makeChange.js

function makeChange(x, coinSet) {
  const mem = []

  const getChangeCoins = (value) => {
    if (!value) {
      return []
    }

    if (mem[value]) {
      return mem[value]
    }

    let change = []
    let newChange
    let residue

    for (let i = 0; i < coinSet.length; i++) {
      const coin = coinSet[i]

      residue = value - coin
    
      if (residue >= 0) {
        newChange = getChangeCoins(residue)
      }

      if (residue >= 0
        && (newChange.length < change.length - 1 || !change.length)
        && (newChange.length || !residue)) {
        change = [coin].concat(newChange)
      }
    }

    mem[value] = change

    return change
  }

  const changeCoins = getChangeCoins(x)

  if (changeCoins.length === 0) {
    throw new Error('Change Not Possible')
  }

  const change = {}
  for (let i = 0; i < changeCoins.length; i++) {
    const coin = changeCoins[i]
    if (!change[coin]) {
      change[coin] = 1
    } else {
      change[coin] += 1
    }
  }

  return change
}

console.log(makeChange(8, [2,5,10,25]))
console.log(makeChange(6, [1,5,10,25]))
console.log(makeChange(6, [3,4]))
console.log(makeChange(6, [1,3,4]))
console.log(makeChange(6, [5,7]))