归并排序的核心思想是 Divide-and-Conquer 算法，即将要解决的size为n的问题，分成a个size为n/b的子问题，这些子问题的结果经过O(n^d)的时间复杂度合并，即可解决最初的问题。所以，这一类的算法，复杂度计算公式为 T(n) = a*T(n/b) + O(n^b)。

经过几天的努力，终于将归并排序用C语言实现了出来：

mergesort.h:

#define BUFF_SIZE 3

typedef struct _array {

        int length;

        int active;

        int *elements;

} array;

int mergesort(array *);

int merge(array , array , array *);

mergesort.c:

#include <stdio.h>

#include <stdlib.h>

#include "mergesort.h"

int main()

{

        int arr[BUFF_SIZE] = {1, 9, 3};

        array arr_main;

        arr_main.length = BUFF_SIZE;

        arr_main.active = 0;

        arr_main.elements = arr;

        mergesort(&arr_main);

        int i = 0;

        for (i = 0; i<BUFF_SIZE; i++)

        {

                printf("%d\n", arr_main.elements[i]);

        }

}

int mergesort(array *array_p)

{

        if (array_p->length > 1)

        {

                // Split the array into two part

                int size_l = array_p->length >> 1;

                int size_r = array_p->length - size_l;

                // the structure to store the left part

                array arr_l;

                arr_l.length = size_l;

                arr_l.active = 0;

                arr_l.elements = (int *)malloc(sizeof(int *) * size_l);

                int length_l = arr_l.length;

                while (length_l-- > 0)

                        arr_l.elements[length_l] = array_p->elements[length_l];

                // the structure to store the right part

                array arr_r;

                arr_r.length = size_r;

                arr_r.active = 0;

                arr_r.elements = (int *)malloc(sizeof(int *) * size_r);

                int length_r = arr_r.length;

                while (length_r-- > 0)

                        arr_r.elements[length_r] = array_p->elements[length_r + arr_l.length];

                // sort the left part of array

                mergesort(&arr_l);

                // sort the left part of array

                mergesort(&arr_r);

                // the structure to store the merge result

                array arr_m;

                arr_m.length = arr_l.length + arr_r.length;

                arr_m.active = 0;

                arr_m.elements = (int *)malloc(sizeof(int *) * arr_m.length);

                // merge the left part and right part

                merge(arr_l, arr_r, &arr_m);

                // return the sort result

                array_p->length = arr_m.length;

                int length_m = arr_m.length;

                while (length_m-- > 0)

                {

                        array_p->elements[length_m] = arr_m.elements[length_m];

                }

        }

}

int merge(array arr_l, array arr_r, array *arr_m)

{

        if (arr_l.length == 0)

        {

                if (arr_r.length == 0) return;

                // return the arr_l array

                while (arr_r.length-- > 0)

                        arr_m->elements[arr_m->active++] = arr_r.elements[arr_r.active++];

                return;

        }

        if (arr_r.length == 0)

        {

                if (arr_l.length == 0) return;

                // return the arr_r array

                while (arr_l.length-- > 0)

                        arr_m->elements[arr_m->active++] = arr_l.elements[arr_l.active++];

                return;

        }

        if (arr_l.elements[arr_l.active] > arr_r.elements[arr_r.active])

        {

                // the next elements of the merge array is bigger one

                arr_m->elements[arr_m->active++] = arr_l.elements[arr_l.active++];

                arr_l.length--;

                // recursively merge the rest array

                merge(arr_l, arr_r, arr_m);

        }

        else

        {

                // the next elements of the merge array is bigger one

                arr_m->elements[arr_m->active++] = arr_r.elements[arr_r.active++];

                arr_r.length--;

                // recursively merge the rest array

                merge(arr_l, arr_r, arr_m);

        }

}

上周日开始写的这个程序，遇到了很多问题，也有很多收获。只要不选择放弃，肯定能解决遇到的问题～！