, key=WindowChecker(window=10)):
    print(list(g))