Leetcode provides a rich set of problems for honing one’s coding skills, and the “Decompress Run-Length Encoded List” problem is a fantastic introductory problem for learning about list manipulation in Python. This article aims to provide an in-depth exploration of the problem, discussing multiple approaches to solving it, their complexities, and how to test your solutions.

## Table of Contents

- Problem Description
- Initial Thoughts and Observations
- Simple Iterative Approach
- Using List Comprehensions
- Using Python’s itertools Library
- Testing and Edge Cases
- Complexity Analysis
- Conclusion

## 1. Problem Description

The task is to decompress a given run-length encoded list and return it as an array. In run-length encoding, the list consists of pairs where the first element represents the frequency and the second element is the value that should be repeated.

### Example

- Input:
`nums = [1,2,3,4]`

- Output:
`[2,4,4,4]`

Here, `1`

is the frequency and `2`

is the value for the first pair, and `3`

is the frequency and `4`

is the value for the second pair.

### Constraints

`2 <= nums.length <= 100`

`nums.length % 2 == 0`

`1 <= nums[i] <= 100`

## 2. Initial Thoughts and Observations

- The list length is guaranteed to be even.
- You can directly use the input list for decompression.

## 3. Simple Iterative Approach

This approach employs a simple loop to iterate over the input list, processing each pair and extending the output list accordingly.

### Algorithm

- Initialize an empty list,
`result`

. - Loop through
`nums`

, processing two elements at a time. - Use
`list.extend()`

to add the decompressed sub-array to`result`

.

### Python Code

```
def decompressRLElist(nums):
result = []
for i in range(0, len(nums), 2):
freq, val = nums[i], nums[i+1]
result.extend([val] * freq)
return result
```

## 4. Using List Comprehensions

Python’s list comprehensions provide a more compact and Pythonic way to solve this problem.

### Algorithm

- Use a list comprehension to generate the decompressed list.

### Python Code

```
def decompressRLElist(nums):
return [nums[i+1] for i in range(0, len(nums), 2) for _ in range(nums[i])]
```

## 5. Using Python’s itertools Library

Python’s `itertools.chain`

can be used to efficiently flatten an iterable of iterables, allowing us to generate the decompressed list in a more elegant way.

### Algorithm

- Use
`itertools.chain`

to flatten the generated sub-arrays.

### Python Code

```
import itertools
def decompressRLElist(nums):
return list(itertools.chain.from_iterable([[nums[i+1]] * nums[i] for i in range(0, len(nums), 2)]))
```

## 6. Testing and Edge Cases

- Test with the minimum allowed length of
`nums`

, i.e., 2. For example,`nums = [1, 2]`

. - Test with high frequencies and values, like
`nums = [50, 50, 50, 50]`

. - Test with multiple distinct frequencies and values.
- Test with the maximum allowed length to check if the algorithm can handle it.

## 7. Complexity Analysis

**Simple Iterative Approach**- Time Complexity: O(n)
- Space Complexity: O(n)

**Using List Comprehensions**- Time Complexity: O(n)
- Space Complexity: O(n)

**Using Python’s itertools Library**- Time Complexity: O(n)
- Space Complexity: O(n)

Here, n is the length of the resulting decompressed list.

## 8. Conclusion

The “Decompress Run-Length Encoded List” problem provides an excellent opportunity to delve into Python list operations and different ways to iterate and manipulate lists. By exploring various approaches, ranging from basic loops to list comprehensions and Python’s itertools, we can appreciate the diversity and richness of Python’s language features.