Useful JS Tips

#29 - Speed up recursive functions with memoization

2016-01-29 by @hingsir

Fibonacci sequence is very familiar to everybody. We can write the following function in 20 seconds.

var fibonacci = function(n) {
  return n < 2 ? n : fibonacci(n - 1) + fibonacci(n - 2);
}

It works, but is not efficient. It did lots of duplicate computing works, we can cache its previously computed results to speed it up.

var fibonacci = (function() {
  var cache = [0, 1]; // cache the value at the n index
  return function(n) {
    if (cache[n] === undefined) {
      for (var i = cache.length; i <= n; ++i) {
        cache[i] = cache[i - 1] + cache[i - 2];
      }
    }
    return cache[n];
  }
})();

Also, we can define a higher-order function that accepts a function as its argument and returns a memoized version of the function.

var memoize = function(func) {
  var cache = {};
  return function() {
    var key = JSON.stringify(Array.prototype.slice.call(arguments));
    return key in cache ? cache[key] : (cache[key] = func.apply(this, arguments));
  }
}
fibonacci = memoize(fibonacci);

And this is an ES6 version of the memoize function.

var memoize = function(func) {
  const cache = {};
  return (...args) => {
    const key = JSON.stringify(args);
    return key in cache ? cache[key] : (cache[key] = func(...args));
  }
}
fibonacci = memoize(fibonacci);

we can use memoize() in many other situations

  • GCD(Greatest Common Divisor)
var gcd = memoize(function(a, b) {
  var t;
  if (a < b) t = b, b = a, a = t;
  while (b != 0) t = b, b = a % b, a = t;
  return a;
});
gcd(27, 183); //=> 3
  • Factorial calculation
var factorial = memoize(function(n) {
  return (n <= 1) ? 1 : n * factorial(n - 1);
})
factorial(5); //=> 120

Learn more about memoization:

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