add max sum contigous subsequence (#1537)

* add max sum contigous subsequence

* fix typo

* Add doctest and type hints

* Create autoblack.yml

dynamic_programming/max_sum_contigous_subsequence.py

@@ -0,0 +1,20 @@
+def max_subarray_sum(nums: list) -> int:
+    """
+    >>> max_subarray_sum([6 , 9, -1, 3, -7, -5, 10])
+    17
+    """
+    if not nums:
+        return 0
+    n = len(nums)
+    s = [0] * n
+    res, s, s_pre = nums[0], nums[0], nums[0]
+    for i in range(1, n):
+        s = max(nums[i], s_pre + nums[i])
+        s_pre = s
+        res = max(res, s)
+    return res
+
+
+if __name__ == "__main__":
+    nums = [6, 9, -1, 3, -7, -5, 10]
+    print(max_subarray_sum(nums))