Merge Sort
最后更新于：2022-04-02 01:06:49
# Merge Sort - 归并排序
核心：将两个有序对数组归并成一个更大的有序数组。通常做法为递归排序，并将两个不同的有序数组归并到第三个数组中。
先来看看动图，归并排序是一种典型的分治应用。
### Python
~~~
#!/usr/bin/env python
class Sort:
def mergeSort(self, alist):
if len(alist) <= 1:
return alist
mid = len(alist) / 2
left = self.mergeSort(alist[:mid])
print("left = " + str(left))
right = self.mergeSort(alist[mid:])
print("right = " + str(right))
return self.mergeSortedArray(left, right)
#@param A and B: sorted integer array A and B.
#@return: A new sorted integer array
def mergeSortedArray(self, A, B):
sortedArray = []
l = 0
r = 0
while l < len(A) and r < len(B):
if A[l] < B[r]:
sortedArray.append(A[l])
l += 1
else:
sortedArray.append(B[r])
r += 1
sortedArray += A[l:]
sortedArray += B[r:]
return sortedArray
unsortedArray = [6, 5, 3, 1, 8, 7, 2, 4]
merge_sort = Sort()
print(merge_sort.mergeSort(unsortedArray))
~~~
### 原地归并
### Java
~~~
public class MergeSort {
public static void main(String[] args) {
int unsortedArray[] = new int[]{6, 5, 3, 1, 8, 7, 2, 4};
mergeSort(unsortedArray);
System.out.println("After sort: ");
for (int item : unsortedArray) {
System.out.print(item + " ");
}
}
private static void merge(int[] array, int low, int mid, int high) {
int[] helper = new int[array.length];
// copy array to helper
for (int k = low; k <= high; k++) {
helper[k] = array[k];
}
// merge array[low...mid] and array[mid + 1...high]
int i = low, j = mid + 1;
for (int k = low; k <= high; k++) {
// k means current location
if (i > mid) {
// no item in left part
array[k] = helper[j];
j++;
} else if (j > high) {
// no item in right part
array[k] = helper[i];
i++;
} else if (helper[i] > helper[j]) {
// get smaller item in the right side
array[k] = helper[j];
j++;
} else {
// get smaller item in the left side
array[k] = helper[i];
i++;
}
}
}
public static void sort(int[] array, int low, int high) {
if (high <= low) return;
int mid = low + (high - low) / 2;
sort(array, low, mid);
sort(array, mid + 1, high);
merge(array, low, mid, high);
for (int item : array) {
System.out.print(item + " ");
}
System.out.println();
}
public static void mergeSort(int[] array) {
sort(array, 0, array.length - 1);
}
}
~~~
时间复杂度为 O(NlogN)O(N \log N)O(NlogN), 使用了等长的辅助数组，空间复杂度为 O(N)O(N)O(N)。
### Reference
- [Mergesort](http://algs4.cs.princeton.edu/22mergesort/) - Robert Sedgewick 的大作，非常清晰。
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