Counting sort is a sorting algorithm that works by counting the number of occurrences of each element in the input array and then using arithmetic to calculate the position of each element in the sorted output array. Its basic logic is to determine the number of elements smaller than each element in the array by counting the number of elements between 0 and the maximum value in the array. This information is then used to place each element in the correct position in the sorted order. The advantage of counting sort is that it can sort elements in linear time, making it faster than comparison-based sorting algorithms such as merge sort and quicksort in certain situations. The main disadvantage of counting sort is that it requires extra memory to store the count array.

Counting Sort is a sorting algorithm that operates on an array or list of integers. It works by counting the number of occurrences of each unique element in the list, and then using the counts to reposition the elements in order.

Here's an example of how Counting Sort would work for an array of integers:

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const countingSort = arr => {
  const max = Math.max(...arr);
  const counts = new Array(max + 1).fill(0);
  const sortedArr = [];

  arr.forEach(num => {
    counts[num]++;
  });

  counts.forEach((count, i) => {
    for (let j = 0; j < count; j++) {
      sortedArr.push(i);
    }
  });

  return sortedArr;
};

console.log(countingSort([3, 2, 1, 4])) // Output: [1, 2, 3, 4]

First, we find the maximum value in the array to determine the size of the counting array. Then, we fill the counting array with zeros and iterate through the input array, incrementing the corresponding count for each number. We then iterate through the counting array, adding each number in the right count to the sorted array. Finally, we return the sorted array.

Counting Sort has a time complexity of O(n+k), where n is the number of elements in the input array and k is the range of input. However, it has a space complexity of O(k), which can be prohibitively large for some inputs.

Sure! Here is a simple implementation of Counting Sort Algorithm in JavaScript:

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function countSort(arr, maxVal) {
   var i, z = 0, count = [];

   // Create a counter array to store count of individual elements
   for (i = 0; i <= maxVal; i++) {
       count[i] = 0;
   }

   // Store count of each element
   for (i=0; i < arr.length; i++) {
       count[arr[i]]++;
   }

   // Modify array and store sorted elements
   for (i = 0; i <= maxVal; i++) {
       while (count[i]-- > 0) {
           arr[z++] = i;
       }
   }

   return arr;
}

// Example Usage
var arr = [1, 4, 1, 2, 7, 5, 2];
var sortedArr = countSort(arr, 7); // maxVal = 7 since the maximum value in the array is 7

console.log(sortedArr); // [1, 1, 2, 2, 4, 5, 7]

In the above implementation, arr represents the array to be sorted and maxVal is the maximum value in the array. The countSort function returns the sorted array.

The Counting Sort algorithm works by counting the number of occurrences of each item and using arithmetic to determine the position of each item in the output sequence.