要求1：两个相同的多项式相加减不会出现错误
//链表实现一元多项式的加法减法乘法
#include <stdio.h>
#include <stdlib.h>
typedef struct node {
float coef; //系数
int expn; //指数
struct node *next;
}
PolyNode; //多项式节点 polynomial node
typedef PolyNode* Polynomial;
Polynomial createPolynomial() { //创建多项式
PolyNode *p, *q, *head = (PolyNode *)malloc(sizeof(PolyNode)); //头节点
head->next = NULL;
float coef;
int expn;
printf("输入该多项式每一项的系数和指数，每项一行，输入0 0结束！\n");
while (scanf("%f %d", &coef, &expn) && coef) { // 默认，按指数递减排列
if (head->next) {
p = head;
while (p->next && expn < p->next->expn)
p = p->next;
if (p->next) {
if (expn == p->next->expn) { //有相同指数的直接把系数加到原多项式
p->next->coef += coef;
if (p->next->coef > -0.000001 && p->next->coef < 0.000001) { //若是相加后系数为0，则舍弃该节点
q = p->next;
p->next = q->next;
free(q);
}
} else {
q = (PolyNode*)malloc(sizeof(PolyNode));
q->coef = coef;
q->expn = expn;
q->next = p->next;
p->next = q;
}
} else {
p->next = (PolyNode*)malloc(sizeof(PolyNode));
p = p->next;
p->coef = coef;
p->expn = expn;
p->next = NULL;
}
} else {
head->next = (PolyNode*)malloc(sizeof(PolyNode));
head->next->coef = coef;
head->next->expn = expn;
head->next->next = NULL;
}
}
return head;
}
Polynomial multiply(Polynomial poly, float coef, int expn) { //多项式与指定单项式相乘，该单项式为 coefx^expn
PolyNode *p, *q, *Poly = (PolyNode*)malloc(sizeof(PolyNode));
p = Poly;
q = poly->next;
while (q) {
p->next = (PolyNode*)malloc(sizeof(PolyNode));
p = p->next;
p->coef = (q->coef*coef);
p->expn = (q->expn + expn);
q = q->next;
}
p->next = NULL;
return Poly;
}
void add(Polynomial poly1, Polynomial poly2) { //把 poly2 加到 poly1 上
PolyNode *p, *q, *r;
r = poly1;
p = poly1->next; //指向第一个节点
q = poly2->next;
poly2->next = NULL;
while (p && q) {
if (p->expn > q->expn) {
r->next = p;
p = p->next;
r = r->next;
} else if (p->expn < q->expn) {
r->next = q;
q = q->next;
r = r->next;
} else {
PolyNode *t;
p->coef += q->coef;
if (!(p->coef > -0.000001 && p->coef < 0.000001)) //系数不为0
{
r->next = p;
r = r->next;
p = p->next;
} else {
t = p;
p = p->next;
free(t);
}
t = q;
q = q->next;
free(t);
}
}
if (p)
r->next = p;
if (q)
r->next = q;
}
Polynomial polySubtract(Polynomial poly1, Polynomial poly2) { //多项式减法 poly1-poly2形成一个新的多项式
//把poly2的系数取相反数，形成一个新的多项式
Polynomial poly = (PolyNode*)malloc(sizeof(PolyNode)); //构造头节点
PolyNode *p, *q;
p = poly;
q = poly2->next;
while (q) {
p->next = (PolyNode*)malloc(sizeof(PolyNode));
p = p->next;
p->coef = -(q->coef); //系数取反
p->expn = q->expn;
q = q->next;
}
p->next = NULL;
add(poly, poly1); //利用加法
return poly;
}
Polynomial polyAdd(Polynomial poly1, Polynomial poly2) { //多项式相加 poly1+poly2形成一个新的多项式
Polynomial poly = (PolyNode*)malloc(sizeof(PolyNode)); //和多项式的头节点
poly->next = NULL;
PolyNode *p, *q, *r;
r = poly;
p = poly1->next;
q = poly2->next;
while (p&&q) {
if (p->expn > q->expn) {
r->next = (PolyNode*)malloc(sizeof(PolyNode));
r = r->next;
r->coef = p->coef;
r->expn = p->expn;
p = p->next;
} else if (p->expn < q->expn) {
r->next = (PolyNode*)malloc(sizeof(PolyNode));
r = r->next;
r->coef = q->coef;
r->expn = q->expn;
q = q->next;
} else {
float m = p->coef + q->coef;
if (!(m > -0.000001 && m < 0.000001)) {
r->next = (PolyNode*)malloc(sizeof(PolyNode));
r = r->next;
r->coef = m;
r->expn = p->expn;
}
q = q->next;
p = p->next;
}
}
while (p) {
r->next = (PolyNode*)malloc(sizeof(PolyNode));
r = r->next;
r->coef = p->coef;
r->expn = p->expn;
p = p->next;
}
while (q) {
r->next = (PolyNode*)malloc(sizeof(PolyNode));
r = r->next;
r->coef = q->coef;
r->expn = q->expn;
q = q->next;
}
r->next = NULL;
return poly;
}
Polynomial polyMultiply(Polynomial poly1, Polynomial poly2) { //多项式相乘
Polynomial poly = (PolyNode*)malloc(sizeof(PolyNode)); //创建多项式和的头节点
poly->next = NULL;
PolyNode *p;
p = poly2->next;
while (p) {
add(poly, multiply(poly1, p->coef, p->expn));
p = p->next;
}
return poly;
}
void printPoly(Polynomial poly) { //打印多项式
if (poly && poly->next) {
PolyNode *p = poly->next; //p指向第一个节点
while (p->next) {
printf("%gx^%d", p->coef, p->expn);
p = p->next;
if (p && (p->coef > 0))
printf("+");
}
if (p->expn == 0)
printf("%g", p->coef); //打印常数项
else
printf("%gx^%d", p->coef, p->expn);
printf("\n");
} else {
printf("0\n");
}
}
void freePoly(Polynomial poly) { //释放内存
if (poly && poly->next) {
PolyNode *p, *q;
p = poly;
while (p) {
q = p->next;
free(p);
p = q;
}
}
poly = NULL;
}
int main() {
printf("用链表实现多项式的加减法\n");
Polynomial poly1, poly2, poly3;
printf("创建多项式一\n");
poly1 = createPolynomial();
printf("多项式一：\n");
printPoly(poly1);
printf("创建多项式二\n");
poly2 = createPolynomial();
printf("多项式二：\n");
printPoly(poly2);
printf("两多项式相加，和为：\n");
poly3 = polyAdd(poly1, poly2);
printPoly(poly3);
freePoly(poly3);
printf("两个多项式相乘，积为：\n");
poly3 = polyMultiply(poly1, poly2);
printPoly(poly3);
freePoly(poly3);
printf("两多项式相减，差为：\n");
poly3 = polySubtract(poly1, poly2);
printPoly(poly3);
freePoly(poly1);
freePoly(poly2);
freePoly(poly3);
system("pause");
return 0;
}
