Time to check the rest of the slopes — you need to minimize the probability of a sudden arboreal stop, after all.

Determine the number of trees you would encounter if, for each of the following slopes, you start at the top-left corner and traverse the map all the way to the bottom:

• Right 1, down 1.
• Right 3, down 1. (This is the slope you already checked.)
• Right 5, down 1.
• Right 7, down 1.
• Right 1, down 2.

Along the same map we used before:

..##.......
#...#...#..
.#....#..#.
..#.#...#.#
.#...##..#.
..#.##.....
.#.#.#....#
.#........#
#.##...#...
#...##....#
.#..#...#.#

these slopes would find 2, 7, 3, 4, and 2 trees respectively.

Assignment

Write a function count_trees that takes three arguments: i) an integer \(r \in \mathbb{N}_0\) (int), ii) an integer \(d \in \mathbb{N}_0\) (int), and iii) the pathname (str) of a text file containing a map of the open squares (.) and trees (#) on a slope. The function must return the number of trees (int) you would encounter when starting at the top-left corner of the map and following a slope of right \(r\) and down \(d\).

Example

In this interactive session we assume the text file slope.txt¹ to be located in the current directory.

>>> count_trees(1, 1, 'slope.txt')
2
>>> count_trees(3, 1, 'slope.txt')
7
>>> count_trees(5, 1, 'slope.txt')
3
>>> count_trees(7, 1, 'slope.txt')
4
>>> count_trees(1, 2, 'slope.txt')
2