euler-problem-15.js

// V1

var cache = {};

function paths(rights, downs) {
  var key = rights + ',' + downs;
  if (cache[key]) return cache[key];

  if (rights === 0 || downs === 0) {
    return 1;
  }

  var value = paths(rights - 1, downs) + paths(rights, downs - 1);
  cache[key] = value;
  return value;
}

console.log(paths(20, 20)); // 6


// V2

function memoize(fn) {
  var cache = {};

  return function (...args) {
    var key = args.join(',');

    if (cache[key] !== undefined) {
      return cache[key];
    }

    var value = fn(...args);
    cache[key] = value;
    return value;
  }
}

function paths(rights, downs) {
  if (rights === 0 || downs === 0) {
    return 1;
  }

  return paths(rights - 1, downs) + paths(rights, downs - 1);
}

paths = memoize(paths);

console.log(paths(20, 20)); // 6