Python/graphs/minimum_path_sum.py

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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()