Python/project_euler/problem_081/sol1.py

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"""
Problem 81: https://projecteuler.net/problem=81
In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right,
by only moving to the right and down, is indicated in bold red and is equal to 2427.
[131] 673 234 103 18
[201] [96] [342] 965 150
630 803 [746] [422] 111
537 699 497 [121] 956
805 732 524 [37] [331]
Find the minimal path sum from the top left to the bottom right by only moving right
and down in matrix.txt (https://projecteuler.net/project/resources/p081_matrix.txt),
a 31K text file containing an 80 by 80 matrix.
"""
import os
def solution(filename: str = "matrix.txt") -> int:
"""
Returns the minimal path sum from the top left to the bottom right of the matrix.
>>> solution()
427337
"""
with open(os.path.join(os.path.dirname(__file__), filename)) as in_file:
data = in_file.read()
grid = [[int(cell) for cell in row.split(",")] for row in data.strip().splitlines()]
dp = [[0 for cell in row] for row in grid]
n = len(grid[0])
dp = [[0 for i in range(n)] for j in range(n)]
dp[0][0] = grid[0][0]
for i in range(1, n):
dp[0][i] = grid[0][i] + dp[0][i - 1]
for i in range(1, n):
dp[i][0] = grid[i][0] + dp[i - 1][0]
for i in range(1, n):
for j in range(1, n):
dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
return dp[-1][-1]
if __name__ == "__main__":
print(f"{solution() = }")