排序小结

插入排序（O（N²））

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//从小到大 void InsertionSort( ElementType A[ ], int N ) {     int j, P;     ElementType Tmp;       for( P = 1; P < N; P++ )     {         Tmp = A[ P ];         for( j = P; j > 0 && A[ j - 1 ] > Tmp; j-- )             A[ j ] = A[ j - 1 ];         A[ j ] = Tmp;     } }   //从大到小 void InsertionSort( ElementType A[ ], int N ) {     int j, P;     ElementType Tmp;       for( P = N - 2; P >= 0; P-- )     {         Tmp = A[ P ];         for( j = P; j < N - 1 && A[ j + 1 ] > Tmp; j++ )             A[ j ] = A[ j + 1 ];         A[ j ] = Tmp;     } }

堆排序（2NlogN-O（NloglogN))

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#define LeftChild( i )  ( 2 * ( i ) + 1 )   void PercDown( ElementType A[ ], int i, int N ) {     int Child;     ElementType Tmp;       for( Tmp = A[ i ]; LeftChild( i ) < N; i = Child )     {         Child = LeftChild( i );         if( Child != N - 1 && A[ Child + 1 ] > A[ Child ] ) // A[ Child + 1 ] < A[ Child ]             Child++;         if( Tmp < A[ Child ] )          //Tmp > A[ Child ]             A[ i ] = A[ Child ];        //两边的比较同时更改的话，就变成从大到小排序         else             break;     }     A[ i ] =Tmp; }   void Heapsort( ElementType A[ ], int N ) {     int i;       for( i = N / 2; i >= 0; i-- )  /* BuildHeap */         PercDown( A, i, N );     for( i = N - 1; i > 0; i-- )     {         Swap( &A[ 0 ], &A[ i ] );  /* DeleteMax */         PercDown( A, 0, i );     } }

归并排序O(NlogN)

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void Merge( ElementType A[ ], ElementType TmpArray[ ],int Lpos, int Rpos, int RightEnd ) {     int i, LeftEnd, NumElements, TmpPos;       LeftEnd = Rpos - 1;     TmpPos = Lpos;     NumElements = RightEnd - Lpos + 1;       /* main loop */     while( Lpos <= LeftEnd && Rpos <= RightEnd )         if( A[ Lpos ] <= A[ Rpos ] )             TmpArray[ TmpPos++ ] = A[ Lpos++ ];         else             TmpArray[ TmpPos++ ] = A[ Rpos++ ];       while( Lpos <= LeftEnd )  /* Copy rest of first half */         TmpArray[ TmpPos++ ] = A[ Lpos++ ];     while( Rpos <= RightEnd ) /* Copy rest of second half */         TmpArray[ TmpPos++ ] = A[ Rpos++ ];       /* Copy TmpArray back */     for( i = 0; i < NumElements; i++, RightEnd-- )         A[ RightEnd ] = TmpArray[ RightEnd ]; }   void MSort( ElementType A[ ], ElementType TmpArray[ ],int Left, int Right ) {     int Center;       if( Left < Right )     {         Center = ( Left + Right ) / 2;         MSort( A, TmpArray, Left, Center );         MSort( A, TmpArray, Center + 1, Right );         Merge( A, TmpArray, Left, Center + 1, Right );     } }   void Mergesort( ElementType A[ ], int N ) {     ElementType *TmpArray;       TmpArray = malloc( N * sizeof( ElementType ) );     if( TmpArray != NULL )     {         MSort( A, TmpArray, 0, N - 1 );         free( TmpArray );     }     else         FatalError( "No space for tmp array!!!" ); }

快速排序O(NlogN)

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/* Return median of Left, Center, and Right */ /* Order these and hide the pivot */ //从小到大 ElementType Median3( ElementType A[ ], int Left, int Right ) {     int Center = ( Left + Right ) / 2;       if( A[ Left ] > A[ Center ] )         Swap( &A[ Left ], &A[ Center ] );     if( A[ Left ] > A[ Right ] )         Swap( &A[ Left ], &A[ Right ] );     if( A[ Center ] > A[ Right ] )         Swap( &A[ Center ], &A[ Right ] );       /* Invariant: A[ Left ] <= A[ Center ] <= A[ Right ] */       Swap( &A[ Center ], &A[ Right - 1 ] );  /* Hide pivot */     return A[ Right - 1 ];                /* Return pivot */ }     //从大到小 ElementType Median3( ElementType A[ ], int Left, int Right ) {     int Center = ( Left + Right ) / 2;       if( A[ Left ] < A[ Center ] )         Swap( &A[ Left ], &A[ Center ] );     if( A[ Left ] < A[ Right ] )         Swap( &A[ Left ], &A[ Right ] );     if( A[ Center ] < A[ Right ] )         Swap( &A[ Center ], &A[ Right ] );       /* Invariant: A[ Left ] >= A[ Center ] >= A[ Right ] */       Swap( &A[ Center ], &A[ Left + 1 ] );  /* Hide pivot */     return A[ Left + 1 ];                /* Return pivot */ }     //从小到大 #define Cutoff ( 3 ) void Qsort( ElementType A[ ], int Left, int Right ) {     int i, j;     ElementType Pivot;       if( Left + Cutoff <= Right )     {         Pivot = Median3( A, Left, Right );         i = Left;         j = Right - 1;         for( ; ; )         {             while( A[ ++i ] < Pivot ) { }             while( A[ --j ] > Pivot ) { }             if( i < j )                 Swap( &A[ i ], &A[ j ] );             else                 break;         }         Swap( &A[ i ], &A[ Right - 1 ] );  /* Restore pivot */           Qsort( A, Left, i - 1 );         Qsort( A, i + 1, Right );     }     else  /* Do an insertion sort on the subarray */         InsertionSort( A + Left, Right - Left + 1 ); }     //从大到小 #define Cutoff ( 3 ) void Qsort( ElementType A[ ], int Left, int Right ) {     int i, j;     ElementType Pivot;       if( Left + Cutoff <= Right )     {         Pivot = Median3( A, Left, Right );         i = Left + 1;         j = Right;         for( ; ; )         {             while( A[ ++i ] > Pivot ) { }             while( A[ --j ] < Pivot ) { }             if( i < j )                 Swap( &A[ i ], &A[ j ] );             else                 break;         }         Swap( &A[ j ], &A[ Left + 1 ] );  /* Restore pivot */           Qsort( A, Left, j - 1 );         Qsort( A, j + 1, Right );     }     else  /* Do an insertion sort on the subarray */         InsertionSort( A + Left, Right - Left + 1 ); }       /* This code doesn't work; it's Figure 7.15. */ //A[i] = A[j] = Pivot时，程序死循环 #if 0 /* START: fig7_15.txt */ i = Left + 1; j = Right - 2; for( ; ; ) {     while( A[ i ] < Pivot ) i++;     while( A[ j ] > Pivot ) j--;     if( i < j )         Swap( &A[ i ], &A[ j ] );     else         break; } #endif   void Quicksort( ElementType A[ ], int N ) {     Qsort( A, 0, N - 1 ); }