--description--

There are four types of common coins in US currency:

<ul> <li>quarters (25 cents)</li> <li>dimes (10 cents)</li> <li>nickels (5 cents), and</li> <li>pennies (1 cent)</li> </ul> <p>There are six ways to make change for 15 cents:</p> <ul> <li>A dime and a nickel</li> <li>A dime and 5 pennies</li> <li>3 nickels</li> <li>2 nickels and 5 pennies</li> <li>A nickel and 10 pennies</li> <li>15 pennies</li> </ul>

--instructions--

Implement a function to determine how many ways there are to make change for a given input, cents, that represents an amount of US pennies using these common coins.

--hints--

countCoins should be a function.

assert(typeof countCoins === 'function');

countCoins(15) should return 6.

assert.equal(countCoins(15), 6);

countCoins(85) should return 163.

assert.equal(countCoins(85), 163);

countCoins(100) should return 242.

assert.equal(countCoins(100), 242);

--seed--

--seed-contents--

function countCoins(cents) {

  return true;
}

--solutions--

function countCoins(cents) {
  const operands = [1, 5, 10, 25];
  const targetsLength = cents + 1;
  const operandsLength = operands.length;
  const t = [1];

  for (let a = 0; a < operandsLength; a++) {
    for (let b = 1; b < targetsLength; b++) {
      // initialise undefined target
      t[b] = t[b] ? t[b] : 0;

      // accumulate target + operand ways
      t[b] += (b < operands[a]) ? 0 : t[b - operands[a]];
    }
  }

  return t[targetsLength - 1];
}