coins - top-down

gistfile1.txt

function change(amount, coins, idx, map = new Array(amount+1).fill(0)){
  if(map[amount][idx] > 0){
    return map[amount][idx];
  }
  if (idx >= coins.length - 1) return 1;
  let coin = coins[idx];
  let combos = 0;
  for (let i=0; i* coin <= amount; i++){
    let amountRemaining = amount - i * coin;
    combos += change(amountRemaining, coins, idx + 1, map);
  }
  map[amount][idx] = combos;
  return combos;
}

change(25,[25,10,5,1],0);