Added maximum non-adjacent sum (#2130)

* Added maximum non-adjacent sum

* Bugfix: flake8 test

* Implemented changes (broke tuple unpacking into 2 lines due to flake8 tests)

* Implemented changes v2.0

* Update max_non_adjacent_sum.py

Co-authored-by: Christian Clauss <cclauss@me.com>

dynamic_programming/max_non_adjacent_sum.py

@@ -0,0 +1,33 @@
+# Video Explaination: https://www.youtube.com/watch?v=6w60Zi1NtL8&feature=emb_logo
+
+from typing import List
+
+
+def maximum_non_adjacent_sum(nums: List[int]) -> int:
+    '''
+    Find the maximum non-adjacent sum of the integers in the nums input list
+
+    >>> print(maximum_non_adjacent_sum([1, 2, 3]))
+    4
+    >>> maximum_non_adjacent_sum([1, 5, 3, 7, 2, 2, 6])
+    18
+    >>> maximum_non_adjacent_sum([-1, -5, -3, -7, -2, -2, -6])
+    0
+    >>> maximum_non_adjacent_sum([499, 500, -3, -7, -2, -2, -6])
+    500
+    '''
+    if not nums:
+        return 0
+    max_including = nums[0]
+    max_excluding = 0
+    for num in nums[1:]:
+        max_including, max_excluding = (
+            max_excluding + num, max(max_including, max_excluding)
+        )
+    return max(max_excluding, max_including)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()