day_20 —— 归并排序学习

Day_20 —— 归并排序

归并排序的基本思想是：

• 先将序列一次次分成子序列，直到子序列长度为1；
• 再将已有序的子序列合并，得到完全有序的序列。

可以看出归并排序运用了 分而治之的思想 。

归并排序是按照分层进行比较的，会分成$lo{g}_{2}n$层；
而每一层的比较次数为$O(n)$；
所以时间复杂度求得$nlo{g}_{2}n$。

C实现：

#include 

#define max 10

int a[11] = { -10, 14, 11, 26, 34, 31, -33, 20, 42, 11, 0 };
int b[10];

void merging(int low, int mid, int high) {
   int l1, l2, i;

   for(l1 = low, l2 = mid + 1, i = low; l1 <= mid && l2 <= high; i++) {
      if(a[l1] <= a[l2])
         b[i] = a[l1++];
      else
         b[i] = a[l2++];
   }
   
   while(l1 <= mid)    
      b[i++] = a[l1++];

   while(l2 <= high)   
      b[i++] = a[l2++];

   for(i = low; i <= high; i++)
      a[i] = b[i];
}

void sort(int low, int high) {
   int mid;
   
   if(low < high) {
      mid = (low + high) / 2;
      sort(low, mid);
      sort(mid+1, high);
      merging(low, mid, high);
   } else { 
      return;
   }   
}

int main() { 
   int i;

   printf("List before sorting\n");
   
   for(i = 0; i <= max; i++)
      printf("%d ", a[i]);

   sort(0, max);

   printf("\nList after sorting\n");
   
   for(i = 0; i <= max; i++)
      printf("%d ", a[i]);
}

python实现：

def merge_sort(collection):
    def merge(left, right):
        result = []
        while left and right:
            result.append((left if left[0] <= right[0] else right).pop(0))
        return result + left + right

    if len(collection) <= 1:
        return collection
    mid = len(collection) // 2
    return merge(merge_sort(collection[:mid]), merge_sort(collection[mid:]))


if __name__ == "__main__":
    user_input = input("Enter numbers separated by a comma:\n").strip()
    unsorted = [int(item) for item in user_input.split(",")]
    print(*merge_sort(unsorted), sep=",")