chem.ts

class Count {
  data: Record<string, number> = Object.create(null)

  merge(other: Count, multiplyBy = 1) {
    for (const key in other.data) {
      this.data[key] = (this.data[key] ?? 0) + other.data[key]! * multiplyBy
    }
  }
}

function count([text]: readonly [string] | TemplateStringsArray): Count {
  const data = new Count()

  const regex = /([A-Za-z]+)\s*(\d*)|\(([^)]+)\)\s*(\d*)/g
  let m: RegExpExecArray | null
  while ((m = regex.exec(text!))) {
    if (m[1]) {
      data.data[m[1]] = (data.data[m[1]] ?? 0) + Number(m[2] ?? 1)
    } else {
      data.merge(count([m[3]!]), +(m[4] ?? 1))
    }
  }

  return data
}

function det(matrix: number[][]) {
  if (matrix.length == 0) {
    return 0
  }

  if (matrix.length == 1) {
    return 1
  }

  if (matrix.length == 2) {
    return matrix[0]![0]! * matrix[1]![1]! - matrix[0]![1]! * matrix[1]![0]!
  }

  let sum = 0

  for (let i = 0; i < matrix.length; i++) {
    const next = withoutColumn(matrix.slice(1), i)
    sum += (i % 2 ? -1 : 1) * matrix[0]![i]! * det(next)
  }

  return sum
}

function withoutColumn(data: number[][], column: number) {
  return data.slice(1).map((x) => {
    const copy = x.slice()
    copy.splice(column, 1)
    return copy
  })
}

function getColumn(data: number[][], col: number) {
  return data.map((row) => row[col]!)
}

function withColumnAs(data: number[][], col: number, colData: number[]) {
  return data.map((row, index) => {
    const copy = row.slice()
    copy[col] = colData[index]!
    return col
  })
}

function solve(data: number[][]) {
  const vars = withoutColumn(data, data.length - 1)

  const D = det(vars)

  return Array.from({ length: vars.length }, (_, index) => {
    return det(withoutColumn(vars, index)) / D
  })
}