**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…..<= xiand xi>= xi+1….. >= xn-1

- A sequence, sorted in increasing order is considered Bitonic with the decreasing part as empty. Similarly, decreasing order sequence is considered Bitonic with the increasing part as empty.
- A rotation of Bitonic Sequence is also bitonic.

**Bitonic Sorting**

It mainly involves two steps.

- Forming a bitonic sequence (discussed above in detail). After this step we reach the fourth stage in below diagram, i.e., the array becomes {3, 4, 7, 8, 6, 5, 2, 1}
- Creating one sorted sequence from bitonic sequence : After first step, first half is sorted in increasing order and second half in decreasing order.

We compare first element of first half with first element of second half, then second element of first half with second element of second and so on. We exchange elements if an element of first half is smaller.

After above compare and exchange steps, we get two bitonic sequences in array. See fifth stage in 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 bitnic 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.

`/* 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 wole 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; ` `} ` |

*chevron_right*

*filter_none*

**Output:**

Sorted array: 1 2 3 4 5 6 7 8

Please refer complete article on Bitonic Sort for more details!

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- C++ Program for Bitonic Sort
- Java Program for Bitonic Sort
- Bitonic Sort
- Sort a Bitonic Array
- Comparison among Bubble Sort, Selection Sort and Insertion Sort
- Program to sort an array of strings using Selection Sort
- C/C++ Program for Odd-Even Sort / Brick Sort
- Java Program for Odd-Even Sort / Brick Sort
- Why Quick Sort preferred for Arrays and Merge Sort for Linked Lists?
- Odd-Even Sort / Brick Sort
- Bucket Sort To Sort an Array with Negative Numbers
- Sort all even numbers in ascending order and then sort all odd numbers in descending order
- Serial Sort v/s Parallel Sort in Java
- Insertion sort to sort even and odd positioned elements in different orders
- Quick Sort vs Merge Sort
- Odd Even Transposition Sort / Brick Sort using pthreads
- Sort an Array which contain 1 to N values in O(N) using Cycle Sort
- Add elements in start to sort the array | Variation of Stalin Sort
- Merge Sort vs. Insertion Sort
- sort() vs. partial_sort() vs. nth_element() + sort() in C++ STL