199 lines
10 KiB
Markdown
199 lines
10 KiB
Markdown
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---
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title: Find the Symmetric Difference
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---
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 Remember to use <a href="https://forum.freecodecamp.org/t/how-to-get-help-when-you-are-stuck/" rel="help">**`Read-Search-Ask`**</a> if you get stuck. Try to pair program and write your own code
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###  Problem Explanation: ###
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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.
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For example, `sym([1, 2, 3], [5, 2, 1, 4])` should yield `[3, 4, 5]`.
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Following above definition, symmetric difference of three sets *A*, *B*, and *C* can be expressed as `(A Δ B) Δ C`.
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#### Relevant Links ####
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* <a href="https://en.wikipedia.org/wiki/Symmetric_difference" target="_blank" rel="nofollow">Symmetric difference - Wikipedia</a>
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* <a href="https://www.youtube.com/watch?v=PxffSUQRkG4" target="_blank" rel="nofollow">Symmetric difference - YouTube</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/reduce" target="_blank"
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rel="nofollow">JavaScript Array.prototype.reduce()</a>
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##  Hint: 1 ##
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The *arguments* object is *Array*-like object that only inherits `Array.length` property. Hence consider converting it to an actual *Array*.
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> _try to solve the problem now_
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##  Hint: 2 ##
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Deem writing a helper function that returns the symmetric difference of two arrays on each call instead of attempting to difference all sets simultaneously.
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> _try to solve the problem now_
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##  Hint: 3 ##
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Apply helper function against the created arguments array reducing its elements pairwise recursively to form the expected output.
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**Note**
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In the event of *odd number of sets* the symmetric difference will include identical elements present in all given sets. For instance;
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A = {1, 2, 3}
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B = {2, 3, 4}
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C = {3, 4, 5}
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(A ⋂ B) ⋂ C = {1, 4} &Intersection {3, 4, 5}
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A ⋂ B = {1, 3, 5}
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> _try to solve the problem now_
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## Spoiler Alert! ##
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**Solution Ahead!**
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##  Basic Code Solution: ##
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```javascript
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function sym() {
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var args = [];
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for (var i = 0; i < arguments.length; i++) {
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args.push(arguments[i]);
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}
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function symDiff(arrayOne, arrayTwo) {
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var result = [];
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arrayOne.forEach(function(item) {
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if (arrayTwo.indexOf(item) < 0 && result.indexOf(item) < 0) {
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result.push(item);
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}
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});
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arrayTwo.forEach(function(item) {
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if (arrayOne.indexOf(item) < 0 && result.indexOf(item) < 0) {
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result.push(item);
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}
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});
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return result;
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}
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// Apply reduce method to args array, using the symDiff function
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return args.reduce(symDiff);
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}
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```
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 <a href="https://repl.it/C4II/0" target="_blank" rel="nofollow">Run Code</a>
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### Code Explanation: ###
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* `push()` is used to break down the *arguments* object to an array, *args*.
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* The `symDiff` function finds the symmetric difference between two sets. It is used as a callback function for the `reduce()` method called on *args*.
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* `arrayOne.forEach()` pushes the elements to *result* which are present only in *arrayOne* as well as not already a part of *result*.
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* `arrayTwo.forEach()` pushes the elements to *result* which are present only in *arrayTwo* as well as not already a part of *result*.
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* The *result*, which is the symmetric difference is returned. This solution works for any number of sets.
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#### Relevant Links ####
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/statements/for" target="_blank" rel="nofollow">JavaScript for</a>
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* <a href="https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/Array/length" target="_blank" rel="nofollow">JavaScript Array.length</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/push" target="_blank" rel="nofollow">JavaScript Array.prototype.push()</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/forEach" target="_blank" rel="nofollow">JavaScript Array.prototype.forEach()</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/indexOf" target="_blank" rel="nofollow">JavaScript Array.prototype.indexOf()</a>
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##  Intermediate Code Solution: ##
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```javascript
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function sym() {
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// Convert the argument object into a proper array
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var args = Array.prototype.slice.call(arguments);
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// Return the symmetric difference of 2 arrays
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var getDiff = function(arr1, arr2) {
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// Returns items in arr1 that don't exist in arr2
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function filterFunction(arr1, arr2) {
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return arr1.filter(function(item) {
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return arr2.indexOf(item) === -1;
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});
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}
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// Run filter function on each array against the other
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return filterFunction(arr1, arr2)
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.concat(filterFunction(arr2, arr1));
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};
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// Reduce all arguments getting the difference of them
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var summary = args.reduce(getDiff, []);
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// Run filter function to get the unique values
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var unique = summary.filter(function(elem, index, self) {
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return index === self.indexOf(elem);
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});
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return unique;
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}
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// test here
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sym([1, 2, 3], [5, 2, 1, 4]);
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```
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 <a href="https://repl.it/CLoc/0" target="_blank" rel="nofollow">Run Code</a>
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### Code Explanation: ###
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* The `slice()` method is used to break down the *arguments* object to an array, *args*.
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* 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*.
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* The first `filterFunction()` returns elements in *arr1* that don't exist in *arr2*.
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* The next `filterFunction()` is run on each array against the other to check the inverse of the first check for uniqueness and concatenate it.
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* *summary* consists of the reduced arguments.
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* `filter()` is used on *summary* to keep only the unique values and *unique* is returned.
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#### Relevant Links ####
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/slice" target="_blank" rel="nofollow">JavaScript Array.prototype.slice()</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/filter" target="_blank" rel="nofollow">JavaScript Array.prototype.filter()</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/concat" target="_blank" rel="nofollow">JavaScript Array.prototype.concat()</a>
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##  Advanced Code Solution: ##
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```javascript
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function sym() {
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let argv = Array.from(arguments).reduce(diffArray);
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return argv.filter((element, index, array) => index === array.indexOf(element));//remove duplicates
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}
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function diffArray(arr1, arr2) {
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return arr1
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.filter(element => !arr2.includes(element))
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.concat(arr2.filter(element => !arr1.includes(element)));
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}
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// test here
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sym([1, 2, 3], [5, 2, 1, 4]);
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```
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 <a href="https://repl.it/@ashenm/Symmetric-Difference" target="_blank" rel="nofollow">Run Code</a>
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### Code Explanation: ###
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* The main function *sym()* creates an array from *arguments* and reduces its elements utilising helper function *diffArray()* to a single array.
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* The function *diffArray()* returns the symmetric difference of two arrays by picking out unique elements in parameterised arrays; *arr1* and *arr2*.
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#### Relevant Links ####
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/from" target="_blank" rel="nofollow">JavaScript Array.from()</a>
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* <a href="https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/filter" target="_blank" rel="nofollow">JavaScript Array.prototype.filter()</a>
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##  NOTES FOR CONTRIBUTIONS: ##
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*  **DO NOT** add solutions that are similar to any existing solutions. If you think it is **_similar but better_**, then try to merge (or replace) the existing similar solution.
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* Add an explanation of your solution.
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* Categorize the solution in one of the following categories — **Basic**, **Intermediate** and **Advanced**. 
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* Please add your username only if you have added any **relevant main contents**. ( **_DO NOT_** _remove any existing usernames_)
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> See  <a href="http://forum.freecodecamp.com/t/algorithm-article-template/14272" target="_blank" rel="nofollow">**`Wiki Challenge Solution Template`**</a> for reference.
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