归并排序 C++解法

#include <iostream>
using namespace std;

void merge(int* a, int start, int mid, int end) {
	int *tmp = new int[end-start+1];
	int i = start;
	int j = mid + 1;
	int k = 0;
	while(i <= mid && j <= end) {
		if (a[i] <= a[j]) tmp[k++] = a[i++];
		else tmp[k++] = a[j++];
	}
	while(i <= mid) tmp[k++] = a[i++];
	while(j <= end) tmp[k++] = a[j++];
	for (i = 0; i < k; i++)
		a[start + i] = tmp[i];
	delete[] tmp;
}
void mergeSortUp2Down(int* a, int start, int end) {
	if(a==NULL || start >= end) return ;
	int mid = (end + start)/2;
	mergeSortUp2Down(a, start, mid);
	mergeSortUp2Down(a, mid+1, end);
	merge(a, start, mid, end);
}
int main() {
	int i;
	int a[] = {80,30,60,40,20,10,50,70};
	int ilen = (sizeof(a)) / (sizeof(a[0]));
	cout << "before sort:";
	for (i=0; i<ilen; i++)
		cout << a[i] << " ";
	cout << endl;
	mergeSortUp2Down(a, 0, ilen-1);
	cout << "after  sort:";
	for (i=0; i<ilen; i++)
		cout << a[i] << " ";
	cout << endl;
	return 0;
}

思路：归并排序采用经典的分治法，将一个数组不断的分解成n个小数组，通过处理小数组且合并，达到排序的目的。但是归并排序需要一个O（n）长度的辅助数组，也就是空间复杂度是O（n）。该算法的时间复杂度为O（nlogn），是一种稳定的排序算法。