# What is Bitonic Sort

**Bitonic sort**is a sorting algorithm that works by repeatedly comparing and swapping pairs of elements in a sequence until the sequence is sorted in ascending or descending order.

Imagine you have a deck of cards that are not in any particular order. Bitonic sort would start by dividing the deck into two equal halves and comparing the cards in each half, swapping any pairs that are out of order. It would then divide each half into two halves and repeat the process, continuing to divide and compare until the entire deck is sorted.

The name "bitonic" comes from the fact that the algorithm works by first sorting the sequence into a "bitonic" sequence, meaning that the elements are first sorted in ascending order and then in descending order. The algorithm then merges these two sequences to produce the final sorted sequence.

## Who invented it?

The

**Bitonic sort**algorithm was originally proposed by Ken Batcher in 1968 as a parallel sorting algorithm that could efficiently be implemented on parallel computer architectures. Batcher was a computer scientist and mathematician who made significant contributions to the development of parallel computing and sorting algorithms.## Pseudocode

```
bitonicSort(arr, low, count, dir)
if count > 1
k = count / 2
bitonicSort(arr, low, k, ascending)
bitonicSort(arr, low + k, k, descending)
bitonicMerge(arr, low, count, dir)
bitonicMerge(arr, low, count, dir)
if count > 1
k = greatestPowerOfTwoLessThan(count)
for i = low to low + count - k - 1
if dir == (arr[i] > arr[i + k])
swap(arr[i], arr[i + k])
bitonicMerge(arr, low, k, dir)
bitonicMerge(arr, low + k, count - k, dir)
greatestPowerOfTwoLessThan(n)
k = 1
while k < n
k = k << 1
return k >> 1
```

In this pseudocode, arr is the array to be sorted, low is the starting index of the subarray to be sorted, count is the number of elements in the subarray to be sorted, and dir specifies the sorting direction (ascending or descending). The bitonicSort function first recursively calls itself to sort the two halves of the subarray, and then calls the bitonicMerge function to merge the two sorted halves.

The bitonicMerge function first finds the largest power of two that is less than count, and then iterates over the subarray, swapping elements if they are out of order according to the sorting direction. It then recursively calls itself to merge the two subarrays resulting from the split, one sorted in ascending order and the other in descending order.

Finally, the greatestPowerOfTwoLessThan function finds the largest power of two that is less than the input n.

The bitonicMerge function first finds the largest power of two that is less than count, and then iterates over the subarray, swapping elements if they are out of order according to the sorting direction. It then recursively calls itself to merge the two subarrays resulting from the split, one sorted in ascending order and the other in descending order.

Finally, the greatestPowerOfTwoLessThan function finds the largest power of two that is less than the input n.

## Sample Code

```
// C++ code snippet
void bitonicSort(int arr[], int low, int count, bool dir) {
if (count > 1) {
int k = count / 2;
bitonicSort(arr, low, k, true);
bitonicSort(arr, low + k, k, false);
bitonicMerge(arr, low, count, dir);
}
}
void bitonicMerge(int arr[], int low, int count, bool dir) {
if (count > 1) {
int k = greatestPowerOfTwoLessThan(count);
for (int i = low; i < low + count - k; i++) {
if (dir == (arr[i] > arr[i + k])) {
swap(arr[i], arr[i + k]);
}
}
bitonicMerge(arr, low, k, dir);
bitonicMerge(arr, low + k, count - k, dir);
}
}
int greatestPowerOfTwoLessThan(int n) {
int k = 1;
while (k < n) {
k = k << 1;
}
return k >> 1;
}
int main() {
int arr[] = { 3, 7, 4, 8, 6, 2, 1, 5 };
int n = sizeof(arr) / sizeof(arr[0]);
bool dir = true; // true for ascending, false for descending
bitonicSort(arr, 0, n, dir);
cout << "Sorted array: ";
for (int i = 0; i < n; i++) {
cout << arr[i] << " ";
}
return 0;
}
```

```
# Python code snippet
def bitonicSort(arr, low, count, dir):
if count > 1:
k = count // 2
bitonicSort(arr, low, k, True)
bitonicSort(arr, low + k, k, False)
bitonicMerge(arr, low, count, dir)
def bitonicMerge(arr, low, count, dir):
if count > 1:
k = greatestPowerOfTwoLessThan(count)
for i in range(low, low + count - k):
if dir == (arr[i] > arr[i + k]):
arr[i], arr[i + k] = arr[i + k], arr[i]
bitonicMerge(arr, low, k, dir)
bitonicMerge(arr, low + k, count - k, dir)
def greatestPowerOfTwoLessThan(n):
k = 1
while k < n:
k = k << 1
return k >> 1
arr = [3, 7, 4, 8, 6, 2, 1, 5]
n = len(arr)
dir = True # True for ascending, False for descending
bitonicSort(arr, 0, n, dir)
print("Sorted array:", arr)
```

```
public class BitonicSort {
public static void main(String[] args) {
int[] arr = {3, 7, 4, 8, 6, 2, 1, 5};
int n = arr.length;
boolean dir = true; // true for ascending, false for descending
bitonicSort(arr, 0, n, dir);
System.out.println("Sorted array: " + Arrays.toString(arr));
}
public static void bitonicSort(int[] arr, int low, int count, boolean dir) {
if (count > 1) {
int k = count / 2;
bitonicSort(arr, low, k, true);
bitonicSort(arr, low + k, k, false);
bitonicMerge(arr, low, count, dir);
}
}
public static void bitonicMerge(int[] arr, int low, int count, boolean dir) {
if (count > 1) {
int k = greatestPowerOfTwoLessThan(count);
for (int i = low; i < low + count - k; i++) {
if (dir == (arr[i] > arr[i + k])) {
int temp = arr[i];
arr[i] = arr[i + k];
arr[i + k] = temp;
}
}
bitonicMerge(arr, low, k, dir);
bitonicMerge(arr, low + k, count - k, dir);
}
}
public static int greatestPowerOfTwoLessThan(int n) {
int k = 1;
while (k < n) {
k = k << 1;
}
return k >> 1;
}
}
```

