---
id: 5a23c84252665b21eecc8046
title: Symmetric difference
challengeType: 5
forumTopicId: 16086
---

## Description
<section id='description'>

Given two <a href="https://rosettacode.org/wiki/set" target="_blank">set</a>s <i>A</i> and <i>B</i>, compute $(A \setminus B) \cup (B \setminus A).$
That is, enumerate the items that are in <i>A</i> or <i>B</i> but not both. This set is called the <a href="https://en.wikipedia.org/wiki/Symmetric difference" target="_blank">symmetric difference</a> of <i>A</i> and <i>B</i>.
In other words: $(A \cup B) \setminus (A \cap B)$ (the set of items that are in at least one of <i>A</i> or <i>B</i> minus the set of items that are in both <i>A</i> and <i>B</i>).
</section>

## Instructions
<section id='instructions'>

Write a function that takes two arrays as parameters and returns the symmetric difference. Sort the resultant array before returning it.
</section>

## Tests
<section id='tests'>

``` yml
tests:
  - text: <code>symmetricDifference</code> should be a function.
    testString: assert(typeof symmetricDifference == 'function', '<code>symmetricDifference</code> should be a function.');
  - text: <code>symmetricDifference(["John", "Bob", "Mary", "Serena"], ["Jim", "Mary", "John", "Bob"])</code> should return an array.
    testString: assert(Array.isArray(symmetricDifference(["John", "Bob", "Mary", "Serena"], ["Jim", "Mary", "John", "Bob"])), '<code>symmetricDifference(["John", "Bob", "Mary", "Serena"], ["Jim", "Mary", "John", "Bob"])</code> should return an array.');
  - text: <code>symmetricDifference(["John", "Bob", "Mary", "Serena"], ["Jim", "Mary", "John", "Bob"])</code> should return <code>["Jim", "Serena"]</code>.
    testString: assert.deepEqual(symmetricDifference(["John", "Bob", "Mary", "Serena"], ["Jim", "Mary", "John", "Bob"]), ["Jim", "Serena"], '<code>symmetricDifference(["John", "Bob", "Mary", "Serena"], ["Jim", "Mary", "John", "Bob"])</code> should return <code>["Jim", "Serena"]</code>.');
  - text: <code>symmetricDifference([1, 2, 3], [3, 4])</code> should return <code>[1, 2, 4]</code>.
    testString: assert.deepEqual(symmetricDifference([1, 2, 3], [3, 4]), [1, 2, 4], '<code>symmetricDifference([1, 2, 3], [3, 4])</code> should return <code>[1, 2, 4]</code>.');
  - text: <code>symmetricDifference([1, 2, 3, 4, 5], [3, 4, 8, 7])</code> should return <code>[1, 2, 5, 7, 8]</code>.
    testString: assert.deepEqual(symmetricDifference([1, 2, 3, 4, 5], [3, 4, 8, 7]), [1, 2, 5, 7, 8], '<code>symmetricDifference([1, 2, 3, 4, 5], [3, 4, 8, 7])</code> should return <code>[1, 2, 5, 7, 8]</code>.');
  - text: <code>symmetricDifference([1, 2, 3, 4, 5, 6, 7, 8], [1, 3, 5, 6, 7, 8, 9])</code> should return <code>[2, 4, 9]</code>.
    testString: assert.deepEqual(symmetricDifference([1, 2, 3, 4, 5, 6, 7, 8], [1, 3, 5, 6, 7, 8, 9]), [2, 4, 9], '<code>symmetricDifference([1, 2, 3, 4, 5, 6, 7, 8], [1, 3, 5, 6, 7, 8, 9])</code> should return <code>[2, 4, 9]</code>.');
  - text: <code>symmetricDifference([1, 2, 4, 7, 9], [2, 3, 7, 8, 9])</code> should return <code>[1, 3, 4, 8]</code>.
    testString: assert.deepEqual(symmetricDifference([1, 2, 4, 7, 9], [2, 3, 7, 8, 9]), [1, 3, 4, 8], '<code>symmetricDifference([1, 2, 4, 7, 9], [2, 3, 7, 8, 9])</code> should return <code>[1, 3, 4, 8]</code>.');
```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function symmetricDifference(A, B) {
  // Good luck!
}
```

</div>
</section>

## Solution
<section id='solution'>

```js
function symmetricDifference(A, B) {
  function relative_complement(A, B) {
    return A.filter(function(elem) {
      return B.indexOf(elem) == -1
    });
  }

  function unique(ary) {
    var u = ary.concat().sort();
    for (var i = 1; i < u.length;) {
      if (u[i - 1] === u[i])
        u.splice(i, 1);
      else
        i++;
    }
    return u;
  }

  return unique(relative_complement(A, B).concat(relative_complement(B, A))).sort();
}
```

</section>