mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
5df8aec66c
* GitHub Action formats our code with psf/black @poyea Your review please. * fixup! Format Python code with psf/black push
57 lines
1.7 KiB
Python
57 lines
1.7 KiB
Python
"""
|
|
Author : Mehdi ALAOUI
|
|
|
|
This is a pure Python implementation of Dynamic Programming solution to the longest increasing subsequence of a given sequence.
|
|
|
|
The problem is :
|
|
Given an array, to find the longest and increasing sub-array in that given array and return it.
|
|
Example: [10, 22, 9, 33, 21, 50, 41, 60, 80] as input will return [10, 22, 33, 41, 60, 80] as output
|
|
"""
|
|
from typing import List
|
|
|
|
|
|
def longest_subsequence(array: List[int]) -> List[int]: # This function is recursive
|
|
"""
|
|
Some examples
|
|
>>> longest_subsequence([10, 22, 9, 33, 21, 50, 41, 60, 80])
|
|
[10, 22, 33, 41, 60, 80]
|
|
>>> longest_subsequence([4, 8, 7, 5, 1, 12, 2, 3, 9])
|
|
[1, 2, 3, 9]
|
|
>>> longest_subsequence([9, 8, 7, 6, 5, 7])
|
|
[8]
|
|
>>> longest_subsequence([1, 1, 1])
|
|
[1, 1, 1]
|
|
"""
|
|
array_length = len(array)
|
|
if (
|
|
array_length <= 1
|
|
): # If the array contains only one element, we return it (it's the stop condition of recursion)
|
|
return array
|
|
# Else
|
|
pivot = array[0]
|
|
isFound = False
|
|
i = 1
|
|
longest_subseq = []
|
|
while not isFound and i < array_length:
|
|
if array[i] < pivot:
|
|
isFound = True
|
|
temp_array = [element for element in array[i:] if element >= array[i]]
|
|
temp_array = longest_subsequence(temp_array)
|
|
if len(temp_array) > len(longest_subseq):
|
|
longest_subseq = temp_array
|
|
else:
|
|
i += 1
|
|
|
|
temp_array = [element for element in array[1:] if element >= pivot]
|
|
temp_array = [pivot] + longest_subsequence(temp_array)
|
|
if len(temp_array) > len(longest_subseq):
|
|
return temp_array
|
|
else:
|
|
return longest_subseq
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|