常见排序算法总结

归纳总结

这个表格总结了各种排序算法的复杂度与稳定性：

下面是关于相关排序的代码实现。

冒泡排序

#include <iostream>

using namespace std;

void bubbleSort(int a[], int len)
{
	int i, j, t;
	//将最小的先放到第一个位置
	for (i = 0; i < len - 1; i++)
	{
		for (j = len - 1; j > i; j--)
		{
			if (a[j] < a[j - 1])
			{
				t = a[j];
				a[j] = a[j - 1];
				a[j - 1] = t;
			}
		}
	}
	//将最大的先放到最后一个位置
	/*for (i = 0; i < len - 1; i++)
	{
		for (j = 0; j <len - 1 - i; j++)
		{
			if (a[j] > a[j + 1])
			{
				t = a[j];
				a[j] = a[j + 1];
				a[j + 1] = t;
			}
		}
	}*/
}

int main()
{
	int array[] = { 34, 65, 12, 43, 67, 5, 78, 10, 3, 70 }, k;
	int len = sizeof(array) / sizeof(int);
	cout << "The orginal array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	bubbleSort(array, len);
	cout << "The sorted array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	system("pause");
	return 0;
}

选择排序

#include <iostream>

using namespace std;

void selectSort(int a[], int len)
{
	int i, j, k, tem;
	for (i = 0; i < len - 1; i++)
	{
		k = i;
		for (j = k + 1; j < len; j++)
		{
			if (a[k] > a[j])
			{
				k = j;
			}
		}
		if (i != k)
		{
			tem = a[i];
			a[i] = a[k];
			a[k] = tem;
		}
	}
}

int main()
{
	int array[] = { 34, 65, 12, 43, 67, 5, 78, 10, 3, 70 }, k;
	int len = sizeof(array) / sizeof(int);
	cout << "The orginal array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	selectSort(array, len);
	cout << "The sorted array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	system("pause");
	return 0;
}

插入排序

#include <iostream>
//直接插入排序
using namespace std;

void insertSort(int arr[], int len)
{
	for (int i = 1; i < len; i++)
	{
		int j = i - 1;
		int t = arr[i];
		//从后往前，比当前值t大则往后移
		while (j > -1 && t < arr[j])
		{
			arr[j + 1] = arr[j];
			j--;
		}
		arr[j + 1] = t;
	}
}

int main()
{
	int array[] = { 34, 65, 12, 43, 67, 5, 78, 10, 3, 70 }, k;
	int len = sizeof(array) / sizeof(int);
	cout << "The orginal array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	insertSort(array, len);
	cout << "The sorted array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	system("pause");
	return 0;
}

快速排序

#include <iostream>

using namespace std;

void quickSort(int a[], int l, int r)
{
	if (l < r)
	{
		int i = l, j = r, x = a[l];
		while (i < j)
		{
			while (i < j&&a[j] >= x)
			{
				j--;
			}
			if (i < j)
			{
				a[i++] = a[j];
			}
			while (i < j&&a[i] <= x)
			{
				i++;
			}
			if (i < j)
			{
				a[j--] = a[i];
			}
		}
		a[i] = x;
		quickSort(a, l, i - 1);
		quickSort(a, i + 1, r);
	}
}

int main()
{
	int array[] = { 34, 65, 12, 43, 67, 5, 78, 10, 3, 70 }, k;
	int len = sizeof(array) / sizeof(int);
	cout << "The orginal array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	quickSort(array, 0, len - 1);
	cout << "The sorted array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	system("pause");
	return 0;
}

归并排序

#include <iostream>

using namespace std;

void merge(int arr[], int tempArr[], int start, int mid, int end)
{
	int i = start, j = mid + 1, k = 0;
	while (i < mid + 1 && j < end + 1)
	{
		//谁小先放谁
		if (arr[i] > arr[j])
			tempArr[k++] = arr[j++];
		else
			tempArr[k++] = arr[i++];
	}
	//最后必有一边剩余，添加到后面即可
	while (i < mid + 1)
	{
		tempArr[k++] = arr[i++];
	}
	while (j < end + 1)
	{
		tempArr[k++] = arr[j++];
	}
	//将排好的内容赋回原数组
	for (i = 0, j = start; j < end + 1; i++, j++)
	{
		arr[j] = tempArr[i];
	}
}

//主要就是递归的实现
void mergeSort(int arr[], int tempArr[], int start, int end)
{
	if (start < end)
	{
		int mid = (start + end) / 2;
		mergeSort(arr, tempArr, start, mid);
		mergeSort(arr, tempArr, mid + 1, end);
		merge(arr, tempArr, start, mid, end);
	}
}


int main()
{
	int array[] = { 34, 65, 12, 43, 67, 5, 78, 10, 3, 70 }, k;
	int len = sizeof(array) / sizeof(int);
	int tempArray[10] = { 0 };
	cout << "The orginal array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	mergeSort(array, tempArray, 0, len - 1);
	cout << "The sorted array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	system("pause");
	return 0;
}

堆排序

#include <iostream>

using namespace std;

//数组arr局部调整为最大堆的实现，i为待调整元素下标，len为数组长度
void heapAdjust(int arr[], int i, int len)
{
	int child, temp;
	for (; 2 * i + 1 < len; i = child)
	{
		// 子结点的位置 = 2 * 父结点的位置 + 1
		child = 2 * i + 1;
		// 得到子结点中键值较大的结点，因为是调整为最大堆
		if (child < len - 1 && arr[child] < arr[child + 1])
		{
			child++;
		}
		//如果较大的子结点大于父结点那么把较大的子结点往上移动，替换它的父结点
		if (arr[i] < arr[child])
		{
			temp = arr[i];
			arr[i] = arr[child];
			arr[child] = temp;
		}
		else
			break;
	}
}

//堆排序的实现
void heapSort(int arr[], int len)
{
	int i;
	//数组arr调整为最大堆，调整完之后第一个元素是序列的最大的元素
	for (i = len / 2 - 1; i >= 0; i--)
	{
		heapAdjust(arr, i, len);
	}
	//将第1个元素与当前最后一个元素交换，保证当前的最后一个位置的元素都是现在的这个序列中最大的
	for (i = len - 1; i > 0; i--)
	{
		int temp = arr[0];
		arr[0] = arr[i];
		arr[i] = temp;
		// 不断缩小调整heap的范围，每一次调整完毕保证第一个元素是当前序列的最大值
		heapAdjust(arr, 0, i);
	}
}

int main()
{
	int array[] = { 34, 65, 12, 43, 67, 5, 78, 10, 3, 70 }, k;
	int len = sizeof(array) / sizeof(int);
	int temparray[10] = { 0 };
	cout << "the orginal array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	heapSort(array, len);
	cout << "the sorted array are:" << endl;
	for (k = 0; k < len; k++)
		cout << array[k] << ",";
	cout << endl;
	system("pause");
	return 0;
}

堆排序的一个实例过程：

参考：

1.各种排序算法总结
2.十大经典排序算法（动图演示）
3.十种排序算法总结