数据结构与算法分析c语言描述（Mark Allen）--多项式ADT链表实现

多项式ADT链表实现

• 使用链表结构存储
• 操作集合
  • 多项式加法
  • 多项式乘法
  • 多项式的显示

---

头文件

//头文件
typedef struct Node *PtrToNode;

struct Node
{
    int Cofficient;
    int Exponent;
    PtrToNode Next;
};
typedef PtrToNode Polynomial;

---

代码部分

#include <stdio.h>
#include <stdlib.h>
#include "PloynomialADTList.h"
#include<time.h>
#define SIZENODE 10
//可视化一个多项式ADT
void ShowAPoly(Polynomial Poly)
{
    Polynomial P1 = Poly;
    for (; P1 != NULL; P1 = P1->Next)
    {
        printf("%d %d ", P1->Cofficient, P1->Exponent);
    }
}

//初始化多项式的例程
Polynomial ZeroPloynomial(Polynomial Poly)
{
    Poly=(Polynomial)malloc(sizeof(struct Node));
    Poly->Next = NULL;
    Poly->Cofficient = 0;
    Poly->Exponent = 0;
    return Poly;
}

Polynomial InsertPolynomial(int Cofficient1, int Exponent1, Polynomial Poly)
{
    Polynomial temp = (Polynomial)malloc(sizeof(struct Node));
    temp->Next = NULL;
    temp->Cofficient = Cofficient1;
    temp->Exponent = Exponent1;
    Polynomial p = Poly;
    while (Poly)
    {
        Polynomial last = NULL;
        if (Poly->Exponent == temp->Exponent)
        {
            Poly->Cofficient += temp->Cofficient;
            continue;
        }
        //多项式的系数还没有找到
        else if (Poly->Exponent < temp->Exponent)
        {
            last = Poly;
            Poly = Poly->Next;
        }
        else if (Poly->Exponent > temp->Exponent)
        {
            last->Next = temp;
            temp->Next = Poly;
        }
    }
    return p;
}
//产生一个随机的多项式ADT
Polynomial RandAPoly(Polynomial Poly)
{
    srand(unsigned(time(NULL)));
    for(int i=0;i<SIZENODE;i++)
    {
        int cofficient=rand()%SIZENODE;
        int exponent=rand()%SIZENODE;
        Poly=InsertPolynomial(cofficient,exponent,Poly);
    }
    return Poly;
}

//两个多项式相加的例程
void AddPloynomial(const Polynomial Poly1, const Polynomial Poly2, Polynomial PloySum)
{
    Polynomial p1 = Poly1;
    Polynomial p2 = Poly2;
    while (p1 && p2)
    {
        if (p1->Exponent == p2->Exponent)
        {
            PloySum->Exponent = p1->Exponent;
            PloySum->Cofficient = p1->Cofficient + p2->Cofficient;
            p1 = p1->Next;
            p2 = p2->Next;
        }
        else if (p1->Exponent < p2->Exponent)
        {
            PloySum->Exponent = p1->Exponent;
            PloySum->Cofficient = p1->Cofficient;
            p1 = p1->Next;
        }
        else
        {
            PloySum->Exponent = p2->Exponent;
            PloySum->Cofficient = p1->Cofficient + p2->Cofficient;
            p2 = p2->Next;
        }
    }
    PloySum->Next = p1 ? p1 : p2;
}

//两个多项式相乘的例程
void MultPloynomial(const Polynomial Poly1, const Polynomial Poly2, Polynomial PloyProd)
{
    Polynomial p1 = Poly1;
    Polynomial p2 = Poly2;

    for (; p1 != NULL; p1 = p1->Next)
    {
        for (; p2 != NULL; p2 = p2->Next)
        {
            int Cofficient = p1->Cofficient * p2->Cofficient;
            int Exponent = p1->Exponent + p2->Exponent;
            PloyProd = InsertPolynomial(Cofficient, Exponent, PloyProd);
        }
    }
}

int main(int argc, char const *argv[])
{
    int number;
    Polynomial p1=nullptr, p2=nullptr, psum=nullptr, pprod=nullptr;
    p1=ZeroPloynomial(p1);
    p2=ZeroPloynomial(p2);
    psum=ZeroPloynomial(psum);
    pprod=ZeroPloynomial(pprod);
    while (1)
    {
        printf("\t\t\tpolynomial realize by list.\n");
        printf("\t\t\tplease intput a intger to choose what you want to do.\n");
        printf("\t\t\t1.insert a node to a poly.\n");
        printf("\t\t\t2.show a poly.\n");
        printf("\t\t\t3.puls two poly.\n");
        printf("\t\t\t4.mult two poly.\n");
        printf("\t\t\t5.get a random poly.\n");
        printf("\t\t\t0.exit\n");
        scanf("%d", &number);
        if (!number)
            break;
        switch (number)
        {
        case 1:
            printf("\t\t\tplease input a intger to choose a poly to insert.\n");
            printf("\t\t\t1.poly1\t2.poly2\n\n");
            int ch1, ch2;
            scanf("%d", &ch1);
            printf("\t\t\tplease intput two number which means a cofficient and its exponent.\n");

            if (ch1 == 1)
            {
                scanf("%d%d", &ch1, &ch2);
                InsertPolynomial(ch1, ch2, p1);
                ShowAPoly(p1);
            }
            else if (ch1 == 2)
            {
                scanf("%d%d", &ch1, &ch2);
                InsertPolynomial(ch1, ch2, p2);
                ShowAPoly(p2);
            }
            break;

        case 2:
            printf("\t\t\tchoose a poly to show.\n");
            printf("\t\t\t1.poly1\t2.poly2\n\n");
            scanf("%d", &ch1);
            if (ch1 == 1)
            {
                ShowAPoly(p1);
            }
            else if (ch1 == 2)
            {
                ShowAPoly(p2);
            }
            break;

        case 3:
            AddPloynomial(p1, p2, psum);
            printf("\n\t\there is the answer.\n");
            ShowAPoly(psum);
            break;

        case 4:
            MultPloynomial(p1, p2, pprod);
            printf("\n\t\there is the answer.\n");
            ShowAPoly(pprod);
            break;

        case 5:
            printf("\t\t\tplease input a intger to choose a poly.\n");
            printf("\t\t\t1.poly1\t2.poly2\n\n");
            scanf("%d", &ch1);
            if (ch1 == 1)
            {
                p1=RandAPoly(p1);
                ShowAPoly(p1);
            }
            else if (ch1 == 2)
            {
                scanf("%d %d", &ch1, &ch2);
                p2=RandAPoly(p2);
                ShowAPoly(p2);
            }
            break;
        }
    }
    system("pause");
    return 0;
}

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