Find number runs with customizable distance between numbers

Question

I have a sorted list of integers and I find want find to the number runs in this list. I have seen many examples when looking for numbers runs that increment by 1, but I also want to look for number runs where the difference between numbers is customizable.

For example, say I have the following list of numbers:

nums = [1, 2, 3, 6, 7, 8, 10, 12, 14, 18, 25, 28, 31, 39]

Using the example found here, I'm able to find the following number runs:

[[1, 2, 3], [6, 7, 8], [10], [12], [14], [18], [25], [28], [31], [39]]

However, I want to look for number runs where the difference between two numbers could be more than just 1. For example, I want all number runs with a distance of less than or equal to 2.

[[1, 2, 3], [6, 7, 8, 10, 12, 14], [18], [25], [28], [31], [39]] 

Or maybe I want all number runs with a distance of less than or equal to 3.

[[1, 2, 3, 6, 7, 8, 10, 12, 14], [18], [25, 28, 31], [39]]

Here is the function that I'm working with now to get number runs with a distance of 1.

def runs(seq, n):
    result = []
    for s in seq:
        if not result or s != result[-1][-1] + n:
            # Start a new run if we can't continue the previous one.
            result.append([])
        result[-1].append(s)
    return result

With the current function, if I set n=1, then I find all consecutive number sequences. If I set n=2, then I only find [8, 10, 12, 14]. How can I modify this function to find number runs that are less than or equal to n?

I want to be able to do this:

runs(num, 2)
[[1, 2, 3], [6, 7, 8, 10, 12, 14], [18], [25], [28], [31], [39]] 

Answer 1

Iterative grouping with for

I'm just fixing your code with this one. To simplify things, you can initialise result with seq[0].

def runs(seq, n):
    result = [[seq[0]]]
    for s in seq[1:]:
        if s - result[-1][-1] > n:  # Keep it simple. Compare the delta.
            result.append([])
        result[-1].append(s)

    return result

>>> runs(nums, 1)
[[1, 2, 3], [6, 7, 8], [10], [12], [14], [18], [25], [28], [31], [39]]
>>> runs(nums, 2)
[[1, 2, 3], [6, 7, 8, 10, 12, 14], [18], [25], [28], [31], [39]]

---

pandas.GroupBy

If you want to get fancy, you can use the groupby idiom, made easy with pandas.

import pandas as pd

def runs2(seq, n):
    s = pd.Series(seq)
    return s.groupby(s.diff().gt(n).cumsum()).apply(pd.Series.tolist).tolist()

>>> runs2(nums, 3)
[[1, 2, 3, 6, 7, 8, 10, 12, 14], [18], [25, 28, 31], [39]]

There are two essential ingredients here: the grouper (the predicate you're grouping on), and the agg function (the function you'll apply on each group)

The grouper is s.diff().gt(n).cumsum(), broken down calculates three things:

1. The element-wise difference in seq using diff
2. A boolean mask indicating whether the diff is greater than n
3. Performing a cumulative sum (or count) to determine the groups

The output of this operation is

s.diff().gt(n).cumsum()

0     0
1     0
2     0
3     1
4     1
5     1
6     1
7     1
8     1
9     2
10    3
11    4
12    5
13    6
dtype: int64

The agg function is pd.Series.tolist, and will convert any series to a list. That's what we need here, a nested list.