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#include<stdio.h>
#include<malloc.h>
typedef struct node /*定义节点*/
{
float coef; /*多项式的系数*/
int exp; /*多项式的指数*/
struct node * next;
}listnode;
listnode * head;
listnode * p;
listnode * q;
listnode * r;
listnode * head1;
listnode * head2;
int head_num = 0;
listnode* point[2];
void input() /*输入的多项式系数和指数*/
{
int j = 0;
float coef; /*节点中存放的多项式的系数*/
int exp; /*节点中存放的多项式的指数*/
head = (listnode *)malloc(sizeof(listnode)); /* malloc 分配内存单元空间给头指针*/
head->next = NULL; /*使头指针指向空,为空链表状态*/
start: printf("请输入系数和指数:");
scanf_s("%f%d", &coef, &exp);
if (exp == 0 && coef == 0)
goto next;
p = (listnode *)malloc(sizeof(listnode));/*malloc 分配内存单元给指针p,通过p去预存输入的系数和指数*/
j++;
p->coef = coef; /*用p节点存储系数*/
p->exp = exp; /*存储指数*/
p->next = head->next; /*将下一个头指针分配给p,连接*/
head->next = p;
goto start;
next: head->exp = j;
point[head_num] = head; /*为了创建两个单链表*/
head_num++;
}
int bubble_sort(listnode * myhead)/*用冒泡排序去将多项式的指数从高到低排序*/
{
int i, j;
listnode * swap; /*用来交换节点*/
listnode * real_myhead;/*将每个多项式排序传递*/
real_myhead = myhead;
int num = myhead->exp;
if (num == 1 && num == 0)
goto next;
for (i = 0; i<num - 1; i++)
{
myhead = real_myhead;
for (j = 0; j<num - 1; j++) /*将所有的多项式进行扫描*/
{
if ((myhead->next->exp)<(myhead->next->next->exp))
{
swap = (listnode *)malloc(sizeof(listnode));
swap->exp = myhead->next->exp; /*将指数小的项传递给swap指针,存储*/
swap->coef = myhead->next->coef;
myhead->next->exp = myhead->next->next->exp;/*将指数大的项排前*/
myhead->next->coef = myhead->next->next->coef;
myhead->next->next->exp = swap->exp;
myhead->next->next->coef = swap->coef;
free(swap);
}
myhead = myhead->next;
}
}
next:return 0;
}
void myprintf(listnode * node)//函数的表现形式
{
listnode * mynode;
mynode = (listnode *)malloc(sizeof(listnode));
mynode->coef = node->coef;
mynode->exp = node->exp;
if ((mynode->coef == 1) && (mynode->exp == 1)) //当系数为1,指数为1,输出X
printf("x");
else if ((mynode->coef == 1) && (mynode->exp != 1)
&& (mynode->exp != 0)) //当系数为1,指数不为1和不为0,就输出X^exp
printf("x^%d", mynode->exp);
else if ((mynode->coef != 1) && (mynode->exp == 1))//系数不为1,指数为1时,输出 coef X
printf("%.2fx", mynode->coef);
else if ((mynode->coef != 0) && (mynode->exp == 0))//系数不为0,指数为0,那么X^exp为0,直接输出 coef
printf("%.f", mynode->coef);
else //其他情况下,输出 coef X^exp
printf("%.2fx^%d", mynode->coef, mynode->exp);
free(mynode);
}
int output(listnode * output) /*输出函数,将多项式输出,还有两个多项式相加的结果输出*/
{
if (output->exp == 0)
{
printf("0\n");
return 0;
}
p = output->next;
if (p->coef>0)
{
myprintf(p);
p = p->next;
}
for (; p->next != NULL; p = p->next)
{
if (p->coef>0)
printf("+");
myprintf(p);
}
if (p->coef>0)
printf("+");
myprintf(p);
printf("\n");
return 0;
}
void plus()
{
head1 = point[0];
head2 = point[1];
head = (listnode *)malloc(sizeof(listnode));
p = head1->next;
q = head2->next;
head = head1;
while (p != NULL && q != NULL)
{
if (p->exp != q->exp)
{
head = p;
p = p->next;
}
else
{
p->coef = p->coef + q->coef;
if (p->coef == 0)
{
listnode *temp1;
listnode *temp2;
temp1 = p;
temp2 = q;
head->next = p->next;
p = p->next;
q = q->next;
delete temp1;
delete temp2;
}
else
{
listnode *temp;
temp = q;
head = p;
p = p->next;
q = q->next;
delete temp;
}
}
}
if (q)
head->next = q;
bubble_sort(head1);
}
int main()
{
printf("请输入第一个多项式的各个项的系数和指数(当系数为0时结束输入)\n");
input();
printf("请输入第二个多项式的各个项的系数和指数(当系数为0时结束输入)\n");
input();
bubble_sort(point[0]);
bubble_sort(point[1]);
printf("第一个多项式为:");
output(point[0]);
printf("第二个多项式为:");
output(point[1]);
printf("多项式1+多项式2=:");
plus();
bubble_sort(head1);
output(head1);
printf("Press any key to exit");
