# 5 Best Ways to Find Non-Intersecting Intervals Relative to a Cut Interval in Python

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π‘ Problem Formulation: You need to compute a list of intervals that do not overlap with a specified ‘cut’ interval. For example, given a list of intervals such as [(1, 4), (5, 7), (8, 10)], and a cut interval (3, 6), the desired output would be [(8, 10)], because the other intervals intersect with the cut interval.

## Method 1: Iterate and Compare

This method involves iterating through a list of intervals and comparing each with the cut interval to detect intersections. The function takes two arguments: a list of intervals and the cut interval, returning only those intervals that do not intersect with the cut interval.

Here’s an example:

```def non_intersecting_intervals(intervals, cut):
non_intersecting = []
for start, end in intervals:
if end = cut[1]:
non_intersecting.append((start, end))
return non_intersecting

# Example usage
intervals = [(1, 4), (5, 7), (8, 10)]
cut_interval = (3, 6)
print(non_intersecting_intervals(intervals, cut_interval))```

Output:

`[(8, 10)]`

This code snippet defines a function `non_intersecting_intervals()` that checks each interval in the list against the cut interval. If an interval does not overlap, it’s added to the result list, which is returned at the end.

## Method 2: List Comprehension

List comprehension in Python provides a concise way to create lists. This method uses a single line of code within a function to filter all intervals that do not intersect with the cut interval.

Here’s an example:

```def non_intersecting_intervals_lc(intervals, cut):
return [(start, end) for start, end in intervals if end = cut[1]]

# Example usage
intervals = [(1, 4), (5, 7), (8, 10)]
cut_interval = (3, 6)
print(non_intersecting_intervals_lc(intervals, cut_interval))```

Output:

`[(8, 10)]`

The function `non_intersecting_intervals_lc()` makes use of list comprehension to build a list of intervals that do not intersect with the cut interval in a more concise and readable manner.

## Method 3: Using filter() and lambda

The `filter()` function constructs an iterator from elements of an iterable for which a function returns true. Here, we use a lambda function as the filter to succinctly test interval non-intersection.

Here’s an example:

```def non_intersecting_intervals_filter(intervals, cut):
return list(filter(lambda interval: interval[1] = cut[1], intervals))

# Example usage
intervals = [(1, 4), (5, 7), (8, 10)]
cut_interval = (3, 6)
print(non_intersecting_intervals_filter(intervals, cut_interval))```

Output:

`[(8, 10)]`

This snippet applies a lambda function within the `filter()` function to select intervals. This method offers a functional programming approach to the problem.

## Method 4: Using NumPy Library

For those who work with numerical data, NumPy offers vectorized operations that can be efficient and concise. This method requires an understanding of NumPy arrays and logic operations.

Here’s an example:

```import numpy as np

def non_intersecting_intervals_np(intervals, cut):
interval_array = np.array(intervals)
return interval_array[(interval_array[:, 1] = cut[1])].tolist()

# Example usage
intervals = [(1, 4), (5, 7), (8, 10)]
cut_interval = (3, 6)
print(non_intersecting_intervals_np(intervals, cut_interval))```

Output:

`[[8, 10]]`

The function `non_intersecting_intervals_np()` utilizes NumPy’s vectorized operations and logical indexing to filter the intervals. It’s a highly efficient method for large datasets.

## Bonus One-Liner Method 5: Using a Generator Expression

Generator expressions are a memory-efficient way that lazily generates items one at a time, instead of generating all items at once as a list. This method is useful for very large sets of intervals.

Here’s an example:

```non_intersecting_intervals_gen = lambda intervals, cut: ((start, end) for start, end in intervals if end = cut[1])

# Example usage
intervals = [(1, 4), (5, 7), (8, 10)]
cut_interval = (3, 6)
print(list(non_intersecting_intervals_gen(intervals, cut_interval)))```

Output:

`[(8, 10)]`

The lambda function `non_intersecting_intervals_gen()` creates a generator expression that can be iterated over, or converted to a list as shown.

## Summary/Discussion

• Method 1: Iterate and Compare. Straightforward and easy to understand. May not be the most efficient for large datasets.
• Method 2: List Comprehension. Concise and pythonic. It’s an in-place operation and as efficient as Method 1.
• Method 3: Using filter() and lambda. Offers a functional approach. Readability may be slightly hampered for those unfamiliar with lambda functions.
• Method 4: Using NumPy Library. Highly efficient for numeric data and large datasets. Requires NumPy knowledge and the use of an additional library.
• Bonus Method 5: Using a Generator Expression. Memory-efficient for very large data, but may not be as intuitive to those unfamiliar with generator expressions.