# 5 Best Ways to Find Total Unique Duration from a List of Intervals in Python

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π‘ Problem Formulation: This article addresses the computation of the total unique duration from a list of time intervals in Python. For example, given intervals in the form of tuples like `[(1, 4), (3, 5), (6, 8)]`, the output for total unique duration should be `5`, considering the overlapping intervals only once.

## Method 1: Using Sorting and Merging

This method involves sorting the list of intervals based on start times and then merging overlapping intervals to calculate the total unique duration. It’s an efficient way to handle overlapping intervals and can be easily implemented in Python.

Here’s an example:

```def merge_intervals(intervals):
sorted_intervals = sorted(intervals)
merged = [sorted_intervals[0]]
for current in sorted_intervals[1:]:
previous = merged[-1]
if current[0] <= previous[1]:
merged[-1] = (previous[0], max(previous[1], current[1]))
else:
merged.append(current)
return sum(interval[1] - interval[0] for interval in merged)

print(merge_intervals([(1, 4), (3, 5), (6, 8)]))```

The output of this code snippet:

`5`

The `merge_intervals()` function sorts the list of intervals and then iterates through it, merging intervals whenever they overlap and adding non-overlapping intervals to the merged list. After merging, the unique duration is obtained by summing up the differences between start and end times for each interval.

## Method 2: Sweep Line Algorithm

The sweep line algorithm takes a geometrical approach to solve interval problems. It visualizes the problem as sweeping a line across the intervals and tracking start and end points to compute the unique duration. It’s useful for larger data sets with complex overlapping.

Here’s an example:

```def sweep_line(intervals):
events = []
for start, end in intervals:
events.append((start, 'start'))
events.append((end, 'end'))

events.sort()
unique_duration, in_interval = 0, False
for i, event in enumerate(events):
if event[1] == 'start':
if not in_interval:
start_time = event[0]
in_interval = True
elif event[1] == 'end':
if i < len(events) - 1 and events[i + 1][1] == 'start' and events[i + 1][0] == event[0]:
continue
unique_duration += event[0] - start_time
in_interval = False
return unique_duration

print(sweep_line([(1, 4), (3, 5), (6, 8)]))```

The output of this code snippet:

`5`

In `sweep_line()`, intervals are broken down into individual events. Events are sorted, and as the algorithm “sweeps” through them, it toggles a boolean indicating if it is currently within an interval. This is used to calculate the unique duration by tracking when an interval starts and ends.

## Method 3: Using Interval Trees

Interval trees are data structures that allow for efficient querying of intervals. They are particularly useful when the list of intervals is dynamic, and intervals are frequently inserted or deleted. This method is more advanced and suitable for applications that require maximum efficiency.

Here’s an example:

```from intervaltree import IntervalTree

def total_unique_duration(intervals):
itree = IntervalTree()
for start, end in intervals:
itree[start:end] = None

itree.merge_overlaps(strict=False)
return sum(iv.end - iv.begin for iv in itree)

print(total_unique_duration([(1, 4), (3, 5), (6, 8)]))```

The output of this code snippet:

`5`

The `total_unique_duration()` function constructs an interval tree from the given intervals, merges any overlaps, then calculates the total unique time by summing the durations of the merged intervals.

## Method 4: Using Counter Object

A counter object from the collections module can be used to track the frequency of each point in the intervals. By counting these frequencies, one can ultimately determine which points mark the beginnings and ends of unique durations.

Here’s an example:

```from collections import Counter

def unique_duration_counter(intervals):
point_counts = Counter()
for start, end in intervals:
point_counts[start] += 1
point_counts[end] -= 1

unique_duration, current, in_interval = 0, 0, False
for point in sorted(point_counts):
current += point_counts[point]
if current > 0 and not in_interval:
start_point = point
in_interval = True
elif current == 0 and in_interval:
unique_duration += point - start_point
in_interval = False
return unique_duration

print(unique_duration_counter([(1, 4), (3, 5), (6, 8)]))```

The output of this code snippet:

`5`

The `unique_duration_counter()` function uses a counter to increment at interval starts and decrement at interval ends. When the counter is positive, it denotes being inside an interval. The total unique duration is calculated based on these transitions.

## Bonus One-Liner Method 5: Using Set Operations

While not the most efficient for large data sets due to the linearity of set operations, this one-liner uses a set to store all the points from intervals and calculates unique duration via set arithmetic.

Here’s an example:

```unique_duration = lambda intervals: len(set.union(*(set(range(start, end)) for start, end in intervals)))
print(unique_duration([(1, 4), (3, 5), (6, 8)]))```

The output of this code snippet:

`5`

The one-liner lambda function calculates the total unique duration by creating sets for each interval and finding the union of these sets. The length of the resulting union set gives the unique duration.

## Summary/Discussion

• Method 1: Sorting and Merging. Efficient and straightforward method. However, it might not be the best for very large datasets due to sorting overhead.
• Method 2: Sweep Line Algorithm. Well-suited for larger datasets with lots of overlaps. Can be more complex to understand and implement.
• Method 3: Interval Trees. High performance and dynamic updates. Requires additional data structure and can be an overkill for smaller problems.
• Method 4: Counter Object. Simple implementation with good performance. Not as intuitive and requires a sorted processing of points.
• Bonus Method 5: Using Set Operations. Very simple one-liner solution. Not efficient for large datasets due to the computational cost of range and set operations.