Add minmum path sum (#5882)

* commit on 'shortest_path_sum'

* minimum_path_sum updated

* commit to 'minimum_path_sum'

* added description to minimum_path_sum

* bot requirements fixed for

* Update minimum_path_sum.py

* Update minimum_path_sum.py

Co-authored-by: John Law <johnlaw.po@gmail.com>

graphs/minimum_path_sum.py

@@ -0,0 +1,63 @@
+def min_path_sum(grid: list) -> int:
+    """
+    Find the path from top left to bottom right of array of numbers
+    with the lowest possible sum and return the sum along this path.
+    >>> min_path_sum([
+    ...     [1, 3, 1],
+    ...     [1, 5, 1],
+    ...     [4, 2, 1],
+    ... ])
+    7
+
+    >>> min_path_sum([
+    ...     [1, 0, 5, 6, 7],
+    ...     [8, 9, 0, 4, 2],
+    ...     [4, 4, 4, 5, 1],
+    ...     [9, 6, 3, 1, 0],
+    ...     [8, 4, 3, 2, 7],
+    ... ])
+    20
+
+    >>> min_path_sum(None)
+    Traceback (most recent call last):
+        ...
+    TypeError: The grid does not contain the appropriate information
+
+    >>> min_path_sum([[]])
+    Traceback (most recent call last):
+        ...
+    TypeError: The grid does not contain the appropriate information
+    """
+
+    if not grid or not grid[0]:
+        raise TypeError("The grid does not contain the appropriate information")
+
+    for cell_n in range(1, len(grid[0])):
+        grid[0][cell_n] += grid[0][cell_n - 1]
+    row_above = grid[0]
+
+    for row_n in range(1, len(grid)):
+        current_row = grid[row_n]
+        grid[row_n] = fill_row(current_row, row_above)
+        row_above = grid[row_n]
+
+    return grid[-1][-1]
+
+
+def fill_row(current_row: list, row_above: list) -> list:
+    """
+    >>> fill_row([2, 2, 2], [1, 2, 3])
+    [3, 4, 5]
+    """
+
+    current_row[0] += row_above[0]
+    for cell_n in range(1, len(current_row)):
+        current_row[cell_n] += min(current_row[cell_n - 1], row_above[cell_n])
+
+    return current_row
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()