Update maximum_subarray.py (TheAlgorithms#7757)

* Update maximum_subarray.py

1. Rectify documentation to indicate the correct output: function doesn't return the subarray, but rather returns a sum.
2. Make the function more Pythonic and optimal.
3. Make function annotation generic i.e. can accept any sequence.
4. Raise value error when the input sequence is empty.

* Update maximum_subarray.py

1. Use the conventions as mentioned in pep-0257.
2. Use negative infinity as the initial value for the current maximum and the answer.

* Update maximum_subarray.py

Avoid type conflict by returning the answer cast to an integer.

* Update other/maximum_subarray.py

Co-authored-by: Andrey <Cjkjvfnby@gmail.com>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update maximum_subarray.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update maximum_subarray.py

Remove typecast to int for the final answer

Co-authored-by: Andrey <Cjkjvfnby@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

other/maximum_subarray.py

@@ -1,20 +1,26 @@
-def max_subarray(nums: list[int]) -> int:
-    """
-    Returns the subarray with maximum sum
-    >>> max_subarray([1,2,3,4,-2])
+from collections.abc import Sequence
+
+
+def max_subarray_sum(nums: Sequence[int]) -> int:
+    """Return the maximum possible sum amongst all non - empty subarrays.
+
+    Raises:
+      ValueError: when nums is empty.
+
+    >>> max_subarray_sum([1,2,3,4,-2])
     10
-    >>> max_subarray([-2,1,-3,4,-1,2,1,-5,4])
+    >>> max_subarray_sum([-2,1,-3,4,-1,2,1,-5,4])
     6
     """
+    if not nums:
+        raise ValueError("Input sequence should not be empty")
 
     curr_max = ans = nums[0]
+    nums_len = len(nums)
 
-    for i in range(1, len(nums)):
-        if curr_max >= 0:
-            curr_max = curr_max + nums[i]
-        else:
-            curr_max = nums[i]
-
+    for i in range(1, nums_len):
+        num = nums[i]
+        curr_max = max(curr_max + num, num)
         ans = max(curr_max, ans)
 
     return ans
@@ -23,4 +29,4 @@ def max_subarray(nums: list[int]) -> int:
 if __name__ == "__main__":
     n = int(input("Enter number of elements : ").strip())
     array = list(map(int, input("\nEnter the numbers : ").strip().split()))[:n]
-    print(max_subarray(array))
+    print(max_subarray_sum(array))