getchar();
getchar();
return 0;
}
#include<stdio.h>
#include<malloc.h>
typedef struct node /*定义节点*/
{
float coef; /*多项式的系数*/
int exp; /*多项式的指数*/
struct node * next;
}listnode;
listnode * head;
listnode * p;
listnode * q;
listnode * r;
listnode * head1;
listnode * head2;
int head_num = 0;
listnode* point[2];
void input() /*输入的多项式系数和指数*/
{
int j = 0;
float coef; /*节点中存放的多项式的系数*/
int exp; /*节点中存放的多项式的指数*/
head = (listnode *)malloc(sizeof(listnode)); /* malloc 分配内存单元空间给头指针*/
head->next = NULL; /*使头指针指向空,为空链表状态*/
start: printf("请输入系数和指数:");
scanf_s("%f%d", &coef, &exp);
if (coef == 0)//////////////系数为0退出
goto next;
p = (listnode *)malloc(sizeof(listnode));/*malloc 分配内存单元给指针p,通过p去预存输入的系数和指数*/
j++;
p->coef = coef; /*用p节点存储系数*/
p->exp = exp; /*存储指数*/
p->next = head->next; /*将下一个头指针分配给p,连接*/
head->next = p;
goto start;
next: head->exp = j;
point[head_num] = head; /*为了创建两个单链表*/
head_num++;
}
int bubble_sort(listnode * myhead)/*用冒泡排序去将多项式的指数从高到低排序*/
{
int i, j,num;
listnode * swap; /*用来交换节点*/
listnode * real_myhead;/*将每个多项式排序传递*/
real_myhead = myhead;
num = myhead->exp;
if (num == 1 || num == 0)
goto next;
for (i = 0; i<num - 1; i++)
{
myhead = real_myhead;
for (j = 0; j<num - 1; j++) /*将所有的多项式进行扫描*/
{
if ((myhead->next->exp)<(myhead->next->next->exp))
{
swap = (listnode *)malloc(sizeof(listnode));
swap->exp = myhead->next->exp; /*将指数小的项传递给swap指针,存储*/
swap->coef = myhead->next->coef;
myhead->next->exp = myhead->next->next->exp;/*将指数大的项排前*/
myhead->next->coef = myhead->next->next->coef;
myhead->next->next->exp = swap->exp;
myhead->next->next->coef = swap->coef;
free(swap);
}
myhead = myhead->next;
}
}
next:return 0;
}
void myprintf(listnode * node)//函数的表现形式
{
listnode * mynode;
mynode = (listnode *)malloc(sizeof(listnode));
mynode->coef = node->coef;
mynode->exp = node->exp;
if ((mynode->coef == 1) && (mynode->exp == 1)) //当系数为1,指数为1,输出X
printf("x");
else if ((mynode->coef == 1) && (mynode->exp != 1)
&& (mynode->exp != 0)) //当系数为1,指数不为1和不为0,就输出X^exp
printf("x^%d", mynode->exp);
else if ((mynode->coef != 1) && (mynode->exp == 1))//系数不为1,指数为1时,输出 coef X
printf("%.2fx", mynode->coef);
else if ((mynode->coef != 0) && (mynode->exp == 0))//系数不为0,指数为0,那么X^exp为0,直接输出 coef
printf("%.f", mynode->coef);
else //其他情况下,输出 coef X^exp
printf("%.2fx^%d", mynode->coef, mynode->exp);
free(mynode);
}
int output(listnode * output) /*输出函数,将多项式输出,还有两个多项式相加的结果输出*/
{
if (output->exp == 0)
{
printf("0\n");
return 0;
}
p = output->next;
if (p->coef>0)
{
myprintf(p);
p = p->next;
}
for (;output->exp>1&&p; p = p->next)
{
if (p->coef>=0)
printf("+");
myprintf(p);
}
printf("\n");
return 0;
}
void plus()
{
int i=0,m=point[0]->exp+point[1]->exp;
listnode *p=point[0];
listnode *tmp;
point[0]->exp=m;
//连接两个链表
for(;p->next;p=p->next);
p->next=point[1]->next;
//连接后整体排序
bubble_sort(point[0]);
//合并,多余的清0
for(p=point[0]->next;p->next;p=p->next)
{
if(p->exp==p->next->exp)
{
p->next->coef=p->coef+p->next->coef;
p->coef=0;
}
}
//消除0系数结点
for(p=point[0];p->next;)
if(p->next->coef==0)
{
tmp=p->next;
p->next=p->next->next;
free(tmp);
}
else p=p->next;
}
int main()
{
printf("请输入第一个多项式的各个项的系数和指数(当系数为0时结束输入)\n");
input();
printf("请输入第二个多项式的各个项的系数和指数(当系数为0时结束输入)\n");
input();
bubble_sort(point[0]);
bubble_sort(point[1]);
printf("第一个多项式为:");
output(point[0]);
printf("第二个多项式为:");
output(point[1]);
printf("多项式1+多项式2=:");
plus();
output(point[0]);
printf("Press any key to exit");
getchar();
getchar();
return 0;
}
//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");
}
}
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;
}