--- Example ---

let example = """..##.......
#...#...#..
.#....#..#.
..#.#...#.#
.#...##..#.
..#.##.....
.#.#.#....#
.#........#
#.##...#...
#...##....#
.#..#...#.#""".strip
echo example

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

type
  StrideMap = object
    data: seq[char]
    stride: int
    height: int

  Shape = tuple[stride, height: int]
proc parse(text: string): StrideMap =
  for line in text.splitLines:
    inc result.height
    result.data.add toSeq(line)
    if result.stride > 0 and line.len != result.stride:
      echo "ParseError: line does not matches stride"
    result.stride = line.len

let map0 = parse example
func shape(m: StrideMap): Shape =
  (m.stride, m.height)

echo "shape:", map0.shape

shape:(stride: 11, height: 11)

let's add coordinates:

type
  Point = tuple[x, y: int]
proc index(p: Point; m: StrideMap): int =
  var x = p.x mod m.stride
  if p.y >= m.height:
    echo "ERROR: point too low!"
  x + p.y * m.stride

proc `[]`(m: StrideMap; p: Point): char =
  m.data[p.index m]

for p in [(3, 1), (6, 2)]:
  echo p
  echo "index: ", p.index(map0)
  echo "on map: ", map0[p]

(3, 1)
index: 14
on map: .
(6, 2)
index: 28
on map: #

type
  Slope = tuple[dx, dy: int]
  Path = seq[Point]
  Ride = tuple[path: Path, ntrees: int]
proc `+`(p: Point; s: Slope): Point =
  result.x = p.x + s.dx
  result.y = p.y + s.dy

proc ride(m: StrideMap; s: Slope): Ride =
  var p: Point
  let ySteps = m.height div s.dy
  for i in 1 ..< ySteps:
    p = p + s
    result.path.add p
    if m[p] == '#':
      inc result.ntrees

let ride0 = ride(map0, (3, 1))
echo "ntrees: ", ride0.ntrees

ntrees: 7

--- Part 1 ---

now we are equipped to solve part1:

let
  input = "2020/input03.txt".readFile
  map1 = parse input
  ride1 = ride(map1, (3, 1))
echo "part1: ", ride1.ntrees

part1: 205

That's the right answer! You are one gold star closer to saving your vacation.

--- Part 2 ---

easy second part

tricky last slope made me discover my implementation bug!

now onto part2 on my puzzle input

part2 = 1
for slope in slopes:
  part2 *= ride(map1, slope).ntrees
echo "part2: ", part2

part2: 3952146825

That's the right answer! You are one gold star closer to saving your vacation.

Visualizations

I want to try to take advantage of the fact that I output html.

I will reproduce the explantory design showing the ride through the example.

proc show(m: StrideMap; r: Ride; repeat = 6) =
  var line = ""
  var
    i = 0
    j = 0
    p: Point = r.path[j]
    c: char
  for y in 0 ..< m.height:
    for x in 0 ..< m.stride:
      line.add m.data[i]
      inc i
    line = line.repeat(repeat)
    if y == p.y:
      c = if m[p] == '.':
        'O' else:
        'X'
      line = line[0 ..< p.x] & "<em>" & $c & "</em>" & line[p.x + 1 .. ^1]
      inc j
      if j < r.path.len:
        p = r.path[j]
    echo line
    line = ""

show(map0, ride0)
echo map1.shape

..##.........##.........##.........##.........##.........##.......
#..O#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
.#....X..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
..#.#...#O#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
.#...##..#..X...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
..#.##.......#.X#.......#.##.......#.##.......#.##.......#.##.....
.#.#.#....#.#.#.#.O..#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
.#........#.#........X.#........#.#........#.#........#.#........#
#.##...#...#.##...#...#.X#...#...#.##...#...#.##...#...#.##...#...
#...##....##...##....##...#X....##...##....##...##....##...##....#
.#..#...#.#.#..#...#.#.#..#...X.#.#..#...#.#.#..#...#.#.#..#...#.#
(stride: 31, height: 323)