【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");
}