Dynamic programming self-tuition - minimal number of coins needed to reach a given total amount

MinimalNumberOfCoins.js

function minNumOfCoins(coinages, amount) {
  if (amount === 0) return 0;
  if (coinages.length === 0 && amount > 0) return Infinity;

  var maxCoinage = Math.max.apply(null, coinages);
  var otherCoinages = coinages.filter(coinage => coinage !== maxCoinage)
  if (amount < maxCoinage) return minNumOfCoins(otherCoinages, amount);

  var coinsWithMaxCoinage = minNumOfCoins(coinages, amount - maxCoinage) + 1;
  var coinsWithoutMaxCoinage = minNumOfCoins(otherCoinages, amount);
  return Math.min(coinsWithMaxCoinage, coinsWithoutMaxCoinage);
}

This one comes from https://codility.com/media/train/15-DynamicProgramming.pdf, and it is kinda uit de lucht gegrepen...
Recursion instead of state matrix.