---
title: Find the Symmetric Difference
---

# Find the Symmetric Difference

---
## Problem Explanation
Symmetric difference (commonly denoted by Δ) of two sets is the set of elements which are in either of the two sets, but not in both.

For example, `sym([1, 2, 3], [5, 2, 1, 4])` should yield `[3, 4, 5]`.

Following above definition, symmetric difference of three sets *A*, *B*, and *C* can be expressed as `(A Δ B) Δ C`.

#### Relevant Links

* [Symmetric difference - Wikipedia](https://en.wikipedia.org/wiki/Symmetric_difference)
* [Symmetric difference - YouTube](https://www.youtube.com/watch?v=PxffSUQRkG4)
* [Array.reduce()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/reduce)


---
## Hints

### Hint 1
The *arguments* object is *Array*-like object that only inherits `Array.length` property. Hence consider converting it to an actual *Array*.


### Hint 2
Deem writing a helper function that returns the symmetric difference of two arrays on each call instead of attempting to difference all sets simultaneously.


### Hint 3
Apply helper function against the created arguments array reducing its elements pairwise recursively to form the expected output.

**Note**
In the event of *odd number of sets* the symmetric difference will include identical elements present in all given sets. For instance;

    A = {1, 2, 3}
    B = {2, 3, 4}
    C = {3, 4, 5}

    (A ⋂ B) ⋂ C = {1, 4} &Intersection {3, 4, 5}
    A ⋂ B = {1, 3, 5}


---
## Solutions

<details><summary>Solution 1 (Click to Show/Hide)</summary>

```javascript
function sym() {
  var args = [];
  for (var i = 0; i < arguments.length; i++) {
    args.push(arguments[i]);
  }

  function symDiff(arrayOne, arrayTwo) {
    var result = [];

    arrayOne.forEach(function(item) {
      if (arrayTwo.indexOf(item) < 0 && result.indexOf(item) < 0) {
        result.push(item);
      }
    });

    arrayTwo.forEach(function(item) {
      if (arrayOne.indexOf(item) < 0 && result.indexOf(item) < 0) {
        result.push(item);
      }
    });

    return result;
  }

  // Apply reduce method to args array, using the symDiff function
  return args.reduce(symDiff);
}
```


#### Code Explanation
* `push()` is used to break down the *arguments* object to an array, *args*.
* The `symDiff` function finds the symmetric difference between two sets. It is used as a callback function for the `reduce()` method called on *args*.
* `arrayOne.forEach()` pushes the elements to *result* which are present only in *arrayOne* as well as not already a part of *result*.
* `arrayTwo.forEach()` pushes the elements to *result* which are present only in *arrayTwo* as well as not already a part of *result*.
* The *result*, which is the symmetric difference is returned. This solution works for any number of sets.

#### Relevant Links

* [Statement for](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/statements/for)
* [Array.length](https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/Array/length)
* [Array.push()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/push)
* [Array.forEach()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/forEach)
* [Array.indexOf()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/indexOf)
</details>

<details><summary>Solution 2 (Click to Show/Hide)</summary>

```javascript
function sym() {
  // Convert the argument object into a proper array
  var args = Array.prototype.slice.call(arguments);

  // Return the symmetric difference of 2 arrays
  var getDiff = function(arr1, arr2) {
    // Returns items in arr1 that don't exist in arr2
    function filterFunction(arr1, arr2) {
      return arr1.filter(function(item) {
        return arr2.indexOf(item) === -1;
      });
    }

    // Run filter function on each array against the other
    return filterFunction(arr1, arr2).concat(filterFunction(arr2, arr1));
  };

  // Reduce all arguments getting the difference of them
  var summary = args.reduce(getDiff, []);

  // Run filter function to get the unique values
  var unique = summary.filter(function(elem, index, self) {
    return index === self.indexOf(elem);
  });
  return unique;
}

// test here
sym([1, 2, 3], [5, 2, 1, 4]);
```


#### Code Explanation
* The `slice()` method is used to break down the *arguments* object to an array, *args*.
* The `getDiff` function finds the symmetric difference between two sets, *arr1* and *arr2*. It is used as a callback function for the `reduce()` method called on *args*.
* The first `filterFunction()` returns elements in *arr1* that don't exist in *arr2*.
* The next `filterFunction()` is run on each array against the other to check the inverse of the first check for uniqueness and concatenate it.
* *summary* consists of the reduced arguments.
* `filter()` is used on *summary* to keep only the unique values and *unique* is returned.

#### Relevant Links

* [Array.slice()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/slice)
* [Array.filter()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/filter)
* [Array.concat()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/concat)
</details>

<details><summary>Solution 3 (Click to Show/Hide)</summary>

```javascript
const diff = (arr1, arr2) => [
  ...arr1.filter(e => !arr2.includes(e)),
  ...arr2.filter(e => !arr1.includes(e))
];

const sym = (...args) => [...new Set(args.reduce(diff))];

// test here
sym([1, 2, 3], [5, 2, 1, 4]);
```


#### Code Explanation

* The main function *sym()* reduces given arrays utilising helper function *diff()* to a single array. Also, it temporary converts the result to *Set* to remove duplicates.

* The function *diff()* returns the symmetric difference of two arrays by picking out elements in parameterised arrays; *arr1* and *arr2*. 

#### Relevant Links
* [Set](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Set)
* [Array.filter()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/filter)

</details>