mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
43 lines
855 B
Python
43 lines
855 B
Python
from __future__ import print_function
|
|
#############################
|
|
# 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
|
|
#############################
|
|
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):
|
|
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__":
|
|
v = [2, 5, 3, 7, 11, 8, 10, 13, 6]
|
|
print(LongestIncreasingSubsequenceLength(v))
|