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//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;
}
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define OK 1
#define ERROR 0
#define TRUE 1
#define FALSE 0
typedef int Status;
typedef int Elemtype;
typedef struct Node{
Elemtype cof;
Elemtype inx;
struct Node *next;
}Node, *LinkList;
Status visit(Elemtype a, Elemtype b)
{
printf("%d %d", a, b);
return OK;
}
Status InitList(LinkList *L)
{
(*L) = (LinkList)malloc(sizeof(Node));
if (!(*L))
return ERROR;
(*L)->next = NULL;
return OK;
}
/* count the length */
int ListLength(LinkList L)
{
int i = 0;
LinkList p;
p = L->next;
while (p) {
i++;
p = p->next;
}
return i;
}
/* get the data of no. i nodes, i start from 1 */
Status GetElem(LinkList L, int i, Elemtype *cof, Elemtype *inx)
{
LinkList p;
int j;
p = L;
j = 1;
while (p && j < i) {
p = p->next;
j++;
}
if (!p)
return ERROR;
*cof=p->next->cof;
*inx=p->next->inx;
return OK;
}
Status ListInsert(LinkList *L, int i, Elemtype cof, Elemtype inx)
{
if(i < 1 || i > ListLength(*L) + 1)
return ERROR;
int j;
LinkList p, q;
p = *L;
j = 1;
while (p && j < i) {
p = p->next;
j++;
}
if (!p || j > i)
return ERROR;
q = (LinkList)malloc(sizeof(Node));
if (!q) {
fprintf(stderr, "malloc error!\n");
return ERROR;
}
q->cof = cof;
q->inx = inx;
q->next = p->next;
p->next = q;
return OK;
}
/*打印L中系数非零的项*/
Status ListTraverse(LinkList L)
{
LinkList p;
p = L->next;
while (p) {
if (p->cof != 0) {
visit(p->cof, p->inx);
printf(" ");
}
p = p->next;
}
printf("\n");
return OK;
}
Status PlusList(LinkList *L3,LinkList L1,LinkList L2)
{
int i, j, k;
Elemtype cof1, inx1;
Elemtype cof2, inx2;
k = i = j = 1;
while ((i <= ListLength(L1)) && (j <= ListLength(L2))) {
GetElem(L1, i, &cof1, &inx1);
GetElem(L2, j, &cof2, &inx2);
if (inx1 == inx2) {
ListInsert(L3, k++, cof1 + cof2, inx1);
i++;
j++;
} else if (inx1 > inx2) {
ListInsert(L3, k++, cof1, inx1);
i++;
} else {
ListInsert(L3, k++, cof2, inx2);
j++;
}
}
return OK;
}
int main()
{
LinkList L1, L2, L3;
int cofn, inxn;
int i;
InitList(&L1);
InitList(&L2);
InitList(&L3);
i = 1;
while(scanf("%d%d", &cofn, &inxn) == 2 && inxn != -1){
ListInsert(&L1, i++, cofn, inxn);
}
i = 1;
while(scanf("%d%d", &cofn, &inxn) == 2 && cofn != -1){
ListInsert(&L2, i++, cofn, inxn);
}
PlusList(&L3, L1, L2);
ListTraverse(L3);
return 0;
}