💡 Problem Formulation: A local peak element in a list of numbers is an element that is not smaller than its neighbors. For an element at index i, this implies that list[i] >= list[i-1] and list[i] >= list[i+1]. The goal is to find all indices of such local peak elements. For instance, given the list [1, 3, 2, 7, 3, 5], the local peak elements are 3 (at index 1), 7 (at index 3), and 5 (at index 5).
Method 1: Iterative Approach
This method involves traversing the list from the second element to the second-to-last element and comparing each element with its neighbors. This method is straightforward and easy to implement. The function will return a list of indices where local peaks occur.
Here’s an example:
def find_local_peaks(lst):
peak_indices = []
for i in range(1, len(lst) - 1):
if lst[i-1] = lst[i+1]:
peak_indices.append(i)
return peak_indices
print(find_local_peaks([1, 3, 2, 7, 3, 5]))The output of this code snippet will be:
[1, 3]
This code snippet defines a function find_local_peaks() that takes a list and returns the indices of all local peak elements, excluding the extreme elements of the list. It’s simple and allows for easy understanding and debugging of the logic involved.
Method 2: Recursive Approach
In this recursive approach, the idea is to reduce the problem into smaller sub-problems by recursively finding local peaks in segments of the list. This method is less intuitive and might be more complex for larger lists, but it’s an excellent demonstration of recursive problem-solving.
Here’s an example:
def find_peak_helper(lst, start, end):
if start == end:
return [start] if lst[start-1] = lst[end+1] else []
mid = (start + end) // 2
peak_indices = find_peak_helper(lst, start, mid) + find_peak_helper(lst, mid + 1, end)
return peak_indices
def find_local_peaks_recursive(lst):
return find_peak_helper(lst, 1, len(lst) - 2)
print(find_local_peaks_recursive([1, 3, 2, 7, 3, 5]))The output of this code snippet will be the same as Method 1:
[1, 3]
The find_local_peaks_recursive() function works by recursively dividing the list and checking each section for local peaks. This solution is more complex and may not be as performance-efficient due to the overhead of recursive calls.
Method 3: Using List Comprehensions
This method takes advantage of Python’s list comprehensions, which provide a concise way to create lists. List comprehensions are elegant and often more readable when performing simple operations and filtering.
Here’s an example:
def find_local_peaks_comprehension(lst):
return [i for i in range(1, len(lst)-1) if lst[i-1] = lst[i+1]]
print(find_local_peaks_comprehension([1, 3, 2, 7, 3, 5]))The output of this code snippet will be:
[1, 3]
The find_local_peaks_comprehension() function uses a list comprehension to filter indices where the current element is a local peak. It provides a clean and pythonic solution that’s easy to read and write.
Method 4: Using Enumerate and Zip
This method uses the built-in functions enumerate() and zip() to pair each element with its neighbors and indices. This approach allows for concise and efficient iteration over the list elements.
Here’s an example:
def find_local_peaks_zip(lst):
lst = [float('-inf')] + lst + [float('-inf')]
return [i for i, (a, b, c) in enumerate(zip(lst, lst[1:], lst[2:])) if a = c]
print(find_local_peaks_zip([1, 3, 2, 7, 3, 5]))The output of this code snippet will be:
[1, 3, 5]
The function find_local_peaks_zip() extends the input list with negative infinity at the ends to handle edge cases and utilizes zip() with list slicing to pair each element with its neighbors. The enumerate() function is then used to also allow access to the current index. This method is efficient and Pythonic, cleverly circumventing edge cases.
Bonus One-Liner Method 5: Using NumPy
If the Python library NumPy is an option, one can solve this problem with a one-liner by utilizing vectorization and advanced slicing. This method is particularly efficient for large datasets and leverages the power of NumPy.
Here’s an example:
import numpy as np
def find_local_peaks_numpy(arr):
return np.where((arr[:-2] = arr[2:]))[0] + 1
arr = np.array([1, 3, 2, 7, 3, 5])
print(find_local_peaks_numpy(arr))The output of this code snippet will be:
[1 3]
The find_local_peaks_numpy() function leverages NumPy’s vectorization capabilities to compare elements and their neighbors in a highly efficient way. NumPy operations are compiled and optimized, resulting in performance gains especially for large arrays.
Summary/Discussion
- Method 1: Iterative Approach. Simple and direct. Performance may degrade with very large lists.
- Method 2: Recursive Approach. Demonstrates classic recursive problem-solving. Not as efficient due to recursion overhead.
- Method 3: List Comprehensions. Elegant and pythonic. Performance is generally good, but can be memory-intensive for very large lists.
- Method 4: Enumerate and Zip. Clever use of Python features. Efficient handling of edge cases and concise code.
- Method 5: NumPy One-Liner. Optimal for large datasets and numerical computations. Requires NumPy installation.