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C++ Program for Bitonic Sort

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Bitonic Sequence:

A sequence is called Bitonic if it is first increasing, then decreasing. In other words, an array arr[0..n-i] is Bitonic if there exists an index i where 0<=i<=n-1 such that

x0 <= x1 …..<= xi  and  xi >= xi+1….. >= xn-1 
  1. A sequence, sorted in increasing order is considered Bitonic with the decreasing part as empty. Similarly, the decreasing order sequence is considered Bitonic with the increasing part as empty.
  2. A rotation of Bitonic Sequence is also bitonic.

Bitonic Sorting

It mainly involves two steps.

  1. Forming a bitonic sequence (discussed above in detail). After this step we reach the fourth stage in the below diagram, i.e., the array becomes {3, 4, 7, 8, 6, 5, 2, 1}
  2. Creating one sorted sequence from the bitonic sequence: After the first step, the first half is sorted in increasing order and the second half in decreasing order. We compare the first element of the first half with the first element of the second half, then the second element of the first half with the second element of the second, and so on. We exchange elements if an element of the first half is smaller. After the above compare and exchange steps, we get two bitonic sequences in the array. See the fifth stage in the below diagram. In the fifth stage, we have {3, 4, 2, 1, 6, 5, 7, 8}. If we take a closer look at the elements, we can notice that there are two bitonic sequences of length n/2 such that all elements in first bitonic sequence {3, 4, 2, 1} are smaller than all elements of second bitonic sequence {6, 5, 7, 8}. We repeat the same process within two bitonic sequences and we get four bitonic sequences of length n/4 such that all elements of leftmost bitonic sequence are smaller and all elements of rightmost. See sixth stage in below diagram, arrays is {2, 1, 3, 4, 6, 5, 7, 8}. If we repeat this process one more time we get 8 bitonic sequences of size n/8 which is 1. Since all these bitonic sequence are sorted and every bitonic sequence has one element, we get the sorted array.

Below is the implementation of the above approach:

C++




/* C++ Program for Bitonic Sort. Note that this program
works only when size of input is a power of 2. */
#include<bits/stdc++.h>
using namespace std;
 
/*The parameter dir indicates the sorting direction, ASCENDING
or DESCENDING; if (a[i] > a[j]) agrees with the direction,
then a[i] and a[j] are interchanged.*/
void compAndSwap(int a[], int i, int j, int dir)
{
    if (dir==(a[i]>a[j]))
        swap(a[i],a[j]);
}
 
/*It recursively sorts a bitonic sequence in ascending order,
if dir = 1, and in descending order otherwise (means dir=0).
The sequence to be sorted starts at index position low,
the parameter cnt is the number of elements to be sorted.*/
void bitonicMerge(int a[], int low, int cnt, int dir)
{
    if (cnt>1)
    {
        int k = cnt/2;
        for (int i=low; i<low+k; i++)
            compAndSwap(a, i, i+k, dir);
        bitonicMerge(a, low, k, dir);
        bitonicMerge(a, low+k, k, dir);
    }
}
 
/* This function first produces a bitonic sequence by recursively
    sorting its two halves in opposite sorting orders, and then
    calls bitonicMerge to make them in the same order */
void bitonicSort(int a[],int low, int cnt, int dir)
{
    if (cnt>1)
    {
        int k = cnt/2;
 
        // sort in ascending order since dir here is 1
        bitonicSort(a, low, k, 1);
 
        // sort in descending order since dir here is 0
        bitonicSort(a, low+k, k, 0);
 
        // Will merge whole sequence in ascending order
        // since dir=1.
        bitonicMerge(a,low, cnt, dir);
    }
}
 
/* Caller of bitonicSort for sorting the entire array of
length N in ASCENDING order */
void sort(int a[], int N, int up)
{
    bitonicSort(a,0, N, up);
}
 
// Driver code
int main()
{
    int a[]= {3, 7, 4, 8, 6, 2, 1, 5};
    int N = sizeof(a)/sizeof(a[0]);
 
    int up = 1; // means sort in ascending order
    sort(a, N, up);
 
    printf("Sorted array: \n");
    for (int i=0; i<N; i++)
        printf("%d ", a[i]);
    return 0;
}


Output

Sorted array: 
1 2 3 4 5 6 7 8 

Time complexity: O(log2n)
Space Complexity: O(n.log2n)

Please refer complete article on Bitonic Sort for more details!



Last Updated : 09 Nov, 2023
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