Advent of Code 2022 - Day 21: Monkey Math Solution

Complex number

Part 1

Straightforward recursion to calculate value

Parsed data

1{
2  root: [ 'pppw', '+', 'sjmn' ],
3  dbpl: 5,
4  cczh: [ 'sllz', '+', 'lgvd' ],
5  zczc: 2,
6  ptdq: [ 'humn', '-', 'dvpt' ],
7  dvpt: 3,
8  lfqf: 4,
9  humn: 5,
10  ljgn: 2,
11  sjmn: [ 'drzm', '*', 'dbpl' ],
12  sllz: 4,
13  pppw: [ 'cczh', '/', 'lfqf' ],
14  lgvd: [ 'ljgn', '*', 'ptdq' ],
15  drzm: [ 'hmdt', '-', 'zczc' ],
16  hmdt: 32
17}

Implementation

1const fs = require("fs")
2
3const getFuncFromOperator = operator =>
4  ({
5    "+": (a, b) => a + b,
6    "-": (a, b) => a - b,
7    "*": (a, b) => a * b,
8    "/": (a, b) => a / b,
9  }[operator])
10
11const readData = () => {
12  const data = fs
13    .readFileSync("./input", "utf-8")
14    .split(/\r?\n/)
15    .filter(Boolean)
16    .map(line => line.split(": "))
17    .map(([key, value]) => [
18      key,
19      Number.isNaN(Number(value)) ? value.split(" ") : Number(value),
20    ])
21
22  return Object.fromEntries(data)
23}
24
25const main = () => {
26  const data = readData()
27
28  const recursion = name => {
29    const value = data[name]
30
31    if (Number.isInteger(value)) return value
32
33    const [operand1, operator, operand2] = value
34    const func = getFuncFromOperator(operator)
35
36    return func(recursion(operand1), recursion(operand2))
37  }
38
39  const res = recursion("root")
40
41  console.log(res)
42}
43
44main()

Part 2

Convert to complex number, unknown humn could be store in imaginary part

Parsed data

1{
2  root: [ 'pppw', '+', 'sjmn' ],
3  dbpl: { real: 5, imag: 0 },
4  cczh: [ 'sllz', '+', 'lgvd' ],
5  zczc: { real: 2, imag: 0 },
6  ptdq: [ 'humn', '-', 'dvpt' ],
7  dvpt: { real: 3, imag: 0 },
8  lfqf: { real: 4, imag: 0 },
9  humn: { real: 0, imag: 1 },
10  ljgn: { real: 2, imag: 0 },
11  sjmn: [ 'drzm', '*', 'dbpl' ],
12  sllz: { real: 4, imag: 0 },
13  pppw: [ 'cczh', '/', 'lfqf' ],
14  lgvd: [ 'ljgn', '*', 'ptdq' ],
15  drzm: [ 'hmdt', '-', 'zczc' ],
16  hmdt: { real: 32, imag: 0 }
17}

Recursively calculate lefh-hand side (LHS), right-hand side (RHS) of root and we will get 2 complex numbers

Calculate imaginary from

1LHS = RHS

to get humn value

Operations for complex number could be refered from Wikipedia or any mathemetic blogs

Implementation

1const fs = require("fs")
2
3const getFuncFromOperator = operator =>
4  ({
5    "+": ({ real: x, imag: y }, { real: u, imag: v }) => ({
6      real: x + u,
7      imag: y + v,
8    }),
9    "-": ({ real: x, imag: y }, { real: u, imag: v }) => ({
10      real: x - u,
11      imag: y - v,
12    }),
13    "*": ({ real: x, imag: y }, { real: u, imag: v }) => ({
14      real: x * u - y * v,
15      imag: x * v + y * u,
16    }),
17    "/": ({ real: x, imag: y }, { real: u, imag: v }) => ({
18      real: (x * u + y * v) / (u ** 2 + v ** 2),
19      imag: (y * u - x * v) / (u ** 2 + v ** 2),
20    }),
21  }[operator])
22
23const readData = () => {
24  const data = fs
25    .readFileSync("./input", "utf-8")
26    .split(/\r?\n/)
27    .filter(Boolean)
28    .map(line => line.split(": "))
29    .map(([key, value]) => [
30      key,
31      Number.isNaN(Number(value))
32        ? value.split(" ")
33        : { real: Number(value), imag: 0 },
34    ])
35
36  return Object.fromEntries(data)
37}
38
39const main = () => {
40  const data = readData()
41
42  const recursion = name => {
43    const value = data[name]
44
45    if (!Array.isArray(value)) return value
46
47    const func = getFuncFromOperator(value[1])
48
49    value[0] = recursion(value[0])
50    value[2] = recursion(value[2])
51
52    return func(value[0], value[2])
53  }
54
55  data["humn"] = { real: 0, imag: 1 }
56  recursion("root")
57
58  let [lhs, _, rhs] = data["root"]
59
60  if (rhs.imag) {
61    ;[lhs, rhs] = [rhs, lhs]
62  }
63
64  const res = Math.floor((rhs.real - lhs.real) / lhs.imag)
65
66  console.log(res)
67}
68
69main()