Python/dynamic_programming/longest_increasing_subsequence_o(nlogn).py
Caeden 07e991d553
Add pep8-naming to pre-commit hooks and fixes incorrect naming conventions (#7062)
* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038)

* refactor: Fix naming conventions (#7038)

* Update arithmetic_analysis/lu_decomposition.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038)

* chore: Fix naming conventions in doctests (#7038)

* fix: Temporarily disable project euler problem 104 (#7069)

* chore: Fix naming conventions in doctests (#7038)

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
2022-10-13 00:54:20 +02:00

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 ceil_index(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 longest_increasing_subsequence_length(v: list[int]) -> int:
"""
>>> longest_increasing_subsequence_length([2, 5, 3, 7, 11, 8, 10, 13, 6])
6
>>> longest_increasing_subsequence_length([])
0
>>> longest_increasing_subsequence_length([0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13,
... 3, 11, 7, 15])
6
>>> longest_increasing_subsequence_length([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[ceil_index(tail, -1, length - 1, v[i])] = v[i]
return length
if __name__ == "__main__":
import doctest
doctest.testmod()