answer.js

const input = '1 4 5 6 7 8'
const arr = input.split(' ').map(Number)

console.log(`\ninput:\n ${input}\n\noutput:`)

for (let i = 1; arr.length > i; i++) {
  compare(arr.slice(0, i), arr.slice(i))
}

function compare(left, right) {
  const lc = allCases(left)
  const rc = allCases(right)
  const rr = Object.keys(rc)
  Object.keys(lc).forEach((lr, i) => {
    const copied = rr.slice()
    const ris = []
    while (copied.indexOf(lr) !== -1) {
      const p = copied.indexOf(lr)
      ris.push(p)
      copied.splice(p, 1)
    }
    ris.forEach((ri) => {
      lc[lr].forEach((la) => {
        rc[rr[ri]].forEach((ra) => {
          console.log(` ${la} = ${ra}`)
        })
      })
    })
  })
}

function allCases(list) {
  if (list.length === 1) {
    const out = {}
    out[list] = list
    return out
  }
  const cases = {}
  const patterns = []
  const operations = ['+', '-', '*']
  const len = list.length - 1
  for (let i = 0; operations.length ** len > i; i++) {
    patterns.push(i.toString(3).padStart(len, '0'))
  }
  patterns.forEach((a) => {
    let p = 1
    const item = list.slice()
    a.split('').map((b, i) => {
      item.splice(i + p, 0, operations[b])
      p += 1
    })
    const ex = item.join('')
    const res = rpn(ex)
    if (!cases[res]) cases[res] = []
    cases[res].push(ex)
  })
  return cases
}

function rpn (input) {
  const p = []
  const s = []
  const prio = (i) => {
    if (i === '+' || i === '-') return 2
    if (i === '*') return 1
    return 0
  }

  input.split('').forEach((n, i) => {
    if (i === 0) return s.push(n)
    const c = prio(n)
    let l = prio(s.slice(-1)[0])
    if (l > c) return s.push(n)
    while (c >= l && s.length !== 0) {
      p.push(s.pop())
      l = prio(s.slice(-1)[0])
    }
    s.push(n)
  })

  const ex = p.concat(s.reverse())
  const t = []

  ex.forEach((item) => {
    if (Number.isInteger(Number(item))) return t.push(Number(item))
    const f = t.pop()
    const s = t.pop()
    if (item === '+') return t.push(s + f)
    if (item === '-') return t.push(s - f)
    if (item === '*') return t.push(s * f)
  })

  return t.pop()
}

計算量減らしたい