Add solution to Project Euler problem 81 (#3408)

* Add solution to problem 81 - project euler

* Update project_euler/problem_081/sol1.py
Co-authored-by: NChristian Clauss <cclauss@me.com>

* Update project_euler/problem_081/sol1.py
Co-authored-by: NChristian Clauss <cclauss@me.com>
Co-authored-by: NChristian Clauss <cclauss@me.com>

project_euler/problem_081/sol1.py

+"""
+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), "r") 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() = }")