1、说明：

链表的应用之一：一元多项式运算，这里先说明一元多项式加法，减法类同

2、代码实现

//一元多项式的运算
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
typedef struct node
{int coef;int exp;struct node* next;}polynode;//创建一元多项式
polynode* Creatlist(int n)
{polynode* head,*p,* r=NULL;int i;head = (polynode*)malloc(sizeof(polynode));head->coef = 0;head->exp = -1;head->next = NULL;p = head;for (i = 1; i <= n; i++){r = (polynode*)malloc(sizeof(polynode));printf("input (coef exp):");scanf("%d%d", &r->coef,&r->exp);p->next = r;p = r;}r->next = NULL;printf("生成完毕\n");return head;}//排序
void Sort(polynode* head)
{polynode* p, * q;int coef;int exp;for (p=head->next;p;p=p->next){for (q=p->next;q;q=q->next){if (p->exp>q->exp){coef = p->coef;p->coef = q->coef;q->coef = coef;exp = p->exp;p->exp = q->exp;q->exp = exp;}}}
}//输出
void Out(polynode*head)
{polynode* p;p= head->next;while (p){printf("%dx^%d",p->coef,p->exp);p = p->next;if (p!=NULL){if (p->coef>=0){printf("+");}}}printf("\n");
}//加法运算
polynode* PolyAdd(polynode*a,polynode*b)
{polynode* c, * p1, * p2, * p3, * r;int sum;p1 = a->next;p2 = b->next;c = a;p3 = c;while (p1&&p2){if (p1->exp<p2->exp){p3->next = p1;p3 = p1; p1 = p1->next;}else if (p1->exp>p2->exp){p3->next = p2;p3 = p2;p2 = p2->next;}else{sum = p1->coef + p2->coef;if (sum){p1->coef = sum;p3->next = p1;p3 = p1;p1 = p1->next;r = p2;p2 = p2->next;free(r);}else{r = p1; p1 = p1->next; free(r);r = p2; p2 = p2->next; free(r);}}}if (p1){p3->next = p1;}else{p3->next = p2;}free(b);return c;
}//减法运算
/*
两个多项式相减得一个新多项式，并且返回新多项式的头结点的指针
相减就是先将减数中每一项的系数变为负，再将两个多项式相加
*/
polynode* Polyminus(polynode* a, polynode* b)
{polynode* c, * p1, * p2, * p3, * r;int sum;p1 = a->next;p2 = b->next;c = a;p3 = c;while (b){// 将pb中每一项的系数变为负 b->coef = 0 - b->coef;b = b->next;}while (p1 && p2){if (p1->exp < p2->exp){p3->next = p1;p3 = p1;p1 = p1->next;}else if (p1->exp > p2->exp){p3->next = p2;p3 = p2;p2 = p2->next;}else{sum = p1->coef + p2->coef;if (sum){p1->coef = sum;p3->next = p1;p3 = p1;p1 = p1->next;r = p2;p2 = p2->next;free(r);}else{r = p1; p1 = p1->next; free(r);r = p2; p2 = p2->next; free(r);}}}if (p1){p3->next = p1;}else{p3->next = p2;}free(b);return c;
}//代入确定的x到多项式中求值 
void Calculate(polynode *p, float x)
{polynode *q = p->next;float sum;float result = 0;//求的结果 while (q) {sum = 1;//利用循环求出每一项x^exp的值for (int i = 1; i <= q->exp; i++) {sum = sum * x;}result += sum * q->coef; //再使系数与sum相乘后求每一项的值，最后累加q = q->next;}printf("将X的值代入多项式中计算的结果为：%.5f\n", result);
}int main()
{polynode* headA,* headB,*headC;int n1, n2;int choice_01;char choice_02;float x;headA = (polynode*)malloc(sizeof(polynode));headB = (polynode*)malloc(sizeof(polynode));headC = (polynode*)malloc(sizeof(polynode));//一元多项式Ado{printf("请输入第一个多项式的项数：");scanf("%d",&n1);if (n1<=0){printf("请重新输入\n");}} while (n1<=0);headA=Creatlist(n1);Sort(headA);printf("A:");Out(headA);getch();//一元多项式Bdo{printf("请输入第二个多项式的项数：");scanf("%d", &n2);if (n2 <= 0){printf("请重新输入\n");}} while (n2 <= 0);headB = Creatlist(n2);Sort(headB);printf("B:");Out(headB);getch();do{printf("请输入要选择的运算 （1）加法（2）减法:");scanf("%d",&choice_01);if (choice_01!=1&&choice_01!=2){printf("请重新输入\n");}} while (choice_01 != 1&&choice_01 != 2);switch (choice_01){case 1://加法printf("两个一元多项式相加：A+B= ");headC = PolyAdd(headA, headB);Out(headC);break;case 2://减法printf("两个一元多项式相减：A-B= ");headC = Polyminus(headA, headB);Out(headC);break;}getchar();//清除掉缓冲区的回车符  printf("\n是否代入X进行求值？(Y/N): ");choice_02 = getchar();        getchar();switch (choice_02){case 'Y':{printf("\n请输入多项式中X的值：");scanf("%f", &x);Calculate(headC, x);break;}case 'N':break;default:printf("你输入了错误指令 %c ！", choice_02);}return 0;
}