【数据结构与算法】第三章 表c实现应用一-----------多项式

可以用表来定义一种关于一元多项式的抽象数据类型。若最高幂数比较小，使用数组来存储幂系数是比较简单的；但如果出现幂数跨度比较大的情况，使用链表结构存储是比较合适的。具体内容参见《数据结构与算法分析：c语言描述》第三种。这里先实现了数组存储数据的简单情况。代码如下：

  
    

   
     #include 
   
     <
   
     stdio.h
   
     >
   
     
#include 
   
     <
   
     stdlib.h
   
     >
   
     


   
     #define
   
      MaxDegree 10
   
     

typedef 
   
     struct
   
      _Polynomial
{
 
   
     int
   
      CoeffArray[ MaxDegree 
   
     +
   
      
   
     1
   
      ];
 
   
     int
   
      HighPower;
} 
   
     *
   
      Polynomial;



   
     //
   
     Max
   
     

   
     int
   
      Max( 
   
     int
   
      a, 
   
     int
   
      b )
{
 
   
     if
   
     ( a 
   
     >=
   
      b )
 
   
     return
   
      a;
 
   
     else
   
     
 
   
     return
   
      b;
}


   
     //
   
     zero
   
     

   
     void
   
     
ZeroPolynomial( Polynomial Poly )
{
 
   
     int
   
      i;
 
   
     for
   
     ( i 
   
     =
   
      
   
     0
   
     ; i 
   
     <=
   
      MaxDegree; i
   
     ++
   
      )
 Poly
   
     ->
   
     CoeffArray[ i ] 
   
     =
   
      
   
     0
   
     ;
 Poly
   
     ->
   
     HighPower 
   
     =
   
      
   
     0
   
     ;
}


   
     //
   
     add
   
     

   
     void
   
     
AddPolynomial( 
   
     const
   
      Polynomial Poly1, 
 
   
     const
   
      Polynomial Poly2,
 Polynomial PolySum )
{
 
   
     int
   
      i;
 ZeroPolynomial( PolySum );
 PolySum
   
     ->
   
     HighPower 
   
     =
   
      Max( Poly1
   
     ->
   
     HighPower, Poly2
   
     ->
   
     HighPower );
 
   
     for
   
     ( i 
   
     =
   
      PolySum
   
     ->
   
     HighPower; i 
   
     >=
   
      
   
     0
   
     ; i
   
     --
   
      )
 PolySum
   
     ->
   
     CoeffArray[i] 
   
     =
   
      Poly1
   
     ->
   
     CoeffArray[i] 
   
     +
   
      Poly2
   
     ->
   
     CoeffArray[i];
}


   
     //
   
     multiplication
   
     

   
     void
   
     
MultPolynomial( 
   
     const
   
      Polynomial Poly1,
 
   
     const
   
      Polynomial Poly2,
 Polynomial PolyProd )
{
 
   
     int
   
      i, j;

 ZeroPolynomial( PolyProd );
 PolyProd
   
     ->
   
     HighPower 
   
     =
   
      Poly1
   
     ->
   
     HighPower 
   
     +
   
      Poly2
   
     ->
   
     HighPower;

 
   
     if
   
     ( PolyProd
   
     ->
   
     HighPower 
   
     >
   
      MaxDegree )
 perror( 
   
     "
   
     Exceeded array size.\n
   
     "
   
      );
 
   
     else
   
     
 
   
     for
   
     ( i 
   
     =
   
      
   
     0
   
     ; i 
   
     <=
   
      Poly1
   
     ->
   
     HighPower; i
   
     ++
   
      )
 
   
     for
   
     ( j 
   
     =
   
      
   
     0
   
     ; j 
   
     <=
   
      Poly2
   
     ->
   
     HighPower; j
   
     ++
   
      )
 PolyProd
   
     ->
   
     CoeffArray[i 
   
     +
   
      j] 
   
     +=
   
      Poly1
   
     ->
   
     CoeffArray[i]
 
   
     *
   
      Poly2
   
     ->
   
     CoeffArray[j];
}


   
     //
   
     print
   
     

   
     void
   
     
PrintPolynomial( 
   
     const
   
      Polynomial Poly )
{
 
   
     int
   
      i;
 printf(
   
     "
   
     F(x) = 
   
     "
   
     );
 
   
     for
   
     ( i 
   
     =
   
      
   
     0
   
     ; i 
   
     <=
   
      Poly
   
     ->
   
     HighPower; i
   
     ++
   
      )
 {
 
   
     if
   
     ( Poly
   
     ->
   
     CoeffArray[i] 
   
     ==
   
      
   
     0
   
      )
 
   
     continue
   
     ;
 
   
     else
   
     
 {
 printf( 
   
     "
   
     %d*X[%d]
   
     "
   
     , Poly
   
     ->
   
     CoeffArray[i], i );
 
   
     if
   
     ( i 
   
     !=
   
      Poly
   
     ->
   
     HighPower 
   
     -
   
      
   
     1
   
      )
 printf(
   
     "
   
      + 
   
     "
   
     );
 }
 }
}


   
     /*
   
     ************************************************************
   
     */
   
     

   
     int
   
      main()
{
 
   
     int
   
      i;
 Polynomial poly1, poly2, polysum, polyprod;

 poly1 
   
     =
   
      ( Polynomial )malloc( 
   
     sizeof
   
     ( 
   
     struct
   
      _Polynomial ) );
 poly2 
   
     =
   
      ( Polynomial )malloc( 
   
     sizeof
   
     ( 
   
     struct
   
      _Polynomial ) );
 polysum 
   
     =
   
      ( Polynomial )malloc( 
   
     sizeof
   
     ( 
   
     struct
   
      _Polynomial ) );
 polyprod 
   
     =
   
      ( Polynomial )malloc( 
   
     sizeof
   
     ( 
   
     struct
   
      _Polynomial ) );

 ZeroPolynomial( poly1 );
 ZeroPolynomial( poly2 );

 
   
     for
   
     ( i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      
   
     5
   
     ; i
   
     ++
   
      )
 {
 poly1
   
     ->
   
     CoeffArray[i] 
   
     =
   
      i ;
 poly2
   
     ->
   
     CoeffArray[i] 
   
     =
   
      i
   
     +
   
     1
   
     ;
 }

 poly1
   
     ->
   
     HighPower 
   
     =
   
      i
   
     -
   
     1
   
     ;
 poly2
   
     ->
   
     HighPower 
   
     =
   
      i;

 AddPolynomial( poly1, poly2, polysum );
 MultPolynomial( poly1, poly2, polyprod );
 
 printf(
   
     "
   
     \npoly1: 
   
     "
   
     );
 PrintPolynomial( poly1 );
 printf(
   
     "
   
     \npoly2: 
   
     "
   
     );
 PrintPolynomial( poly2 );
 printf(
   
     "
   
     \npolysum: 
   
     "
   
     );
 PrintPolynomial( polysum );
 printf(
   
     "
   
     \npolyprod: 
   
     "
   
     );
 PrintPolynomial( polyprod );
 printf(
   
     "
   
     \n
   
     "
   
     );
}