02-线性结构2 一元多项式的乘法与加法运算 (20分)

设计函数分别求两个一元多项式的乘积与和。

输入格式:

输入分2行，每行分别先给出多项式非零项的个数，再以指数递降方式输入一个多项式非零项系数和指数（绝对值均为不超过1000的整数）。数字间以空格分隔。

输出格式:

输出分2行，分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。数字间以空格分隔，但结尾不能有多余空格。零多项式应输出0 0。

输入样例:

4 3 4 -5 2  6 1  -2 03 5 20  -7 4  3 1

输出样例:

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0

解：多项式加法和多项式乘法，数据的存储是使用链表的形式，将多项式的数据形式以及操作函数封装在头文件中。难点在于0多项式以及常数多项式时运算逻辑不能够死循环，判断跳出。

头文件：

#ifndef POLYNOMIAL_H_#define POLYNOMIAL_H_#include <iostream>#include <stdlib.h>using namespace std;typedef int ElementType;typedef struct PolyNode *Polynomial;struct PolyNode{ElementType coef;ElementType expon;Polynomial next;};Polynomial Initialize();Polynomial Find_kth(int k, Polynomial L);Polynomial Insert(ElementType x, int i, Polynomial L);Polynomial Delete(int i, Polynomial L);int Length(Polynomial L);Polynomial Read(int len);void PrintPolynomial(Polynomial L);Polynomial read(Polynomial L);void attach(int xishu, int zhishu, Polynomial *p);Polynomial Sum(Polynomial L1, Polynomial L2);Polynomial Multiplication(Polynomial L1, Polynomial L2);Polynomial Initialize(){Polynomial L;L = (Polynomial)malloc(sizeof(struct PolyNode));L->next = NULL;return L;}Polynomial Find_kth(int k, Polynomial L){Polynomial Lp = L;int i = 1;while(Lp != NULL && i < k){Lp = Lp->next;i++;}if(i == k){return Lp;}else{return NULL;}}//在第i个节点前面Polynomial Insert(ElementType xishu, ElementType zhishu, int i, Polynomial L){Polynomial p,s;if(i == 1){s = (Polynomial)malloc(sizeof(struct PolyNode));s->coef = xishu;s->expon = zhishu;s->next = L;return s;}p = Find_kth(i-1, L);if(p == NULL)return NULL;else{s = (Polynomial)malloc(sizeof(struct PolyNode));s->coef = xishu;s->expon = zhishu;s->next = p->next;p->next = s;return L;}}Polynomial Delete(int i, Polynomial L){Polynomial p, s;if(i == 1){s = L;if(L != NULL)L = L->next;elsereturn NULL;free(s);return L;}p = Find_kth(i-1, L);if(p == NULL){return NULL;}else if(p->next == NULL){return NULL;}else{s = p->next;p->next = s->next;free(s);return L;}}int Length(Polynomial L){Polynomial Lp = L;int i = 0;while(Lp){i++;Lp = Lp->next;}return i;}void PrintPolynomial(Polynomial L){Polynomial Lp = L;int i = 0;while(Lp){if(i){cout<<' ';}cout<<Lp->coef<<' '<<Lp->expon;i++;if(Lp->next == NULL)break;Lp = Lp->next;}if(Lp == NULL){cout<<0<<' '<<0;}}Polynomial read(int len, Polynomial L){int xishu, zhishu;for(int i = 0; i < len; i++){cin>>xishu>>zhishu;L = Insert(xishu, zhishu, i+1, L);}L = Delete(len+1, L);return L;}void attach(int xishu, int zhishu, Polynomial *p){Polynomial P;P = Initialize();P->coef = xishu;P->expon = zhishu;P->next = NULL;(*p)->next = P;*p = P;}Polynomial Sum(Polynomial L1, Polynomial L2){if(!L1 && !L2){if(!L1){return L2;}else{return L1;}}Polynomial L, p, s;int sum;L = Initialize();p = Initialize();s = Initialize();L = p;while(L1 && L2){if(L1->expon < L2->expon){if(L2->coef){attach(L2->coef, L2->expon, &p);}L2 = L2->next;}else if(L1->expon > L2->expon){if(L1->coef){attach(L1->coef, L1->expon, &p);}L1 = L1->next;}else{sum = L1->coef + L2->coef;if(sum){attach(sum, L2->expon, &p);}L1 = L1->next;L2 = L2->next;}}if(L1){for(; L1; L1 = L1->next){attach(L1->coef, L1->expon, &p);}}if(L2){for(; L2; L2 = L2->next){attach(L2->coef, L2->expon, &p);}}p->next = NULL;s = L;L = L->next;free(s);return L;}Polynomial Multiplication(Polynomial P1, Polynomial P2){    Polynomial P, temp1, temp2, Rear, temp;    int c, e;    if(!P1 || !P2)        return NULL;    temp1 = P1;    temp2 = P2;    P = Initialize();    P->next = NULL;    Rear = P;    while(temp2){        c = temp1->coef * temp2->coef;        e = temp1->expon + temp2->expon;        if(c != 0){            attach(c, e, &Rear);        }        temp2 = temp2->next;    }    temp1 = temp1->next;    while(temp1){        temp2 = P2, Rear = P;        while(temp2){            c = temp1->coef * temp2->coef;            e = temp1->expon + temp2->expon;            if(c != 0){                while(Rear->next && Rear->next->expon > e)                    Rear = Rear->next;                if(Rear->next && Rear->next->expon == e){                    if(Rear->next->coef + c)                        Rear->next->coef += c;                    else{                        temp = Rear->next;                        Rear->next = temp->next;                        free(temp);                    }                }                else{                    temp = Initialize();                    temp->coef = c;                    temp->expon = e;                    temp->next = Rear->next;                    Rear->next = temp;                    Rear = Rear->next;                }            }            temp2 = temp2->next;        }        temp1 = temp1->next;    }    temp = P;    P = P->next;    free(temp);    return P;}#endif /* POLYNOMIAL_H_ */

主函数部分：

#include <iostream>#include "Polynomial.h"using namespace std;int main(){Polynomial L1;Polynomial L2;L1 = Initialize();L2 = Initialize();int len;cin>>len;L1 = read(len, L1);cin>>len;L2 = read(len, L2);PrintPolynomial(Multiplication(L1, L2));cout<<endl;PrintPolynomial(Sum(L1, L2));return 0;}

2017-4-15 待续