The optimal solution to shuffle an Array in Javascript

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I recently met a small issue on creating a new randomly ordered array based on an old one. To speak shortly, the final goal is to get a shuffled array.

The following is my solution after a few moment's experiment before I search the web. (I thought I could do it myself :p)

var arr = [1, 2, 3, 4, 5, 6, 7]

function shuffle (arr) {
  let i = 0,
      res = [],
      index

  while (i <= arr.length - 1) {
    index = Math.floor(Math.random() * arr.length)

    if (!res.includes(arr[index])) {
      res.push(arr[index])
      i++
    }
  }

  return res
}

// expected
arr = shuffle(arr)
// [6, 3, 4, 1, 7, 2, 5]

As you can see that this is not a good way handle shuffling, so I decide to do some researches over it.

After looking for some answers on google and stackoverflow, I found a most satisfying solution to shuffle an array. (The answer has been there since 2010... But, very qualified indeed.)

First things first, let's take a look at the answer. It's quite simple but fast enough.

function shuffle(array) {
  var currentIndex = array.length, temporaryValue, randomIndex;

  // While there remain elements to shuffle...
  while (0 !== currentIndex) {

    // Pick a remaining element...
    randomIndex = Math.floor(Math.random() * currentIndex);
    currentIndex -= 1;

    // And swap it with the current element.
    temporaryValue = array[currentIndex];
    array[currentIndex] = array[randomIndex];
    array[randomIndex] = temporaryValue;
  }

  return array;
}

Why My Solution is Bad

At the beginning, I was just thinking about creating new random indexes within a while loop and push the old array element to a new array as return.

while (i <= arr.length - 1) {
  // create random index
  index = Math.floor(Math.random() * arr.length)

  // insert the element to new array
  if (!res.includes(arr[index])) {
    res.push(arr[index])
    i++
  }
}

It works well with very satisfying returnings. But the time complexity was pretty bad. In the while loop, it checks if the element to be inserted exists in the new array for each of the loop round. This results in O(n2).

If an array isn't that big, then my function was just fine. But the truth is, my project needs to generate a list with more than 1000 elements. So it's better to optimize the algorithm. (I think it's always better to do such optimization. Don't be afraid to mean to computers :D)

The Fisher–Yates Shuffle

The stackoverflow's answer seems quite simple, however in fact it uses an algorithm invented by Ronald Fisher and Frank Yates.

The Fisher–Yates shuffle is an algorithm for generating a random permutation of a finite sequence—in plain terms, the algorithm shuffles the sequence.

...and is also known as the Knuth shuffle after Donald Knuth.

-- From Wikipedia

There's an old blog article that visualizes the shuffle algorithm. https://bost.ocks.org/mike/shuffle/

The shuffle function is a description of the algorithm.

function shuffle(array) {
  var currentIndex = array.length, temporaryValue, randomIndex;

  // While there remain elements to shuffle...
  while (0 !== currentIndex) {

    // Create a random index to pick from the original array
    randomIndex = Math.floor(Math.random() * currentIndex);
    currentIndex -= 1;

    // Cache the value, and swap it with the current element
    temporaryValue = array[currentIndex];
    array[currentIndex] = array[randomIndex];
    array[randomIndex] = temporaryValue;
  }

  return array;
}

The solution is very good, but it still has some improving potentials. I believe making a pure function here makes more sense. So I'd rather return a new array than modifying the original argument as a side effect.

To avoid modifying the original data, I can also create a clone while passing the arugment.

shuffle(arr.slice(0))

Other Variations

There are some honorable alternatives to the solution I found on stackoverflow which I think is properly optimized.

The Durstenfeld Shuffle

This solution appears on the stackoverflow page. I found a gist memo in the end.

https://gist.github.com/webbower/8d19b714ded3ec53d1d7ed32b79fdbac

// Pre-ES6
function shuffleArray(array) {
  for (var i = array.length - 1; i > 0; i--) {
    var j = Math.floor(Math.random() * (i + 1));
    var temp = array[i];
    array[i] = array[j];
    array[j] = temp;
  }
}

// ES6+
function shuffleArray(array) {
  for (let i = array.length - 1; i > 0; i--) {
    let j = Math.floor(Math.random() * (i + 1));
    [array[i], array[j]] = [array[j], array[i]];
  }
}

Array extension method

Actually, I'd prefer this one due to its simplicity and a small trick of round numbers. The trick here is to use >>> (unsigned right shift operator) instead of Math.floor.

Array.prototype.shuffle = function() {
  let m = this.length, i;
  while (m) {
    i = (Math.random() * m--) >>> 0;
    [this[m], this[i]] = [this[i], this[m]]
  }
  return this;
}

Okay, that's all for the research. Hope you also get a good understanding of the shuffle algorithm from this article. If you think this article is great, please share it on social networks.

Thank you reading!

References