From 0d91f0757ea6f1d84b5ec7d39b0fdebbd3bcd821 Mon Sep 17 00:00:00 2001 From: FiTeen Date: Fri, 20 Dec 2019 19:48:14 +0800 Subject: [PATCH] feat: add MergeSort --- MergeSort/README.md | 53 +++++++++++++++++++++++++++++++++++++++ MergeSort/merge-sort.gif | Bin 0 -> 514371 bytes MergeSort/merge_sort.c | 39 ++++++++++++++++++++++++++++ README.md | 2 +- 4 files changed, 93 insertions(+), 1 deletion(-) create mode 100644 MergeSort/README.md create mode 100644 MergeSort/merge-sort.gif create mode 100644 MergeSort/merge_sort.c diff --git a/MergeSort/README.md b/MergeSort/README.md new file mode 100644 index 0000000..a3cae8e --- /dev/null +++ b/MergeSort/README.md @@ -0,0 +1,53 @@ +## 归并排序 + +归并排序(Merge Sort)是建立在**归并**操作上的一种排序算法。它和快速排序一样,采用了**分治法**。 + +### 基本思想 + +归并的含义是将两个或两个以上的有序表组合成一个新的有序表。也就是说,从几个数据段中逐个选出最小的元素移入新数据段的末尾,使之有序。 + +那么归并排序的算法我们可以这样理解: + +假如初始序列含有 n 个记录,则可以看成是 n 个有序的子序列,每个子序列的长度为 1。然后两两归并,得到 n/2 个长度为2或1的有序子序列;再两两归并,……,如此重复,直到得到一个长度为 n 的有序序列为止,这种排序方法称为 **二路归并排序**,下文介绍的也是这种排序方式。 + +### 动图演示 + +![](merge-sort.gif) + +### 代码实现 + +#### C语言 + +```c +/* 将 arr[L..M] 和 arr[M+1..R] 归并 */ +void merge(int arr[], int L, int M, int R) { + int LEFT_SIZE = M - L + 1; + int RIGHT_SIZE = R - M; + int left[LEFT_SIZE]; + int right[RIGHT_SIZE]; + int i, j, k; + // 以 M 为分割线,把原数组分成左右子数组 + for (i = L; i <= M; i++) left[i - L] = arr[i]; + for (i = M + 1; i <= R; i++) right[i - M - 1] = arr[i]; + // 再合并成一个有序数组(从两个序列中选出最小值依次插入) + i = 0; j = 0; k = L; + while (i < LEFT_SIZE && j < RIGHT_SIZE) arr[k++] = left[i] < right[j] ? left[i++] : right[j++]; + while (i < LEFT_SIZE) arr[k++] = left[i++]; + while (j < RIGHT_SIZE) arr[k++] = right[j++]; +} + +void merge_sort(int arr[], int L, int R) { + if (L == R) return; + // 将 arr[L..R] 平分为 arr[L..M] 和 arr[M+1..R] + int M = (L + R) / 2; + // 分别递归地将子序列排序为有序数列 + merge_sort(arr, L, M); + merge_sort(arr, M + 1, R); + // 将两个排序后的子序列再归并到 arr + merge(arr, L, M, R); +} +``` + +### 算法分析 + +归并排序是**稳定排序**,它和选择排序一样,性能不受输入数据的影响,但表现比选择排序更好,它的时间复杂度始终为 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zEq`{c;CQVFwO*{bUTVMoB7D8PV7;*~7u&8(rZ7Z^Hq6pOveba9`Vozc{F@7DPDlO{N)mkB5zzZ2F4R zZgc@(ssUbry_;Kd-dh<@Q6cilN$hNX-{M~!MoDv1eVlXWPCLu=|y3&7WAJ)DVY4L{aAdick3nKu?kn9t7#VQ4n+w3sU zI?CzVO;X6=%R;&Kl-=J*as{Pyrs4PVdyf*+|t|7%(wqyQkn z?I&Jo2KZhP`#r_f!3kM9UBF%bUFCQUoUU?o3$YiynV6+K;0Wg}5{ux~CrvRm9b_jo z*|K$Hk-L9XIl?=eg#6!{iQk!FD$_)57o<;v*nJ*u*oR+rC}oGuOB>WlA4Tv=L?dM* zk!?P3_S$|4U1^>YF@lrokq_@49^OnlWGN)@Zj&Y;_uc!s#-2NCu z&CvrHK!HZh`%)bRefZyUc&u1K+lMIczq5Zs>NbiPCh_ + +/* 将 arr[L..M] 和 arr[M+1..R] 归并 */ +void merge(int arr[], int L, int M, int R) { + int LEFT_SIZE = M - L + 1; + int RIGHT_SIZE = R - M; + int left[LEFT_SIZE]; + int right[RIGHT_SIZE]; + int i, j, k; + // 以 M 为分割线,把原数组分成左右子数组 + for (i = L; i <= M; i++) left[i - L] = arr[i]; + for (i = M + 1; i <= R; i++) right[i - M - 1] = arr[i]; + // 再合并成一个有序数组(从两个序列中选出最小值依次插入) + i = 0; j = 0; k = L; + while (i < LEFT_SIZE && j < RIGHT_SIZE) arr[k++] = left[i] < right[j] ? left[i++] : right[j++]; + while (i < LEFT_SIZE) arr[k++] = left[i++]; + while (j < RIGHT_SIZE) arr[k++] = right[j++]; +} + +void merge_sort(int arr[], int L, int R) { + if (L == R) return; + // 将 arr[L..R] 平分为 arr[L..M] 和 arr[M+1..R] + int M = (L + R) / 2; + // 分别递归地将子序列排序为有序数列 + merge_sort(arr, L, M); + merge_sort(arr, M + 1, R); + // 将两个排序后的子序列再归并到 arr + merge(arr, L, M, R); +} + +int main() { + int arr[] = {7, 2, 6, 3, 1, 5, 8, 4}; + int n = sizeof(arr) / sizeof(*arr); + merge_sort(arr, 0, n - 1); + printf("Sort result:\n"); + for (int i = 0; i < n; i++) + printf("%d ", arr[i]); + return 0; +} diff --git a/README.md b/README.md index db45cee..1b22811 100644 --- a/README.md +++ b/README.md @@ -14,7 +14,7 @@ - [希尔排序](ShellSort) - [选择排序](SelectionSort) - [堆排序](HeapSort) -- 归并排序 +- [归并排序](MergeSort) **非比较类排序**:不通过比较来决定元素间的相对次序,其时间复杂度可以突破 O(nlogn),以线性时间运行。属于非比较类的有: