Longest Increasing Subsequence using DP

Author: OmkarPathak

Dynamic Programming/P02_LongestIncreasingSubsequence.py

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+# Author:  OMKAR PATHAK
+
+# 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 and LIS is {10, 22, 33, 50, 60, 80}.
+
+def longest_increaing_subsequence(myList):
+    # Initialize list with some value
+    lis = [1] * len(myList)
+    # list for storing the elements in an lis
+    elements = [0] * len(myList)
+
+    # Compute optimized LIS values in bottom up manner
+    for i in range (1 , len(myList)):
+        for j in range(0 , i):
+            if myList[i] > myList[j] and lis[i]< lis[j] + 1:
+                lis[i] = lis[j]+1
+                elements[i] = j
+
+    idx = 0
+
+    # find the maximum of the whole list and get its index in idx
+    maximum = max(lis)              # this will give us the count of longest increasing subsequence
+    idx = lis.index(maximum)
+
+    # for printing the elements later
+    seq = [myList[idx]]
+    while idx != elements[idx]:
+        idx = elements[idx]
+        seq.append(myList[idx])
+
+    return (maximum, reversed(seq))
+
+# define elements in an array
+myList = [10, 22, 9, 33, 21, 50, 41, 60]
+ans = longest_increaing_subsequence(myList)
+print ('Length of lis is', ans[0])
+print ('The longest sequence is', ', '.join(str(x) for x in ans[1]))
+
+# OUTPUT:
+# Length of lis is 5
+# The longest sequence is 10, 22, 33, 50, 60