多项式ADT(数组存储多项式系数和指数)笔记

fatal.h

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

#define Error( Str )        FatalError( Str )
#define FatalError( Str )   fprintf( stderr, "%s
", Str ), exit( 1 )

poly.c

/* This code doesn't really do much */
/* Thus I haven't bothered testing it */

#include "fatal.h"

#define MaxDegree 100 // 幂的最大次数是100

static int
Max(int A, int B)
{
    return A > B ? A : B;
}

/* START: fig3_18.txt */
typedef struct
{
    int CoeffArray[MaxDegree + 1]; // 系数数组，这里定义了数组是很大的，所以下面要单独用一个HighPower来存最高次幂
    int HighPower; // 高次幂
} *Polynomial;
/* END */

/* START: fig3_19.txt */
// 多项式初始化为零
void
ZeroPolynomial(Polynomial Poly)
{
    int i;

    for (i = 0; i <= MaxDegree; i++)
        Poly->CoeffArray[i] = 0;
    Poly->HighPower = 0;
}
/* END */

/* START: fig3_20.txt */
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];
}
/* END */

/* START: fig3_21.txt */
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)
        Error("Exceeded array size");
    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];
}
/* END */

#if 0
/* START: fig3_23.txt */
        typedef struct Node *PtrToNode;

        struct Node
        {
            int Coefficient; // 系数
            int Exponent; // 指数
            PtrToNode Next;
        };

        typedef PtrToNode Polynomial;  /* Nodes sorted by exponent */ // 按指数排序的节点
/* END */
#endif

void
PrintPoly(const Polynomial Q)
{
    int i;

    for (i = Q->HighPower; i > 0; i--)
        printf("%dx^%d + ", Q->CoeffArray[i], i); // CoeffArray[i]代表系数，i代表指数
    printf("%d
", Q->CoeffArray[0]);
}

// 测试函数
int main()
{
    Polynomial P, Q;

    P = malloc(sizeof(*P));
    Q = malloc(sizeof(*Q));

    P->HighPower = 1;
    P->CoeffArray[0] = 1;
    P->CoeffArray[1] = 1; // P = x + 1
    MultPolynomial(P, P, Q); // Q = P * P = x^2 + 2x + 1
    MultPolynomial(Q, Q, P); // P = Q * Q = x^4 + 4x^3 + 6x^2 + 4x + 1
    AddPolynomial(P, P, Q); // Q = P + P = 2x^4 + 8x^3 + 12x^2 + 8x^1 + 2
    // 打印结果
    PrintPoly(Q);

    return 0;
}

输出结果：

注：书中页码：P39