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46 lines
1.4 KiB
Python
46 lines
1.4 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 (
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ARRAY_LENGTH <= 1
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): # 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]))
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