Improve doctest and comment for maximum sub-array problem (#1503)

* Doctest and comment for maximum sub-array problem

More examples and description for max_sub_array.py

* Update max_sub_array.py

* Update max_sub_array.py

* Fix doctest

Author: poyea

dynamic_programming/max_sub_array.py

@@ -2,9 +2,6 @@
 author : Mayank Kumar Jha (mk9440)
 """
 from typing import List
-import time
-import matplotlib.pyplot as plt
-from random import randint
 
 
 def find_max_sub_array(A, low, high):
@@ -43,15 +40,23 @@ def find_max_cross_sum(A, low, mid, high):
 
 def max_sub_array(nums: List[int]) -> int:
     """
-     Finds the contiguous subarray (can be empty array)
-     which has the largest sum and return its sum.
+    Finds the contiguous subarray which has the largest sum and return its sum.
 
-    >>> max_sub_array([-2,1,-3,4,-1,2,1,-5,4])
+    >>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
     6
+    
+    An empty (sub)array has sum 0.
     >>> max_sub_array([])
     0
-    >>> max_sub_array([-1,-2,-3])
+    
+    If all elements are negative, the largest subarray would be the empty array, 
+    having the sum 0.
+    >>> max_sub_array([-1, -2, -3])
     0
+    >>> max_sub_array([5, -2, -3])
+    5
+    >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
+    187
     """
     best = 0
     current = 0
@@ -64,6 +69,12 @@ def max_sub_array(nums: List[int]) -> int:
 
 
 if __name__ == "__main__":
+    """
+    A random simulation of this algorithm.
+    """
+    import time
+    import matplotlib.pyplot as plt
+    from random import randint
     inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
     tim = []
     for i in inputs: