---
title: Find the Symmetric Difference
---
 Remember to use **`Read-Search-Ask`** if you get stuck. Try to pair program and write your own code
###  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
* Symmetric difference - YouTube
* JavaScript Array.prototype.reduce()
##  Hint: 1 ##
The *arguments* object is *Array*-like object that only inherits `Array.length` property. Hence consider converting it to an actual *Array*.
> _try to solve the problem now_
##  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.
> _try to solve the problem now_
##  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}
> _try to solve the problem now_
## Spoiler Alert! ##
**Solution Ahead!**
##  Basic Code Solution: ##
```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);
}
```
 Run Code
### 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 ####
* JavaScript for
* JavaScript Array.length
* JavaScript Array.prototype.push()
* JavaScript Array.prototype.forEach()
* JavaScript Array.prototype.indexOf()
##  Intermediate Code Solution: ##
```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]);
```
 Run Code
### 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 ####
* JavaScript Array.prototype.slice()
* JavaScript Array.prototype.filter()
* JavaScript Array.prototype.concat()
##  Advanced Code Solution: ##
```javascript
function sym() {
let argv = Array.from(arguments).reduce(diffArray);
return argv.filter((element, index, array) => index === array.indexOf(element));//remove duplicates
}
function diffArray(arr1, arr2) {
return arr1
.filter(element => !arr2.includes(element))
.concat(arr2.filter(element => !arr1.includes(element)));
}
// test here
sym([1, 2, 3], [5, 2, 1, 4]);
```
 Run Code
### Code Explanation: ###
* The main function *sym()* creates an array from *arguments* and reduces its elements utilising helper function *diffArray()* to a single array.
* The function *diffArray()* returns the symmetric difference of two arrays by picking out unique elements in parameterised arrays; *arr1* and *arr2*.
#### Relevant Links ####
* JavaScript Array.from()
* JavaScript Array.prototype.filter()
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