Python/dynamic_programming/longest_increasing_subsequence_O(nlogn).py

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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
v = [2, 5, 3, 7, 11, 8, 10, 13, 6]
print(LongestIncreasingSubsequenceLength(v))