Given an array of Numbers that contain any frequency of exactly three unique elements. Our task is to sort this array using JavaScript.

Examples: 

Input: arr[] = [3, 1, 3, 2, 1, 2, 1, 3, 2]
Output: [1, 1, 1, 2, 2, 2,3,3,3]

Input = arr[] =[1,2,3,1,2,3]
Output: [1,1,2,2,3,3]

Counting Sort with Extra Space

In this approach, we use counting sort to sort the array. We count the occurrences of each unique element and then construct the sorted array based on the counts.

Example: Implementation of a program to sort an array of exactly three unique repeating elements using Counting Sort with Extra Space

function sortArray(arr) {
    const counts = {};
    arr.forEach(num => {
        counts[num] = (counts[num] || 0) + 1;
    });

    const sortedArr = [];
    for (let i = 0; i < 3; i++) {
        const num = i + 1;
        if (counts[num]) {
            sortedArr.push(...Array(counts[num]).fill(num));
        }
    }

    return sortedArr;
}

const arr = [3, 1, 3, 2, 1, 2, 1, 3, 2];
const sortedArr = sortArray(arr);
console.log("Sorted array:", sortedArr);

Sorted array: [
  1, 1, 1, 2, 2,
  2, 3, 3, 3
]

Time Complexity: O(n)

Auxiliary Space: O(n)

Three-Way Partitioning

In this approach we use three-way partitioning technique to sort the array in place. Here we maintain three pointers (low, mid, and high) to partition the array into three sections and thus sortiing them.

Example: Implementation of program to sort array of exactly three unique repeating elements using Three-Way Partitioning

function sortArray(arr) {
    let l = 0, m = 0, h = arr.length - 1;

    while (m <= h) {
        if (arr[m] === 1) {
            [arr[l], arr[m]] = [arr[m], arr[l]];
            l++;
            m++;
        } else if (arr[m] === 2) {
            m++;
        } else {
            [arr[m], arr[h]] = [arr[h], arr[m]];
            h--;
        }
    }

    return arr;
}

const arr = [3, 1, 3, 2, 1, 2, 1, 3, 2];
const sortedArr = sortArray(arr);
console.log("Sorted array:", sortedArr);

Sorted array: [
  1, 1, 1, 2, 2,
  2, 3, 3, 3
]

Time Complexity: O(N),where n is the length of the input array

Auxiliary Space: O(1)