双调排序

双调排序是一种data-independent的排序，标准的双调序列个数为2的幂次方个。如果将序列画成波形以理解整个排序过程，则首先将看到随机的折现通过Merge，从最初的4个数字为一组的多个波峰，两两Merge形成一个波峰；而后通过Sort，把一个波峰拆成4个数字为一组的多个波峰，每次拆解对应进行数字的换位；通过这两个步骤实现排序。

参考链接：https://blog.csdn.net/xbinworld/article/details/76408595

以下为源代码：

// Source : https://www.geeksforgeeks.org/bitonic-sort/

/* C++ Program for Bitonic Sort. Note that this program
   works only when size of input is a power of 2. */

#include <algorithm>
#include <iostream>

/*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]))
        std::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);

    std::cout << "Sorted array: \n";
    for (int i = 0; i < N; i++) std::cout << a[i] << " ";
    return 0;
}