added visualization for day 7 puzzle 2

src/day7/puzzle2.typ

@@ -1,4 +1,5 @@
 #import "/src/utils.typ": *
+#import "@preview/cetz:0.3.1": canvas, draw
 
 #let concat(a, b) = {
   return int(str(a) + str(b))
@@ -53,8 +54,144 @@
   return total
 }
 
+#let visualize(input) = {
+  let get-solution(values, target) = {
+    if values.len() == 1 {
+      return (values.last() == target, (target,))
+    }
+
+    let values = values
+    let v = values.pop()
+    if calc.rem(target, v) == 0 {
+      let r = get-solution(values, target / v)
+      if r.first() {
+        return (true, r.last() + ("*", v))
+      }
+    }
+    let str-target = str(target)
+    let str-v = str(v)
+    if str-target == str-v {
+      return (false, ())
+    }
+    if str-target.ends-with(str-v) {
+      let target2 = str-target.slice(
+        0,
+        str-target.len() - str-v.len()
+      )
+      let r = get-solution(values, int(target2))
+      if r.first() {
+        return (true, r.last() + ("||", v))
+      }
+    }
+    if v > target {
+      return (false, ())
+    }
+
+    let r = get-solution(values, target - v)
+    if r.first() {
+      return (true, r.last() + ("+", v))
+    }
+    return (false, ())
+  }
+  let num(v, x, y, name) = {
+    draw.circle(
+      (x, y),
+      radius: 0.4,
+      fill: gray.lighten(60%),
+      name: name
+    )
+    draw.content((x, y), str(v))
+  }
+  let ope(o, x, y, name) = {
+    let s = (
+      "+": sym.plus,
+      "*": sym.times,
+      "||": sym.bar + sym.bar
+    ).at(o)
+    draw.circle(
+      (x, y),
+      radius: 0.3,
+      fill: orange.lighten(60%),
+      name: name
+    )
+    draw.content((x, y), s)
+  }
+
+  let equations = input.split("\n")
+  let diags = ()
+  for equation in equations {
+    let (target, values) = equation.split(": ")
+    target = int(target)
+    values = values.split(" ").map(int)
+
+    let r = get-solution(values, target)
+    if not r.first() {
+      continue
+    }
+    let diag = canvas({
+      let lvl = 0
+      let steps = r.last()
+      let prev = none
+      let v = steps.remove(0)
+
+      while true {
+        num(v, lvl, -lvl, str(lvl) + "-0")
+
+        if lvl != 0 {
+          draw.line(
+            str(lvl - 1) + "-1",
+            str(lvl) + "-0"
+          )
+        }
+
+        if steps.len() == 0 {
+          break
+        }
+
+        let op = steps.remove(0)
+        let v2 = steps.remove(0)
+
+        ope(op, lvl + 1, -lvl, str(lvl) + "-1")
+        num(v2, lvl + 2, -lvl, str(lvl) + "-2")
+        draw.line(
+          str(lvl) + "-0",
+          str(lvl) + "-1"
+        )
+        draw.line(
+          str(lvl) + "-2",
+          str(lvl) + "-1"
+        )
+        if op == "+" {
+          v += v2
+        } else if op == "*" {
+          v *= v2
+        } else if op == "||" {
+          v = int(str(v) + str(v2))
+        }
+
+        lvl += 1
+      }
+    })
+    diags.push(diag)
+  }
+
+  diags.last() = grid.cell(
+    colspan: 3 - calc.rem(diags.len() - 1, 3),
+    diags.last()
+  )
+
+  grid(
+    columns: 3,
+    stroke: (paint: black, dash: "dashed"),
+    align: center + horizon,
+    inset: 0.4em,
+    ..diags
+  )
+}
+
 #show-puzzle(
   7, 2,
   solve,
-  example: 11387
+  example: 11387,
+  visualize: visualize
 )