Algorithm-Symmetric-Difference.md

Algorithm Symmetric Difference

Problem Explanation:

Symmetric Difference is the difference between two sets.

So in the Symmetric Difference Algorithm you would work through the arrays of numbers something like this -

sym(A, B, C) Translates to sym(sym(A,B),C)

Or in plain English - First find the Symmetric Difference of Set A and Set B. Then find the Symmetric Difference of this new set and Set C.

So -

sym([1, 2, 5], [2, 3, 5], [3, 4, 5])

would equal

[1,4,5]

Here's a nice video tutorial (with an awful fake British accent!) -

YouTube - Symmetric Difference

Hint: 1

The arguments object is not an Array. It is similar to an Array, but does not have any Array properties except length. For example, it does not have the pop method. However it can be converted to a real Array:

var args = Array.prototype.slice.call(arguments);

Hint: 2

Write a function that returns the symmetric difference of array1 and array2.

yourFunction([1, 2, 3], [2, 4, 6]) must return [1, 3, 4, 6]

Hint: 3

Use Array.prototype.reduce along with yourFunction to repeat the process on multiple arguments

Something a bit strange about the definition of symmetric difference is that if one identical item occurs in three different sets, it is a member of the symmetric difference. An example is easier to explain:

a = [1, 2, 5]
b = [2, 3, 5]
c = [3, 4, 5]

sym(a, b) = [1, 3]
sym([1, 3], c) = [1, 4, 5]

Spoiler Alert!

Solution ahead!

Code Solution 1:

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 symarray = args.reduce(getDiff, []);

  // Run filter function to get the unique values
  var unique = symarray.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 1:

• 1. The reason you want to break down the arguments object to a array is if you want to use functional methods like reduce and

• filter, the data needs to be in array form.

• 1. getDiff is first checking arr2 if it doesn't have any element(item) in arr1. (A unique number) with filterFunction.

• next getDiff will check the inverse of the first check for uniqueness and concatinate it to the array.

• 1. symarray uses getDiff. It's used as the callback function here and starts the reduce function with an empty array. Why do this? The reduce function is calling our filter function everytime (and runs the cross check needed from filterFunction). The function will essentially return an array with all symmetric differences (but with double values at this point).
• 1. unique uses the filter method and creates a new array from the reduced and filtered array of symarray and getDiff. This filter checks if the index the filter is currently at its equal to the index of the element in the orginal array. The reason this is done is to filter out double values in the symmetric difference symarray. You can only have one index per unique number which is why it'll return false for any double value.

Code Solution 2:

//jshint esversion: 6
function sym() {
  // difference between set A and set B
  const diff = (A, B) => new Set([...A].filter(n => !B.has(n)));
  // spread operator to convert array like object to array
  const result = [...arguments]
    // map elements in arguments (array) to Set
    .map(arr => new Set(arr))
    // using the formula in https://en.wikipedia.org/wiki/Symmetric_difference
    // i reduce it by uniting the diff(A, B) and diff(B, A)
    .reduce((acc, set) => new Set([...diff(acc, set), ...diff(set, acc)])); 

  // convert the set to array by using spread operator again
  return [...result];
}

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

🚀 Run Code

Code Explaination 2:

• Read comments in code

Related Links

• Symmetric Difference
• Array.reduce()

Credits:

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