09-排序2 Insert or Merge (25分) (2020浙大Mooc数据结构配套题)

According to Wikipedia:

Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. Each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.

Merge sort works as follows: Divide the unsorted list into N sublists, each containing 1 element (a list of 1 element is considered sorted). Then repeatedly merge two adjacent sublists to produce new sorted sublists until there is only 1 sublist remaining.

Now given the initial sequence of integers, together with a sequence which is a result of several iterations of some sorting method, can you tell which sorting method we are using?

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤100). Then in the next line, N integers are given as the initial sequence. The last line contains the partially sorted sequence of the N numbers. It is assumed that the target sequence is always ascending. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in the first line either “Insertion Sort” or “Merge Sort” to indicate the method used to obtain the partial result. Then run this method for one more iteration and output in the second line the resuling sequence. It is guaranteed that the answer is unique for each test case. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input 1:

10
3 1 2 8 7 5 9 4 6 0
1 2 3 7 8 5 9 4 6 0

Sample Output 1:

Insertion Sort
1 2 3 5 7 8 9 4 6 0

Sample Input 2:

10
3 1 2 8 7 5 9 4 0 6
1 3 2 8 5 7 4 9 0 6

Sample Output 2:

Merge Sort
1 2 3 8 4 5 7 9 0 6

  题目是意思是给一串原始数据（Origin）和一串排序未完成的数据(Check)，然后根据这两串数据判断是归并排序还是插入排序，判断好了就打印是什么排序并且多执行一次打印出这串数据，简单是方法是在两个排序算法里添加一个检测函数（Indicate），然后两个排序一步步执行，每次都判断一下是不是和Check一样，然后得出结论。

示例代码：

#include
#include

typedef long ElementType;
 
int Insertion_Sort(ElementType A[], int N);
void Merge_pass( ElementType A[], ElementType TmpA[], int N, int length ); 
void Merge_Sort( ElementType A[], int N );
int Indicate();
void Reset();

ElementType Origin[100];
ElementType Check[100];
ElementType temp[100];
int N;


int main()
{
	int i;
	scanf("%d",&N);
	for(i = 0; i < N; i++){
		scanf("%d",&Origin[i]);
	}
	for(i = 0; i < N; i++){
		scanf("%d",&Check[i]);
	}
	Reset();
	if(!Insertion_Sort(temp,N)){
		return 0;
	}
//	Insertion_Sort(temp,N);
	Reset();
	Merge_Sort(temp,N);
	
} 

void Reset(){
	int i;
	for(i = 0; i < N; i++){
		temp[i] = Origin[i];
	}
}

//一遍遍检测发现不一样就返回0 
int Indicate()
{
	int i;
	for(i = 0; i < N; i++){
		if(temp[i] != Check[i]){
			return 0;
		}
	}
	return 1;
}

void PrintNum(){
	int i;
	for(i = 0; i < N; i++){
		if(i == 0){
			printf("%d",temp[i]);
		}else{
			printf(" %d",temp[i]);
		}
	}
}

//插入排序,O(n^2),稳定 
int Insertion_Sort(ElementType A[], int N)
{
	int i,j;
	ElementType temp;
	for(i = 1; i < N; i++){
		temp = A[i];//保存要比较的元素 
		for(j = i - 1; j >= 0 && A[j] > temp; j--)//当temp是比前一个元素小的时候,前面的元素往后移位 
			A[j + 1] = A[j]; 
		A[j + 1] = temp;
            
		if( Indicate() ){
			printf("Insertion Sort\n");
			i++;
			temp = A[i];//保存要比较的元素 
			for(j = i - 1; j >= 0 && A[j] > temp; j--){//当temp是比前一个元素小的时候,前面的元素往后移位 
				A[j + 1] = A[j]; 
			}
			A[j + 1] = temp;
			PrintNum();
			return 0;
		}
		
	} 
	return 1;
}

/* L = 左边起始位置, R = 右边起始位置, RightEnd = 右边终点位置*/
void Merge( ElementType A[], ElementType TmpA[], int L, int R, int RightEnd )
{ /* 将有序的A[L]~A[R-1]和A[R]~A[RightEnd]归并成一个有序序列 */
     int LeftEnd, NumElements, Tmp;
     int i;
      
     LeftEnd = R - 1; /* 左边终点位置 */
     Tmp = L;         /* 有序序列的起始位置 */
     NumElements = RightEnd - L + 1;
      
     while( L <= LeftEnd && R <= RightEnd ) {
         if ( A[L] <= A[R] )
             TmpA[Tmp++] = A[L++]; /* 将左边元素复制到TmpA */
         else
             TmpA[Tmp++] = A[R++]; /* 将右边元素复制到TmpA */
     }
 
     while( L <= LeftEnd )
         TmpA[Tmp++] = A[L++]; /* 直接复制左边剩下的 */
     while( R <= RightEnd )
         TmpA[Tmp++] = A[R++]; /* 直接复制右边剩下的 */
          
     for( i = 0; i < NumElements; i++, RightEnd -- )
         A[RightEnd] = TmpA[RightEnd]; /* 将有序的TmpA[]复制回A[] */
}

//归并排序,速度快空间开销大
void Merge_Sort( ElementType A[], int N )
{ 
	int length; 
	ElementType *TmpA;
	length = 1; /* 初始化子序列长度*/
	TmpA = (ElementType*)malloc( N * sizeof( ElementType ) );
	if ( TmpA != NULL ) {
		while( length < N ) {
			if( !Indicate() ){
				Merge_pass( A, TmpA, N, length );
				length *= 2;
			}else{
				Merge_pass( A, TmpA, N, length );
				printf("Merge Sort\n");
				PrintNum();
				return;
			}
			if( !Indicate() ){
				Merge_pass( TmpA, A, N, length );
				length *= 2;
			}else{
				Merge_pass( TmpA, A, N, length );
				printf("Merge Sort\n");
				PrintNum();
				return;
			}
			
		}
		free( TmpA );
	}
	else printf( "空间不足" );
}

 
void Merge_pass( ElementType A[], ElementType TmpA[], int N, int length )
{ /* 两两归并相邻有序子列 */
     int i, j;
       
     for ( i=0; i <= N-2*length; i += 2*length )
         Merge( A, TmpA, i, i+length, i+2*length-1 );
     if ( i+length < N ) /* 归并最后2个子列*/
         Merge( A, TmpA, i, i+length, N-1);
     else /* 最后只剩1个子列*/
         for ( j = i; j < N; j++ ) TmpA[j] = A[j];
}