归并排序

算法思想

分治思想

时间复杂度和空间复杂度

归并排序最好和最坏情况的时间复杂度都是O(n)log(n)，空间复杂度度是O(n)

稳定性

稳定

python实现

def merge_sort(nums, left, right, result):
    if right != left:
        merge_sort(nums, left, (right+left)//2, result)
        merge_sort(nums, (right+left)//2+1, right, result)
        merge(nums, left, right, result)
        for i in range(left, right+1):
            nums[i] = result[i]

def merge(nums, left, right, result):
    mid = (right+left)//2
    k = left
    p = mid + 1
    while left <= mid:
        if p <= right:
            if nums[left] < nums[p]:
                result[k] = nums[left]
                k += 1
                left += 1
            else:
                result[k] = nums[p]
                k += 1
                p += 1
        else:
            result[k] = nums[left]
            k += 1
            left += 1
    for i in range(p, right+1):
        result[k] = nums[p]
        k += 1
        p += 1

if __name__ == '__main__':
    nums = list(map(int, input().strip().split(' ')))
    result = [0] * len(nums)
    merge_sort(nums, 0, len(nums)-1, result)
    print(result)
    print(nums)

 

C++实现

int merge(int nums[], int left, int right, int result[])
{
    int mid = (left + right) / 2;
    int i = left;
    int j = mid + 1;
    int k = left;
    while(i <= mid)
    {
        if(j <= right)
        {
            if(nums[i] < nums[j])
            {
                result[k] = nums[i];
                k++;
                i++;
            }
            else
            {
                result[k] = nums[j];
                k++;
                j++;
            }
        }
        else
        {
            result[k] = nums[i];
            k++;
            i++;
        }
    }
    while(j <= right)
    {
        result[k] = nums[j];
        k++;
        j++;
    }
}

void merge_sort(int nums[], int left, int right, int result[])
{
    if(left < right)
    {
        merge_sort(nums, left, (left+right)/2, result);
        merge_sort(nums, (left+right)/2+1, right, result);
        merge(nums, left, right, result);
        for(int i=left; i<=right; i++)
            nums[i] = result[i];
    }
}