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The program returns now the longest increasing subsequence instead of returning only the length. Code optimized and well commented

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Mehdi ALAOUI 2017-04-07 03:19:02 +01:00
parent 7ae9759220
commit 628f184af5
1 changed files with 35 additions and 11 deletions
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dynamic_programming/longest_increasing_subsequence.py
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"""
The Longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. For example, the length of LIS for {10, 22, 9, 33, 21, 50, 41, 60, 80} is 6
"""
def LIS(arr):
n= len(arr)
lis = [1]*n
'''
Author : Mehdi ALAOUI
for i in range(1, n):
for j in range(0, i):
if arr[i] > arr[j] and lis[i] <= lis[j]:
lis[i] = lis[j] + 1
return max(lis)
This is a pure Python implementation of Dynamic Programming solution to the longest increasing subsequence of a given sequence.
The problem is :
Given an ARRAY, to find the longest and increasing sub ARRAY in that given ARRAY and return it.
Example: [10, 22, 9, 33, 21, 50, 41, 60, 80] as input will return [10, 22, 33, 41, 60, 80] as output
'''
def longestSub(ARRAY): #This function is recursive
ARRAY_LENGTH = len(ARRAY)
if(ARRAY_LENGTH <= 1): #If the array contains only one element, we return it (it's the stop condition of recursion)
return ARRAY
#Else
PIVOT=ARRAY[0]
LONGEST_SUB=[] #This array will contains the longest increasing sub array
for i in range(1,ARRAY_LENGTH):
if (ARRAY[i] < PIVOT): #For each element from the array (except the 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)
LONGEST_SUB = TEMPORARY_ARRAY
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
return TEMPORARY_ARRAY
else: #And we return the longest one
return LONGEST_SUB
#Some examples
print(longestSub([4,8,7,5,1,12,2,3,9]))
print(longestSub([9,8,7,6,5,7]))