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41 lines
1.3 KiB
Python
41 lines
1.3 KiB
Python
'''
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Author : Mehdi ALAOUI
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This is a pure Python implementation of Dynamic Programming solution to the longest increasing subsequence of a given sequence.
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The problem is :
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Given an ARRAY, to find the longest and increasing sub ARRAY in that given ARRAY and return it.
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Example: [10, 22, 9, 33, 21, 50, 41, 60, 80] as input will return [10, 22, 33, 41, 60, 80] as output
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'''
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def longestSub(ARRAY): #This function is recursive
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ARRAY_LENGTH = len(ARRAY)
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if(ARRAY_LENGTH <= 1): #If the array contains only one element, we return it (it's the stop condition of recursion)
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return ARRAY
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#Else
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PIVOT=ARRAY[0]
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isFound=False
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i=1
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LONGEST_SUB=[]
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while(not isFound and i<ARRAY_LENGTH):
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if (ARRAY[i] < PIVOT):
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isFound=True
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TEMPORARY_ARRAY = [ element for element in ARRAY[i:] if element >= ARRAY[i] ]
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TEMPORARY_ARRAY = longestSub(TEMPORARY_ARRAY)
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if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ):
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LONGEST_SUB = TEMPORARY_ARRAY
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else:
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i+=1
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TEMPORARY_ARRAY = [ element for element in ARRAY[1:] if element >= PIVOT ]
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TEMPORARY_ARRAY = [PIVOT] + longestSub(TEMPORARY_ARRAY)
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if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ):
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return TEMPORARY_ARRAY
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else:
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return LONGEST_SUB
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#Some examples
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print(longestSub([4,8,7,5,1,12,2,3,9]))
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print(longestSub([9,8,7,6,5,7])) |