Create maximum_subsequence.py (TheAlgorithms#7811)

Author: pronoym99

Diff for: DIRECTORY.md

@@ -716,6 +716,7 @@
   * [Lru Cache](other/lru_cache.py)
   * [Magicdiamondpattern](other/magicdiamondpattern.py)
   * [Maximum Subarray](other/maximum_subarray.py)
+  * [Maximum Subsequence](other/maximum_subsequence.py)
   * [Nested Brackets](other/nested_brackets.py)
   * [Password](other/password.py)
   * [Quine](other/quine.py)

Diff for: other/maximum_subsequence.py

@@ -0,0 +1,42 @@
+from collections.abc import Sequence
+
+
+def max_subsequence_sum(nums: Sequence[int] | None = None) -> int:
+    """Return the maximum possible sum amongst all non - empty subsequences.
+
+    Raises:
+      ValueError: when nums is empty.
+
+    >>> max_subsequence_sum([1,2,3,4,-2])
+    10
+    >>> max_subsequence_sum([-2, -3, -1, -4, -6])
+    -1
+    >>> max_subsequence_sum([])
+    Traceback (most recent call last):
+        . . .
+    ValueError: Input sequence should not be empty
+    >>> max_subsequence_sum()
+    Traceback (most recent call last):
+        . . .
+    ValueError: Input sequence should not be empty
+    """
+    if nums is None or not nums:
+        raise ValueError("Input sequence should not be empty")
+
+    ans = nums[0]
+    for i in range(1, len(nums)):
+        num = nums[i]
+        ans = max(ans, ans + num, num)
+
+    return ans
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Try on a sample input from the user
+    n = int(input("Enter number of elements : ").strip())
+    array = list(map(int, input("\nEnter the numbers : ").strip().split()))[:n]
+    print(max_subsequence_sum(array))