freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-31-coin-sums.english.md

id, challengeType, title

id	challengeType	title
5900f38b1000cf542c50fe9e	5	Problem 31: Coin sums

Description

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p). It is possible to make £2 in the following way: 1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p How many different ways can £(n) be made using any number of coins?

Instructions

Tests

tests:
  - text: <code>coinSums(50)</code> should return 451.
    testString: assert(coinSums(50) == 451, '<code>coinSums(50)</code> should return 451.');
  - text: <code>coinSums(100)</code> should return 4563.
    testString: assert(coinSums(100) == 4563, '<code>coinSums(100)</code> should return 4563.');
  - text: <code>coinSums(150)</code> should return 21873.
    testString: assert(coinSums(150) == 21873, '<code>coinSums(150)</code> should return 21873.');
  - text: <code>coinSums(200)</code> should return 73682.
    testString: assert(coinSums(200) == 73682, '<code>coinSums(200)</code> should return 73682.');

Challenge Seed

function coinSums(n) {
  // Good luck!
  return n;
}

coinSums(200);

Solution

const coinSums = (n) => {
  const getWays = (n, m=8, c=[1, 2, 5, 10, 20, 50, 100, 200]) => {
    if (n === 0) return 1;
    if (m === 0 || n < 0) return 0;
    return getWays(n - c[m - 1], m, c) + getWays(n, m - 1, c);
  };
  return getWays(n);
};