第2章 算法基础（合并排序，逆序对）

#include<stdio.h>
#include<stdlib.h>
#include<time.h>
#include<string.h>
#define MAXINT (1<<30)
void InsertSort(int *a, int n)
{
	int tmp, j;
	for (int i = 1; i < n; ++i){
		tmp = a[i];
		j = i - 1;
		while (j >= 0 && a[j]>tmp){
			a[j + 1] = a[j];
			--j;
		}
		a[j + 1] = tmp;
	}
}
void merge(int *a, int p, int q, int r)
{
	int n1 = q - p + 1;
	int n2 = r - q;
	int *L = (int*)malloc((n1 + 1)*sizeof(int));
	int *R = (int*)malloc((n2 + 1)*sizeof(int));
	for (int i = 0; i < n1; ++i)
		L[i] = a[p + i];
	for (int i = 0; i < n2; ++i)
		R[i] = a[q + 1 + i];
	L[n1] = R[n2] = MAXINT;
	int i, j;
	i = j = 0;
	for (int k = p; k <= r; ++k){
		if (L[i] < R[j]){
			a[k] = L[i];
			++i;
		}
		else{
			a[k] = R[j];
			++j;
		}
	}
	free(L);
	free(R);
}
void mergeSort(int *a, int p, int r)
{
	if (p < r){
		int q = (r + p) / 2;
		mergeSort(a, p, q);
		mergeSort(a, q + 1, r);
		merge(a, p, q, r);
	}
}

void printArray(int *a, int n)
{
	for (int i = 0; i < n; ++i)
		printf("%d	", a[i]);
	printf("
");
}
//逆序对 n^2
int inversion(int *a, int n)
{
	int count = 0;
	for (int i = 0; i < n - 1; ++i)
		for (int j = i + 1; j < n; ++j)
			if (a[i]>a[j]) ++count;
	return count;
}

//逆序对 nlgn
int InversionMerge(int *a, int p, int q, int r)
{
	int n1 = q - p + 1;
	int n2 = r - q;
	int *L = (int*)malloc((n1 + 1)*sizeof(int));
	int *R = (int*)malloc((n2 + 1)*sizeof(int));
	for (int i = 0; i < n1; ++i)
		L[i] = a[p + i];
	for (int i = 0; i < n2; ++i)
		R[i] = a[q + 1 + i];
	L[n1] = R[n2] = MAXINT;
	int i, j, count;
	i = j = count = 0;
	for (int k = p; k <= r; ++k){
		if (L[i] <= R[j]){
			a[k] = L[i];
			++i;
		}
		else{
			a[k] = R[j];
			++j;
			count += n1 - i;	//L中有 n1-i 个大于 R[j] 的项，此操作会使数组的逆序对减少 n1-i 个
		}
	}
	free(L);
	free(R);
	return count;
}
int InversionMergeSort(int *a, int p, int r)
{
	int count = 0;
	if (p < r){
		int q = (r + p) / 2;
		count += InversionMergeSort(a, p, q) + InversionMergeSort(a, q + 1, r) + InversionMerge(a, p, q, r);
	}
	return count;
}
int main()
{
	srand(time(NULL));
	const int cnt = 10;
	int a[cnt];
	for (int i = 0; i < cnt; ++i)
		a[i] = rand() % 100;
	//mergeSort(a, 0,cnt-1);
	for (int i = 0; i < cnt; ++i)
		printf("%d	", a[i]);
	printf("
");
	printf("%d
", inversion(a, cnt));
	printf("%d
", InversionMergeSort(a, 0, cnt - 1));

}