Added longest increasing subsequence implementation using dynamic programming

Author: OmkarPathak

pygorithm/dynamic_programming/lis.py

@@ -0,0 +1,42 @@
+'''
+Author: Omkar Pathak
+Created At: 25th August 2017
+'''
+
+def longest_increasing_subsequence(_list):
+    '''
+    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}.
+    '''
+    # Initialize list with some value
+    lis = [1] * len(_list)
+    # list for storing the elements in an lis
+    elements = [0] * len(_list)
+
+    # Compute optimized LIS values in bottom up manner
+    for i in range (1 , len(_list)):
+        for j in range(0 , i):
+            if _list[i] > _list[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)
+    idx = lis.index(maximum)
+
+    # for printing the elements later
+    seq = [_list[idx]]
+    while idx != elements[idx]:
+        idx = elements[idx]
+        seq.append(_list[idx])
+
+    return (maximum, seq[::-1])
+
+def get_code():
+    """
+    returns the code for the longest_increasing_subsequence function
+    """
+    return inspect.getsource(longest_increasing_subsequence)