Create longest-increasing-subsequence.py

dp/longest-increasing-subsequence.py

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+# A naive Python implementation of LIS problem 
+
+# global variable to store the maximum 
+global maximum 
+
+def _lis(arr , n ): 
+
+	# to allow the access of global variable 
+	global maximum 
+
+	# Base Case 
+	if n == 1 : 
+		return 1
+
+	# maxEndingHere is the length of LIS ending with arr[n-1] 
+	maxEndingHere = 1
+
+	"""Recursively get all LIS ending with arr[0], arr[1]..arr[n-2] 
+	IF arr[n-1] is maller than arr[n-1], and max ending with 
+	arr[n-1] needs to be updated, then update it"""
+	for i in xrange(1, n): 
+		res = _lis(arr , i) 
+		if arr[i-1] < arr[n-1] and res+1 > maxEndingHere: 
+			maxEndingHere = res +1
+
+	# Compare maxEndingHere with overall maximum. And 
+	# update the overall maximum if needed 
+	maximum = max(maximum , maxEndingHere) 
+
+	return maxEndingHere 
+
+def lis(arr): 
+
+	# to allow the access of global variable 
+	global maximum 
+
+	# lenght of arr 
+	n = len(arr) 
+
+	# maximum variable holds the result 
+	maximum = 1
+
+	# The function _lis() stores its result in maximum 
+	_lis(arr , n) 
+
+	return maximum 
+
+# Driver program to test the above function 
+arr = [10 , 22 , 9 , 33 , 21 , 50 , 41 , 60] 
+n = len(arr) 
+print "Length of lis is ", lis(arr)