递归时间复杂度（master），时间复杂度为O(NlogN)的排序

归并排序：

#include<iostream>
#include<string>
#include<fstream>
using namespace std;

void merge(int arr[], int L, int R, int mid)
{
	
	int* help = new int[R - L + 1];
	int i = 0;
	int p1 = L;
	int p2 = mid + 1;
	while (p1 <= mid && p2 <= R)
	{
		help[i++] = arr[p1] <= arr[p2] ? arr[p1++] : arr[p2++];
	}
	while (p1 <= mid)
	{
		help[i++] = arr[p1++];
	}
	while (p2 <= R)
	{
		help[i++] = arr[p2++];
	}
	for (int j = 0;j < i;j++)
	{
		arr[L + j] = help[j];
	}
	delete[] help;

}
void Process(int arr[],int L,int R)
{
	if (L == R)
	{
		return;
	}
	int mid = L + ((R - L) >> 1);
	Process(arr, L, mid);
	Process(arr, mid + 1, R);
	merge(arr, L, R, mid);
	
}

int main()
{
	int arr[] = { 11,3,5,9,9,26,113 };
	int len = sizeof(arr) / sizeof(arr[0]);
	Process(arr, 0, len-1);
	for (int i = 0;i < len;i++)
	{
		cout << arr[i] << " ";
	}
	return 0;
}

 小和问题：

#include<iostream>
#include<string>
#include<fstream>
using namespace std;

int merge(int arr[], int L, int R, int mid)
{
	
	int* help = new int[R - L + 1];
	int i = 0;
	int p1 = L;
	int p2 = mid + 1;
	int sort = 0;
	while (p1 <= mid && p2 <= R)
	{
		sort += arr[p1] < arr[p2] ? (R - p2 + 1) * arr[p1] : 0;
		help[i++] = arr[p1] < arr[p2] ? arr[p1++] : arr[p2++];
	}
	while (p1 <= mid)
	{
		help[i++] = arr[p1++];
	}
	while (p2 <= R)
	{
		help[i++] = arr[p2++];
	}
	for (int j = 0;j < i;j++)
	{
		arr[L + j] = help[j];
	}
	delete[] help;
	return sort;

}
int Process(int arr[],int L,int R)
{
	if (L == R)
	{
		return 0;
	}
	int mid = L + ((R - L) >> 1);
	return 
	Process(arr, L, mid)+
	Process(arr, mid + 1, R)+
	merge(arr, L, R, mid);
	
}

int main()
{
	int arr[] = { 11,3,5,9,9,26,113 };
	int len = sizeof(arr) / sizeof(arr[0]);
	cout << Process(arr, 0, len - 1) << endl;
	for (int i = 0;i < len;i++)
	{
		cout << arr[i] << " ";
	}
	return 0;
}

逆序对问题：

#include<iostream>
#include<string>
#include<fstream>
using namespace std;

int merge(int arr[], int L, int R, int mid)
{

	int* help = new int[R - L + 1];
	int i = 0;
	int p1 = L;
	int p2 = mid + 1;
	int sort = 0;
	while (p1 <= mid && p2 <= R)
	{

		sort += arr[p2] < arr[p1] ? (p1 - L + 1) : 0;
		int j = 0;
		while (arr[p2] < arr[p1] && j + p1 < p2)
		{
			cout << arr[p1 + (j++)] << " : " << arr[p2] << endl;
		}
		help[i++] = arr[p2] < arr[p1] ? arr[p2++] : arr[p1++];
	}
	while (p1 <= mid)
	{
		help[i++] = arr[p1++];
	}
	while (p2 <= R)
	{
		help[i++] = arr[p2++];
	}
	for (int j = 0;j < i;j++)
	{
		arr[L + j] = help[j];
	}
	delete[] help;
	return sort;

}
int Process(int arr[], int L, int R)
{
	if (L == R)
	{
		return 0;
	}
	int mid = L + ((R - L) >> 1);
	return
		Process(arr, L, mid) +
		Process(arr, mid + 1, R) +
		merge(arr, L, R, mid);

}

int main()
{
	int arr[] = { 1,3,4,2,5 };
	int len = sizeof(arr) / sizeof(arr[0]);
	cout << Process(arr, 0, len - 1) << endl;
	for (int i = 0;i < len;i++)
	{
		cout << arr[i] << " ";
	}
	return 0;
}

 荷兰国旗问题：

#include<iostream>
#include<string>
#include<fstream>
using namespace std;

void swap(int &a, int &b)
{
	int tmp = a;
	a = b;
	b = tmp;
}
void Sort(int arr[], int len)
{
	int p1 = -1;
	int p2 = len;
	int i = 0;
	int num = arr[len - 1];
	while (i < p2)
	{
		if (arr[i] < num)
		{
			swap(arr[i++], arr[++p1]);
		}
		else if (arr[i] > num)
		{
			swap(arr[i], arr[--p2]);
		}
		else
		{
			i++;
		}
		

	}
}

int main()
{
	int arr[] = { 1,3,4,2,5,3,2,1,4,5,7,5,5 };
	int len = sizeof(arr) / sizeof(arr[0]);
	Sort(arr, len);
	for (int i = 0;i < len;i++)
	{
		cout << arr[i] << " ";
	}
	return 0;
}