Python Program for Bitonic Sort

A sequence is bitonic if it first increases and then decreases. Formally, an array arr[0..n-1] is bitonic if there exists an index i (0 ≤ i ≤ n−1) such that:

x0 <= x1 …..<= xi and xi >= xi+1….. >= xn-1

• A fully increasing or fully decreasing sequence is also considered bitonic.
• Any rotation of a bitonic sequence remains bitonic.

Bitonic Sort is a parallel sorting algorithm that works efficiently when the number of elements is a power of 2.

How Bitonic Sort Works

It mainly works in two steps:

1. Form a bitonic sequence: divide the array into two halves- one sorted in ascending order and the other in descending order.
2. Merge: compare and swap elements to form smaller bitonic sequences until the entire array is sorted.

Python Implementation

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Explanation:

• bitonicSort(a, low, cnt, dire): recursively divides the array and sorts halves in opposite directions to form a bitonic sequence.
• bitonicMerge(a, low, cnt, dire): compares and swaps elements based on direction to merge the bitonic sequence into sorted order.
• k = cnt // 2: splits the current sequence into two equal halves.
• dire == 1 / 0: determines sorting order - 1 for ascending, 0 for descending.
• sort(a, N, up): wrapper function that initiates bitonic sorting on the full array.

Related Articles:

• Counting Sort - Python
• Merge Sort in Python