Merge pull request #147 from aravindiiitb/master

Added Code in Dynamic Programming section for Longest Strictly Increasing Subsequence in O(nlogn) time

dynamic_programming/longest_increasing_subsequence_O(nlogn).py

@@ -0,0 +1,40 @@
+#############################
+# 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)