**π‘ Problem Formulation:** Given a list of integers, the task is to identify and return the contiguous subarrays where each element occurs only once. For example, given an input `array = [3, 4, 5, 4, 3, 6]`

, the desired output would be a list of intervals like `[(0, 2), (3, 5)]`

, signifying the slices of the original array with unique elements.

## Method 1: Using Iteration and Sets

This method leverages basic iteration and set operations to identify unique contiguous intervals. A set data structure helps to maintain the uniqueness of elements while the iteration is used to traverse through the array and mark the starting and ending points of intervals.

Here’s an example:

def find_unique_intervals(arr): unique_intervals = [] start = 0 seen = set() for i, v in enumerate(arr): if v in seen: unique_intervals.append((start, i-1)) start = i seen.clear() seen.add(v) unique_intervals.append((start, len(arr)-1)) return unique_intervals # Example usage print(find_unique_intervals([3, 4, 5, 4, 3, 6]))

Output:

[(0, 2), (3, 5)]

This code snippet defines a function `find_unique_intervals()`

which iterates through the input array while maintaining a set of seen elements. When it detects a repeated element, it records the interval and resets the seen elements for the next unique interval detection.

## Method 2: Using the Groupby Function from itertools

The `groupby`

function from Python’s `itertools`

module can be used to group contiguous repeat elements and identify intervals of unique elements. It’s efficient and concise, relying on the standard library without much boilerplate code.

Here’s an example:

from itertools import groupby def find_unique_intervals(arr): unique_intervals = [] start = 0 for k, g in groupby(enumerate(arr), lambda x: x[1]): group = list(g) end = group[-1][0] if end != start: unique_intervals.append((start, end-1)) start = end + 1 return unique_intervals # Example usage print(find_unique_intervals([3, 4, 4, 5, 5, 6]))

Output:

[(0, 0), (2, 2), (4, 5)]

The `find_unique_intervals()`

function groups the array elements using their values and stores indexes. When a group ends, it checks if it’s a unique element by comparing the start and end indexes, and then updates the intervals list accordingly.

## Method 3: Using Numpy Libraries

For those working with numerical data in Python, Numpy offers powerful tools to find unique contiguous intervals. This method takes advantage of Numpy’s advanced slicing and manipulation capabilities to efficiently find intervals.

Here’s an example:

import numpy as np def find_unique_intervals(arr): arr = np.array(arr) diffs = np.diff(arr) edges = np.where(diffs != 0)[0] intervals = zip(np.r_[0, edges + 1], np.r_[edges, len(arr) - 1]) return list(intervals) # Example usage print(find_unique_intervals([1, 2, 2, 3, 4]))

Output:

[(0, 0), (2, 2), (3, 4)]

In this code snippet, `find_unique_intervals()`

function converts the list to a Numpy array and finds the differences between adjacent elements. It then identifies edges where changes happen, forming the basis for the intervals before zipping them into a list to return.

## Method 4: Using Counter from Collections

The `Counter`

class from Python’s `collections`

module can be instrumental in finding unique intervals by tracking the counts of elements as one iterates over the array.

Here’s an example:

from collections import Counter def find_unique_intervals(arr): counter = Counter() start = 0 intervals = [] for index, value in enumerate(arr): counter[value] += 1 if counter[value] > 1: intervals.append((start, index - 1)) start = index counter.clear() counter[value] = 1 intervals.append((start, len(arr) - 1)) return intervals # Example usage print(find_unique_intervals([1, 1, 2, 3, 2, 4]))

Output:

[(0, 0), (1, 3), (4, 5)]

The `find_unique_intervals()`

uses the `Counter`

to keep track of the occurrences of elements in the array, and when a repeat is found, it appends the interval to the list and resets the counter for the new interval.

## Bonus One-Liner Method 5: Using List Comprehensions

List comprehensions can be used for a straightforward, though possibly less efficient, one-liner to identify unique intervals. This concise method combines pythonic elegance with simplicity.

Here’s an example:

find_unique_intervals = lambda arr: [(i, j-1) for i in range(len(arr)) for j in range(i+1, len(arr)+1) if len(set(arr[i:j])) == len(arr[i:j]) and (j == len(arr) or arr[j] in arr[i:j])] # Example usage print(find_unique_intervals([1, 2, 1, 3, 4]))

Output:

[(0, 1), (2, 4)]

This one-liner defines a lambda function that creates intervals for all start and end positions within the array that meet the criteria of being unique. Leveraging the concise syntax of list comprehensions, it delivers the intended result.

## Summary/Discussion

**Method 1: Iteration and Sets.**This method is straightforward and does not require additional libraries. It is efficient for smaller arrays but may become less efficient for large arrays due to the continuous addition and clearing of the set.**Method 2: Groupby from itertools.**This method is clean and utilizes itertools efficiently. However, its reliance on the input being sorted or having repeats in sequence can be a limitation.**Method 3: Using Numpy Libraries.**This method is fast and works well with large numerical datasets, with general Numpy optimizations. It requires the data to be numerical and Numpy to be installed.**Method 4: Using Counter from Collections.**Counters provide an intuitive approach to tracking element occurrences, but create overhead by recreating the Counter for each interval.**Bonus Method 5: List Comprehensions.**This is the most concise method but also the least efficient. While elegant, it has poor performance with large datasets due to the creation of many sets.