added visualization for day 10 puzzle 1

src/day10/puzzle1.typ

@@ -1,4 +1,5 @@
 #import "/src/utils.typ": *
+#import "@preview/cetz:0.3.1": canvas, draw, matrix
 
 #let offsets = (
   (-1, 0),
@@ -41,6 +42,38 @@
   return tails.len()
 }
 
+#let get-paths(grid, w, h, ox, oy) = {
+  let paths = ()
+  let tails = ()
+  let in-grid = in-grid.with(w, h)
+
+  let to-visit = ((ox, oy),)
+  while to-visit.len() != 0 {
+    let (x, y) = to-visit.remove(0)
+    let v = grid.at(y).at(x)
+    for (dx, dy) in offsets {
+      let (x2, y2) = (x + dx, y + dy)
+      if not in-grid(x2, y2) {
+        continue
+      }
+      let v2 = grid.at(y2).at(x2)
+      if v2 == v + 1 {
+        let pos2 = (x2, y2)
+        if v2 == 9 {
+          if pos2 not in tails {
+            tails.push(pos2)
+            paths.push(((ox, oy), (x2, y2)))
+          }
+        } else {
+          to-visit.push(pos2)
+        }
+      }
+    }
+  }
+
+  return paths
+}
+
 #let solve(input) = {
   let grid = input.split("\n").map(l => l.clusters().map(int))
 
@@ -61,8 +94,50 @@
   return total
 }
 
+#let visualize(input) = {
+  let grid = input.split("\n").map(l => l.clusters().map(int))
+
+  let w = grid.first().len()
+  let h = grid.len()
+
+  let count-paths = count-paths.with(grid, w, h)
+  let get-paths = get-paths.with(grid, w, h)
+
+  let total = 0
+  canvas({
+    let starts = ()
+    let c
+    for y in range(h) {
+      for x in range(w) {
+        c = grid.at(y).at(x)
+        draw.rect(
+          (x, -y),
+          (x + 1, -y - 1),
+          fill: black.lighten((9 - c) / 9 * 90% + 10%)
+        )
+        if c == 0 {
+          starts.push((x, y))
+        }
+      }
+    }
+    for (ox, oy) in starts {
+      let paths = get-paths(ox, oy)
+      for path in paths {
+        draw.line(
+          ..path.map(
+            ((x, y)) => (x + .5, -y - .5)
+          ),
+          stroke: red,
+          mark: (end: ">")
+        )
+      }
+    }
+  })
+}
+
 #show-puzzle(
   10, 1,
   solve,
-  example: 36
+  example: 36,
+  visualize: visualize
 )