mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
b8fdd81f28
* 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>
64 lines
1.5 KiB
Python
64 lines
1.5 KiB
Python
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()
|