Doctest and typing for longest_increasing_subsequence.py (#1526)

* Update longest_increasing_subsequence.py

* Update longest_increasing_subsequence.py

* Format longest_increasing_subsequence.py to PEP8

* Update longest_increasing_subsequence.py

Author: poyea

dynamic_programming/longest_increasing_subsequence.py

@@ -4,42 +4,52 @@
 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.
+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)
+from typing import List
+
+
+def longest_subsequence(array: List[int]) -> List[int]:  # This function is recursive
+    """
+    Some examples
+    >>> longest_subsequence([10, 22, 9, 33, 21, 50, 41, 60, 80])
+    [10, 22, 33, 41, 60, 80]
+    >>> longest_subsequence([4, 8, 7, 5, 1, 12, 2, 3, 9])
+    [1, 2, 3, 9]
+    >>> longest_subsequence([9, 8, 7, 6, 5, 7])
+    [8]
+    >>> longest_subsequence([1, 1, 1])
+    [1, 1, 1]
+    """
+    array_length = len(array)
     if (
-        ARRAY_LENGTH <= 1
+        array_length <= 1
     ):  # If the array contains only one element, we return it (it's the stop condition of recursion)
-        return ARRAY
+        return array
         # Else
-    PIVOT = ARRAY[0]
+    pivot = array[0]
     isFound = False
     i = 1
-    LONGEST_SUB = []
-    while not isFound and i < ARRAY_LENGTH:
-        if ARRAY[i] < PIVOT:
+    longest_subseq = []
+    while not isFound and i < array_length:
+        if array[i] < pivot:
             isFound = True
-            TEMPORARY_ARRAY = [element for element in ARRAY[i:] if element >= ARRAY[i]]
-            TEMPORARY_ARRAY = longestSub(TEMPORARY_ARRAY)
-            if len(TEMPORARY_ARRAY) > len(LONGEST_SUB):
-                LONGEST_SUB = TEMPORARY_ARRAY
+            temp_array = [element for element in array[i:] if element >= array[i]]
+            temp_array = longest_subsequence(temp_array)
+            if len(temp_array) > len(longest_subseq):
+                longest_subseq = temp_array
         else:
             i += 1
 
-    TEMPORARY_ARRAY = [element for element in ARRAY[1:] if element >= PIVOT]
-    TEMPORARY_ARRAY = [PIVOT] + longestSub(TEMPORARY_ARRAY)
-    if len(TEMPORARY_ARRAY) > len(LONGEST_SUB):
-        return TEMPORARY_ARRAY
+    temp_array = [element for element in array[1:] if element >= pivot]
+    temp_array = [pivot] + longest_subsequence(temp_array)
+    if len(temp_array) > len(longest_subseq):
+        return temp_array
     else:
-        return LONGEST_SUB
-
-
-# Some examples
+        return longest_subseq
+    
 
-print(longestSub([4, 8, 7, 5, 1, 12, 2, 3, 9]))
-print(longestSub([9, 8, 7, 6, 5, 7]))
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()