归并排序(Merge Sort)
归并排序是建立在归并操作上的一种有效的排序算法,该算法是采用分治法(Divide and Conquer)的一个非常典型的应用。将已有序的子序列合并,得到完全有序的序列;即先使每个子序列有序,再使子序列段间有序。若将两个有序表合并成一个有序表,称为二路归并。
示例:
public class Program {
public static void Main(string[] args) {
int[] array = { 43, 69, 11, 72, 28, 21, 56, 80, 48, 94, 32, 8 };
MergeSort(array, 0, array.Length - 1);
ShowSord(array);
Console.ReadKey();
}
private static void ShowSord(int[] array) {
foreach (var num in array) {
Console.Write($"{num} ");
}
Console.WriteLine();
}
public static void MergeSort(int[] array, int low, int high) {
if (low < high) {
int mid = (low + high) / 2;
MergeSort(array, low, mid);
MergeSort(array, mid + 1, high);
Merge(array, low, mid, high);
}
}
private static void Merge(int[] array, int low, int mid, int high) {
int[] mergeArr = new int[high - low + 1];
int left = low;
int right = mid + 1;
int merge = 0;
while (left <= mid && right <= high) {
if (array[left] <= array[right]) {
mergeArr[merge++] = array[left++];
}
else {
mergeArr[merge++] = array[right++];
}
}
while (left <= mid) {
mergeArr[merge++] = array[left++];
}
while (right <= high) {
mergeArr[merge++] = array[right++];
}
merge = 0;
while (low <= high) {
array[low++] = mergeArr[merge++];
}
}
}
以上是归并排序算法的一种实现,以下是这个案例的输出结果:
8 11 21 28 32 43 48 56 69 72 80 94
分析:归并排序算法的时间复杂度不难证明为: 。
AlgorithmMan:
AlgorithmMan by Iori,AlgorithmMan是使用Winform技术开发的一套用于算法演示的工具。