From e7dca331dc26d36341c1f86e7eccc0b8b4017a08 Mon Sep 17 00:00:00 2001
From: John Law <johnlaw.po@gmail.com>
Date: Mon, 28 Oct 2019 23:46:57 +0800
Subject: [PATCH 1/4] Doctest and comment for maximum sub-array problem

More examples and description for max_sub_array.py
---
 dynamic_programming/max_sub_array.py | 16 +++++++++++++---
 1 file changed, 13 insertions(+), 3 deletions(-)

diff --git a/dynamic_programming/max_sub_array.py b/dynamic_programming/max_sub_array.py
index eb6ab41bf52d..22817c9c2574 100644
--- a/dynamic_programming/max_sub_array.py
+++ b/dynamic_programming/max_sub_array.py
@@ -43,15 +43,22 @@ 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
+    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 +71,9 @@ def max_sub_array(nums: List[int]) -> int:
 
 
 if __name__ == "__main__":
+    """
+    A random simulation of this algorithm.
+    """
     inputs = [10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
     tim = []
     for i in inputs:

From 8c1bbd2d7f05911964558ff9b6a7c47cfd9279c3 Mon Sep 17 00:00:00 2001
From: John Law <johnlaw.po@gmail.com>
Date: Tue, 29 Oct 2019 00:11:19 +0800
Subject: [PATCH 2/4] Update max_sub_array.py

---
 dynamic_programming/max_sub_array.py | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/dynamic_programming/max_sub_array.py b/dynamic_programming/max_sub_array.py
index 22817c9c2574..62e1f6846087 100644
--- a/dynamic_programming/max_sub_array.py
+++ b/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):
@@ -48,9 +45,11 @@ def max_sub_array(nums: List[int]) -> int:
 
     >>> max_sub_array([-2, 1, -3, 4, -1, 2, 1, -5, 4])
     6
+    
     An empty (sub)array has sum 0.
     >>> max_sub_array([])
     0
+    
     If all elements are negative, the largest subarray would be the empty array, 
     having the sum 0.
     >>> max_sub_array([-1,-2,-3])
@@ -74,6 +73,9 @@ def max_sub_array(nums: List[int]) -> int:
     """
     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:

From deb0b927479f06fd7373a92c14478117cb1bcaaf Mon Sep 17 00:00:00 2001
From: John Law <johnlaw.po@gmail.com>
Date: Tue, 29 Oct 2019 00:12:37 +0800
Subject: [PATCH 3/4] Update max_sub_array.py

---
 dynamic_programming/max_sub_array.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/dynamic_programming/max_sub_array.py b/dynamic_programming/max_sub_array.py
index 62e1f6846087..d17b3818767f 100644
--- a/dynamic_programming/max_sub_array.py
+++ b/dynamic_programming/max_sub_array.py
@@ -40,8 +40,7 @@ def find_max_cross_sum(A, low, mid, high):
 
 def max_sub_array(nums: List[int]) -> int:
     """
-    Finds the contiguous subarray 
-    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])
     6

From 322ce031fc4e724b9b5e5d85965a09c21965db27 Mon Sep 17 00:00:00 2001
From: John Law <johnlaw.po@gmail.com>
Date: Tue, 29 Oct 2019 00:17:43 +0800
Subject: [PATCH 4/4] Fix doctest

---
 dynamic_programming/max_sub_array.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/dynamic_programming/max_sub_array.py b/dynamic_programming/max_sub_array.py
index d17b3818767f..f7c8209718ef 100644
--- a/dynamic_programming/max_sub_array.py
+++ b/dynamic_programming/max_sub_array.py
@@ -51,11 +51,11 @@ def max_sub_array(nums: List[int]) -> int:
     
     If all elements are negative, the largest subarray would be the empty array, 
     having the sum 0.
-    >>> max_sub_array([-1,-2,-3])
+    >>> max_sub_array([-1, -2, -3])
     0
-    >>> max_sub_array([5,-2,-3])
+    >>> max_sub_array([5, -2, -3])
     5
-    >>> max_sub_array([31, −41, 59, 26, −53, 58, 97, −93, −23, 84])
+    >>> max_sub_array([31, -41, 59, 26, -53, 58, 97, -93, -23, 84])
     187
     """
     best = 0