mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
9200a2e543
* from __future__ import annotations
* fixup! from __future__ import annotations
* fixup! from __future__ import annotations
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
56 lines
1.3 KiB
Python
56 lines
1.3 KiB
Python
#############################
|
|
# Author: Aravind Kashyap
|
|
# File: lis.py
|
|
# comments: This programme outputs the Longest Strictly Increasing Subsequence in
|
|
# O(NLogN) Where N is the Number of elements in the list
|
|
#############################
|
|
from __future__ import annotations
|
|
|
|
|
|
def CeilIndex(v, l, r, key): # noqa: E741
|
|
while r - l > 1:
|
|
m = (l + r) // 2
|
|
if v[m] >= key:
|
|
r = m
|
|
else:
|
|
l = m # noqa: E741
|
|
return r
|
|
|
|
|
|
def LongestIncreasingSubsequenceLength(v: list[int]) -> int:
|
|
"""
|
|
>>> LongestIncreasingSubsequenceLength([2, 5, 3, 7, 11, 8, 10, 13, 6])
|
|
6
|
|
>>> LongestIncreasingSubsequenceLength([])
|
|
0
|
|
>>> LongestIncreasingSubsequenceLength([0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3,
|
|
... 11, 7, 15])
|
|
6
|
|
>>> LongestIncreasingSubsequenceLength([5, 4, 3, 2, 1])
|
|
1
|
|
"""
|
|
if len(v) == 0:
|
|
return 0
|
|
|
|
tail = [0] * len(v)
|
|
length = 1
|
|
|
|
tail[0] = v[0]
|
|
|
|
for i in range(1, len(v)):
|
|
if v[i] < tail[0]:
|
|
tail[0] = v[i]
|
|
elif v[i] > tail[length - 1]:
|
|
tail[length] = v[i]
|
|
length += 1
|
|
else:
|
|
tail[CeilIndex(tail, -1, length - 1, v[i])] = v[i]
|
|
|
|
return length
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|