Doctest, type hints and bug in LIS_O(nlogn) (TheAlgorithms#1525)

* Update longest_increasing_subsequence_o(nlogn).py

* Update longest_increasing_subsequence_o(nlogn).py

Author: poyea

dynamic_programming/longest_increasing_subsequence_o(nlogn).py

@@ -4,18 +4,29 @@
 # comments: This programme outputs the Longest Strictly Increasing Subsequence in O(NLogN)
 #           Where N is the Number of elements in the list
 #############################
+from typing import List
+
 def CeilIndex(v, l, r, key):
     while r - l > 1:
-        m = (l + r) / 2
+        m = (l + r) // 2
         if v[m] >= key:
             r = m
         else:
             l = m
-
     return r
 
 
-def LongestIncreasingSubsequenceLength(v):
+def LongestIncreasingSubsequenceLength(v: List[int]) -> int:
+    """
+    >>> LongestIncreasingSubsequenceLength([2, 5, 3, 7, 11, 8, 10, 13, 6])
+    6
+    >>> LongestIncreasingSubsequenceLength([])
+    0
+    >>> LongestIncreasingSubsequenceLength([0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15])
+    6
+    >>> LongestIncreasingSubsequenceLength([5, 4, 3, 2, 1])
+    1
+    """
     if len(v) == 0:
         return 0
 
@@ -37,5 +48,5 @@ def LongestIncreasingSubsequenceLength(v):
 
 
 if __name__ == "__main__":
-    v = [2, 5, 3, 7, 11, 8, 10, 13, 6]
-    print(LongestIncreasingSubsequenceLength(v))
+    import doctest
+    doctest.testmod()