Path sum: three ways
Problem 82
NOTE: This problem is a more challenging version of Problem 81.
The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to 994.
Find the minimal path sum from the left column to the right column in matrix.txt (right click and "Save Link/Target As..."), a 31K text file containing an 80 by 80 matrix.
from tools import load_data_table_integers
def run(matrix=None):
if matrix is None:
matrix = load_data_table_integers(82, ',')
size = len(matrix)
out_of_bounds = float('inf')
cost = {}
left = 1
above = 2
below = 3
def search(y, x, whence=left):
if x == size - 1:
return matrix[y][x]
try:
return cost.setdefault((y, x), {})[whence]
except KeyError:
r, d, u = [out_of_bounds] * 3
if x + 1 < size:
r = search(y, x + 1, left)
if y + 1 < size and (whence == left or whence == above):
d = search(y + 1, x, above)
if y - 1 >= 0 and (whence == left or whence == below):
u = search(y - 1, x, below)
c = matrix[y][x] + min(r, d, u)
cost[(y, x)][whence] = c
# print y, x, cost[(y, x)]
return c
search(0, 0)
return min([min(cost[(y, 0)].values()) for y in range(size)])
def test():
m = [
[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],
]
assert run(m) == 994
if __name__ == '__main__':
test()