Added Manhattan distance algorithm (#7790)

* Added Manhattan distance algorithm, Fixes: #7776

* Forgot that isinstance can accept a tuple

* Apply suggestions from code review

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

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* Update manhattan_distance.py

* Update manhattan_distance.py

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

maths/manhattan_distance.py

@@ -0,0 +1,126 @@
+def manhattan_distance(point_a: list, point_b: list) -> float:
+    """
+    Expectts two list of numbers representing two points in the same
+    n-dimensional space
+
+    https://en.wikipedia.org/wiki/Taxicab_geometry
+
+    >>> manhattan_distance([1,1], [2,2])
+    2.0
+    >>> manhattan_distance([1.5,1.5], [2,2])
+    1.0
+    >>> manhattan_distance([1.5,1.5], [2.5,2])
+    1.5
+    >>> manhattan_distance([-3, -3, -3], [0, 0, 0])
+    9.0
+    >>> manhattan_distance([1,1], None)
+    Traceback (most recent call last):
+         ...
+    ValueError: Missing an input
+    >>> manhattan_distance([1,1], [2, 2, 2])
+    Traceback (most recent call last):
+         ...
+    ValueError: Both points must be in the same n-dimensional space
+    >>> manhattan_distance([1,"one"], [2, 2, 2])
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found str
+    >>> manhattan_distance(1, [2, 2, 2])
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found int
+    >>> manhattan_distance([1,1], "not_a_list")
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found str
+    """
+
+    _validate_point(point_a)
+    _validate_point(point_b)
+    if len(point_a) != len(point_b):
+        raise ValueError("Both points must be in the same n-dimensional space")
+
+    return float(sum(abs(a - b) for a, b in zip(point_a, point_b)))
+
+
+def _validate_point(point: list[float]) -> None:
+    """
+    >>> _validate_point(None)
+    Traceback (most recent call last):
+         ...
+    ValueError: Missing an input
+    >>> _validate_point([1,"one"])
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found str
+    >>> _validate_point(1)
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found int
+    >>> _validate_point("not_a_list")
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found str
+    """
+    if point:
+        if isinstance(point, list):
+            for item in point:
+                if not isinstance(item, (int, float)):
+                    raise TypeError(
+                        f"Expected a list of numbers as input, "
+                        f"found {type(item).__name__}"
+                    )
+        else:
+            raise TypeError(
+                f"Expected a list of numbers as input, found {type(point).__name__}"
+            )
+    else:
+        raise ValueError("Missing an input")
+
+
+def manhattan_distance_one_liner(point_a: list, point_b: list) -> float:
+    """
+    Version with one liner
+
+    >>> manhattan_distance_one_liner([1,1], [2,2])
+    2.0
+    >>> manhattan_distance_one_liner([1.5,1.5], [2,2])
+    1.0
+    >>> manhattan_distance_one_liner([1.5,1.5], [2.5,2])
+    1.5
+    >>> manhattan_distance_one_liner([-3, -3, -3], [0, 0, 0])
+    9.0
+    >>> manhattan_distance_one_liner([1,1], None)
+    Traceback (most recent call last):
+         ...
+    ValueError: Missing an input
+    >>> manhattan_distance_one_liner([1,1], [2, 2, 2])
+    Traceback (most recent call last):
+         ...
+    ValueError: Both points must be in the same n-dimensional space
+    >>> manhattan_distance_one_liner([1,"one"], [2, 2, 2])
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found str
+    >>> manhattan_distance_one_liner(1, [2, 2, 2])
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found int
+    >>> manhattan_distance_one_liner([1,1], "not_a_list")
+    Traceback (most recent call last):
+         ...
+    TypeError: Expected a list of numbers as input, found str
+    """
+
+    _validate_point(point_a)
+    _validate_point(point_b)
+    if len(point_a) != len(point_b):
+        raise ValueError("Both points must be in the same n-dimensional space")
+
+    return float(sum(abs(x - y) for x, y in zip(point_a, point_b)))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()