A Beginner's Guide to Implementing 3-way Merge Sort: An Example in JavaScript.

3-way merge sort, also known as "multi-way merge sort," is a sorting algorithm that is similar to traditional merge sort, but with the added capability of sorting items with duplicate keys.

This is achieved by partitioning the input data into three subarrays: less than a certain value, equal to that value, and greater than that value. These subarrays are then recursively sorted and merged back together to produce a final sorted output.

In the example I provided, the threeWayMergeSort function takes in an array as an argument and checks if the array is empty or has one element, in that case it returns the array.

Then, the function assigns three empty arrays, "less," "equal," and "greater," and assigns the first element of the array to a pivot variable.

The function then uses a for loop to iterate through the input array and compares each element to the pivot value. Elements that are less than the pivot value are pushed to the "less" array, elements that are greater than the pivot value are pushed to the "greater" array, and elements that are equal to the pivot value are pushed to the "equal" array.

After the for loop completes, the function recursively sorts the "less" and "greater" arrays using the threeWayMergeSort function and then concatenates the "less," "equal," and "greater" arrays together to produce a final sorted output.

3-way merge sort is a efficient sorting algorithm when input array contains large number of duplicate keys and it can sort them in linear time. However, it is not as efficient as traditional merge sort when there are fewer duplicate keys.

It is important to note that the pivot element chosen in the example is the first element of the array, for a real-world scenario it is generally advised to choose a pivot element randomly to avoid worst case scenarios.

Additionally, the time complexity of 3-way merge sort is O(n log n) and the space complexity is O(n).

Here is an example of how to implement 3-way merge sort in JavaScript:

function threeWayMergeSort(arr) {
  if (arr.length < 2) return arr;
  let less = [], equal = [], greater = [];
  let pivot = arr[0];
  for (let i = 0; i < arr.length; i++) {
    if (arr[i] < pivot) less.push(arr[i]);
    else if (arr[i] > pivot) greater.push(arr[i]);
    else equal.push(arr[i]);
  }
  return threeWayMergeSort(less).concat(equal, threeWayMergeSort(greater));
}
console.log(threeWayMergeSort([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]));

In this example, the threeWayMergeSort function takes in an array as an argument and checks if the array is empty or has one element, in that case it returns the array.

Then, the function assigns three empty arrays, "less," "equal," and "greater," and assigns the first element of the array to a pivot variable.

The function then uses a for loop to iterate through the input array and compares each element to the pivot value. Elements that are less than the pivot value are pushed to the "less" array, elements that are greater than the pivot value are pushed to the "greater" array, and elements that are equal to the pivot value are pushed to the "equal" array.

After the for loop completes, the function recursively sorts the "less" and "greater" arrays using the threeWayMergeSort function and then concatenates the "less," "equal," and "greater" arrays together to produce a final sorted output.

3-way merge sort is a efficient sorting algorithm when input array contains large number of duplicate keys and it can sort them in linear time. However, it is not as efficient as traditional merge sort when there are fewer duplicate keys.

It is important to note that the pivot element chosen in the example is the first element of the array, for a real-world scenario it is generally advised to choose a pivot element randomly to avoid worst case scenarios.