## longest increasing subsequence o(nlogn)

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```
#############################
# 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 typing import List
def CeilIndex(v, l, r, key):
while r - l > 1:
m = (l + r) // 2
if v[m] >= key:
r = m
else:
l = m
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()
```