## Time and Space Complexity

The time complexity of the Bitonic Sort algorithm is O(n*log^2(n)), where n is the number of elements to be sorted.

The space complexity of the algorithm is O(n*log(n)). This is because Bitonic Sort is a comparison-based sorting algorithm and, as such, it requires a temporary buffer of size n*log(n) for merging the sorted sub-arrays. Additionally, the recursive calls made by the algorithm also require space on the stack, which contributes to the overall space complexity.

It is worth noting that while the time complexity of Bitonic Sort is the same as other popular comparison-based sorting algorithms like Merge Sort and Quick Sort, it is generally considered to be less efficient in practice due to its higher constant factors and the need for a larger buffer for merging sub-arrays. However, Bitonic Sort does have some advantages over other sorting algorithms, such as being highly parallelizable and having a regular memory access pattern, which make it well-suited for some specialized applications.

The space complexity of the algorithm is O(n*log(n)). This is because Bitonic Sort is a comparison-based sorting algorithm and, as such, it requires a temporary buffer of size n*log(n) for merging the sorted sub-arrays. Additionally, the recursive calls made by the algorithm also require space on the stack, which contributes to the overall space complexity.

It is worth noting that while the time complexity of Bitonic Sort is the same as other popular comparison-based sorting algorithms like Merge Sort and Quick Sort, it is generally considered to be less efficient in practice due to its higher constant factors and the need for a larger buffer for merging sub-arrays. However, Bitonic Sort does have some advantages over other sorting algorithms, such as being highly parallelizable and having a regular memory access pattern, which make it well-suited for some specialized applications.

## Advantages

- Bitonic Sort is a highly parallelizable sorting algorithm, which makes it well-suited for use in hardware or software implementations that support parallel processing.
- The algorithm has a regular memory access pattern, which can lead to better cache utilization and overall performance on modern processors.
- Bitonic Sort can be used to sort data in both ascending and descending order without the need for additional modifications to the algorithm.
- The algorithm has a relatively simple and intuitive structure, making it easy to implement and understand.

## Disadvantages

- The main disadvantage of Bitonic Sort is that it requires a buffer of size n*log(n) for merging the sorted sub-arrays, which can be a significant overhead for large datasets.
- The algorithm has a worst-case time complexity of O(n*log^2(n)), which is the same as other popular comparison-based sorting algorithms like Merge Sort and Quick Sort, but slower in practice due to higher constant factors and the need for a larger buffer.
- Bitonic Sort is not an in-place sorting algorithm, meaning that it requires additional memory to store the intermediate results during the sorting process, which can be a limitation in memory-constrained environments.
- Overall, the choice of sorting algorithm depends on a variety of factors, such as the size of the dataset, the available hardware and software resources, and the specific requirements of the application. Bitonic Sort can be a good choice in certain circumstances, such as when parallel processing is available or when the data needs to be sorted in both ascending and descending order, but it may not always be the most efficient algorithm for general-purpose sorting.