Python/dynamic_programming/longest_increasing_subsequence_o(nlogn).py

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))