euler15.js

function countPossibilities(n, m) {
  if (n === -1 || m === -1) {
    return 0;
  } else if (n === 0 && m === 0) {
    return 1;
  }

  return countPossibilities(n-1, m) + countPossibilities(n, m-1);
}

function memoize(f) {
  let memoTable = {};
  return function (...args) {
    const key = JSON.stringify(args);

    if (!memoTable[key]) {
      memoTable[key] = f(...args);
    }

    return memoTable[key];
  }
}

countPossibilities = memoize(countPossibilities);


function fac(n) {
  let res = 1;

  while (n > 0) {
    res *= n;
    n -= 1;
  }

  return res;
}

function combinations(n, k) {
  return fac(n)/(fac(k) * fac(n-k));
}

function efficientCountPossibilities(n) {
  return Math.round(combinations(n*2, n));
}