Code optimized and complexity decreased

dynamic_programming/longest_increasing_subsequence.py

@@ -15,19 +15,24 @@ def longestSub(ARRAY): 			#This function is recursive
 		return ARRAY
 								#Else
 	PIVOT=ARRAY[0]
-	LONGEST_SUB=[]				#This array will contains the longest increasing sub array
-	for i in range(1,ARRAY_LENGTH):			#For each element from the array (except the pivot),
-		if (ARRAY[i] < PIVOT):				#if the element is smaller than the pivot, it won't figure on the sub array that contains the pivot
-			TEMPORARY_ARRAY = [ element for element in ARRAY[i:] if element >= ARRAY[i] ]	#But it cas figure in an increasing sub array starting from this element
-			TEMPORARY_ARRAY = longestSub(TEMPORARY_ARRAY)									#We calculate the longest sub array that starts from this element
-			if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ):									#And we save the longest sub array that begins from an element smaller than the pivot (in LONGEST_SUB)
+	isFound=False
+	i=1
+	LONGEST_SUB=[]
+	while(not isFound and i<ARRAY_LENGTH):
+		if (ARRAY[i] < PIVOT):
+			isFound=True
+			TEMPORARY_ARRAY = [ element for element in ARRAY[i:] if element >= ARRAY[i] ]
+			TEMPORARY_ARRAY = longestSub(TEMPORARY_ARRAY)
+			if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ):
 				LONGEST_SUB = TEMPORARY_ARRAY
+		else:
+			i+=1
 
-	TEMPORARY_ARRAY = [ element for element in ARRAY[1:] if element >= PIVOT ]				#Then we delete these elements (smaller than the pivot) from the initial array
-	TEMPORARY_ARRAY = [PIVOT] + longestSub(TEMPORARY_ARRAY)									#And we calculate the longest sub array containing the pivot (in TEMPORARY_ARRAY)
-	if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ):											#Then we compare the longest array between TEMPORARY_ARRAY and LONGEST_SUB
+	TEMPORARY_ARRAY = [ element for element in ARRAY[1:] if element >= PIVOT ]
+	TEMPORARY_ARRAY = [PIVOT] + longestSub(TEMPORARY_ARRAY)
+	if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ):
 		return TEMPORARY_ARRAY
-	else:																					#And we return the longest one
+	else:
 		return LONGEST_SUB
 
 #Some examples