归并排序(Merge-Sort)的C语言实现
归并排序是分治法(Divide-and-Conquer)的典型应用:
Divide the problem into a number of subproblems.
Conquer the subproblems by solving them recursively. if the subproblem sizes are small enough, just sovle the subproblems in a straightforward manner.
Combine the solutions to the subproblems into the solution for the original problem.
对于归并排序,需要考量的是:
递:将待排序数组划分为左边和右边,并对于左边和右边进行递归地排序。直到左边和右边只剩下一个元素——直接求解。
归:递归合并结果得到最终解。
代码:
#include "stdafx.h" #define MAX 99999; #define SIZE 7 void PrintNewLine(); void PrintArray(int arr[]); void MergeSort(int arr[], int p, int r); void Merge(int arr[], int p, int q, int r); int _tmain(int argc, _TCHAR* argv[]) { int original[] = {6,4,3,1,7,5,2}; PrintArray(original); PrintNewLine(); MergeSort(original,0,SIZE - 1); PrintArray(original); PrintNewLine(); char wait = getchar(); return 0; } void MergeSort(int arr[], int p, int r) { if( r > p ) { //divide&conqurer by recursion int q = (p + r) / 2; MergeSort(arr, p, q); MergeSort(arr, q+1, r); //combine Merge(arr, p, q, r); printf("Merge(%d,%d,%d) => ",p,q,r); PrintArray(arr); PrintNewLine(); } } void Merge(int arr[], int p, int q, int r) { //calc left side and right side int nLeft = (q - p) + 1; int nRight = r - q; int* leftArr = new int[nLeft]; int* rightArr = new int[nRight]; //copy element to left&right side for(int i = 0; i < nLeft; i++) { leftArr[i]=arr[p+i]; } for(int j=0; j<nRight; j++) { rightArr[j]=arr[(q+j) + 1]; } //sentinel leftArr[nLeft] = MAX; rightArr[nRight] = MAX; //pick the small card in original array int i = 0, j = 0; for(int k = p; k <= r; k++) { if(leftArr[i] < rightArr[j]) //sentinel takes effect { arr[k] = leftArr[i]; i++; } else { arr[k] = rightArr[j]; j++; } } } void PrintArray(int arr[]) { for(int i = 0; i < SIZE; i++) printf("%d ",arr[i]); } void PrintNewLine() { printf("\n"); }
输出:
6 4 3 1 7 5 2 Merge(0,0,1) => 4 6 3 1 7 5 2 Merge(2,2,3) => 4 6 1 3 7 5 2 Merge(0,1,3) => 1 3 4 6 7 5 2 Merge(4,4,5) => 1 3 4 6 5 7 2 Merge(4,5,6) => 1 3 4 6 2 5 7 Merge(0,3,6) => 1 2 3 4 5 6 7 1 2 3 4 5 6 7
递归排序的算法复杂度为:O(nlgn)。