Bitonic sort is a parallel sorting algorithm that works by recursively constructing a bitonic sequence (a sequence that is first monotonically increasing and then monotonically decreasing) and then merging the sequence into a sorted one. It is particularly effective in parallel computing environments. Bitonic sort has a time complexity of O(log^2 n) when implemented in a parallel setting.
Consider an array with the following elements:
[3, 7, 4, 8, 6, 2, 1, 5]
To sort this array using bitonic sort, follow these steps:
Let's apply these steps to the example array:
Below is the pseudo code for the bitonic sort algorithm:
function bitonicSort(array, low, cnt, direction)
if cnt > 1 then
k = cnt / 2
bitonicSort(array, low, k, 1)
bitonicSort(array, low + k, k, 0)
bitonicMerge(array, low, cnt, direction)
end if
end function
function bitonicMerge(array, low, cnt, direction)
if cnt > 1 then
k = cnt / 2
for i = low to low + k - 1 do
if (direction == 1 and array[i] > array[i + k]) or
(direction == 0 and array[i] < array[i + k]) then
swap(array[i], array[i + k])
end if
end for
bitonicMerge(array, low, k, direction)
bitonicMerge(array, low + k, k, direction)
end if
end function
Explanation:
def bitonic_sort(arr, low, cnt, direction):
if cnt > 1:
k = cnt // 2
bitonic_sort(arr, low, k, 1) # Ascending order
bitonic_sort(arr, low + k, k, 0) # Descending order
bitonic_merge(arr, low, cnt, direction)
def bitonic_merge(arr, low, cnt, direction):
if cnt > 1:
k = cnt // 2
for i in range(low, low + k):
if (direction == 1 and arr[i] > arr[i + k]) or (direction == 0 and arr[i] < arr[i + k]):
arr[i], arr[i + k] = arr[i + k], arr[i]
bitonic_merge(arr, low, k, direction)
bitonic_merge(arr, low + k, k, direction)
def sort(arr, n, up):
bitonic_sort(arr, 0, n, up)
# Example usage:
array = [3, 7, 4, 8, 6, 2, 1, 5]
print("Original array:", array)
sort(array, len(array), 1)
print("Sorted array:", array) # Output: [1, 2, 3, 4, 5, 6, 7, 8]
This Python program defines functions to perform bitonic sort on an array. The bitonic_sort function creates the bitonic sequence, and the bitonic_merge function merges the sequences to create a sorted array. The sort function initializes the process by calling bitonic_sort with the entire array.