一元n次多项式定义如下：
其中Ai为实数，i为不小于0的整数。在完成"一元n次多项式输入输出"题目的基础上实现一元n次多项式的加法。要求用链表实现上述一元n次多项式的操作。
输入格式:
有两个一元n次多项式，例如分别为：
f(X)=3X2+ X+1
g(X)=−2X2−X-1
其中系数为实数 ,指数取不小于0的整数 。输入分为2行，第1行为第1个一元n次多项式，第1个一元n次多项式按照第1项系数,指数 第2项系数,指数 .... 的格式输入，系数和指数以","分割，各项的系数和指数之间以空格分割，输入一元n次多项式不要求按指数有序排列，最后以 0,0（即系数=0,指数=0）表示结束。第2行为第2个一元n次多项式，输入格式与第1个一元n次多项式相同。对上面的两个一元n次多项式：
输入样例:
3,2 1,1 1,0 0,0
-2,2 -1,1 -1,0 0,0
输出格式:
输出分为以下3行：第1行输出第1个一元n次多项式，第2行输出第2个一元n次多项式，第3行输出两个一元n次多项式的和。输出要求一元n次多项式的高次项在前，低次项在后，即按指数由大到小排列，实数保留小数点后面1位数，一元多项式为f(X)=0时，输出为f(X)=0.0。对上面2个一元n次多项式的输出为：
输出样例:
f(X)=3.0X^2+X+1.0
g(X)=-2.0X^2-X-1.0
f(X)+g(X)=X^2
cpp
#include <stdio.h>
#include <stdlib.h>
typedef struct PolynomialNode //定义了一个名为PolynomialNode的结构体，用于表示多项式中的一项
{
double coefficient; //系数
int exponent; //指数
struct PolynomialNode *next; //指针域
} PolynomialNode;
PolynomialNode* createNode(double coefficient, int exponent)
{
PolynomialNode *newNode = (PolynomialNode*)malloc(sizeof(PolynomialNode));
newNode->coefficient = coefficient;
newNode->exponent = exponent;
newNode->next = NULL;
return newNode;
}
void insertNode(PolynomialNode** head, double coefficient, int exponent)
{ //将一个新的项插入到多项式链表中
PolynomialNode* newNode = createNode(coefficient, exponent);
if (*head == NULL || exponent > (*head)->exponent) {
newNode->next = *head; //如果新项的指数大于当前链表头部的指数
*head = newNode; //或者链表为空，则将新项置于链表头部
}
else
{ //否则，遍历链表找到合适的位置插入新项
PolynomialNode* current = *head;
while (current->next!= NULL && current->next->exponent > exponent)
{ //当前节点的下指针不为空&&当前节点的下指针的指数>当前节点的
current = current->next; //refresh当前与下一个
}
if (current->exponent == exponent) //如果新项的指数与链表中的某项指数相同，则合并系数
{
current->coefficient += coefficient;
free(newNode);
}
else
{
newNode->next = current->next;
current->next = newNode;
}
}
}
void printPolynomial(PolynomialNode* head, const char* name)
{
if (head == NULL)
{
printf("%s=0.0\n", name);
return;
}
PolynomialNode* current = head;
int firstTerm = 1;
printf("%s=", name);
while (current!= NULL)
{
if (current->coefficient == 0) //系数为0
{
current = current->next; //跳过当前项
continue;
}
if (current->coefficient < 0) //系数小于0
{
if (!firstTerm) //不是第一项
{
if (current->exponent == 1)
{
printf("-X");
}
else if (current->exponent > 1)
{
if (current->coefficient == -1.0) //特殊判断
{
printf("-X^%d", current->exponent);
}
else
{
printf("%.1fX^%d", current->coefficient, current->exponent);
}
}
else //是第一项
{
printf("%.1f", current->coefficient);
}
}
else
{
if (current->exponent == 1)
{
printf("-X");
}
else if (current->exponent > 1)
{
if (current->coefficient == -1.0)
{
printf("-X^%d", current->exponent);
}
else
{
printf("%.1fX^%d", current->coefficient, current->exponent);
}
}
else
{
printf("%.1f", current->coefficient);
}
firstTerm = 0;
}
}
else //系数大于0
{
if (!firstTerm)
{
if (current->exponent == 1)
{
printf("+X");
}
else if (current->exponent > 1)
{
if (current->coefficient == 1.0)
{
printf("+X^%d", current->exponent);
}
else
{
printf("+%.1fX^%d", current->coefficient, current->exponent);
}
}
else
{
printf("+%.1f", current->coefficient);
}
}
else
{
if (current->exponent == 1)
{
printf("X");
}
else if (current->exponent > 1)
{
if (current->coefficient == 1.0)
{
printf("X^%d", current->exponent);
}
else
{
printf("%.1fX^%d", current->coefficient, current->exponent);
}
}
else
{
printf("%.1f", current->coefficient);
}
firstTerm = 0;
}
}
current = current->next;
}
printf("\n");
}
void freePolynomial(PolynomialNode* head)
{
PolynomialNode* current = head;
while (current!= NULL)
{
PolynomialNode* next = current->next;
free(current);
current = next;
}
}
PolynomialNode* addPolynomials(PolynomialNode* poly1, PolynomialNode* poly2)
{
PolynomialNode* result = NULL;
PolynomialNode* current1 = poly1;
PolynomialNode* current2 = poly2;
while (current1!= NULL || current2!= NULL)
{ //循环会一直执行，直到两个输入链表都遍历完
double coefficient;
int exponent;
if (current1 == NULL) //第一个多项式链表已经遍历完
{ //从第二个多项式链表current2中取当前项的系数和指数
coefficient = current2->coefficient;
exponent = current2->exponent;
current2 = current2->next;
}
else if (current2 == NULL) //第二个多项式链表已经遍历完
{ //从第一个多项式链表current1中取当前项的系数和指数
coefficient = current1->coefficient;
exponent = current1->exponent;
current1 = current1->next;
}
else if (current1->exponent > current2->exponent) //第一个多项式链表中的项指数较大
{ //取第一个多项式链表当前项的系数和指数
coefficient = current1->coefficient;
exponent = current1->exponent;
current1 = current1->next;
}
else if (current1->exponent < current2->exponent) //第二个多项式链表中的项指数较大
{ //取第二个多项式链表当前项的系数和指数
coefficient = current2->coefficient;
exponent = current2->exponent;
current2 = current2->next;
}
else //两个多项式链表当前项的指数相同，将它们的系数相加作为新的系数
{
coefficient = current1->coefficient + current2->coefficient;
exponent = current1->exponent;
current1 = current1->next;
current2 = current2->next;
}
if (coefficient!= 0)
{
insertNode(&result, coefficient, exponent);
}
}
return result;
}
int main()
{
PolynomialNode* poly1 = NULL;
PolynomialNode* poly2 = NULL;
double coefficient;
int exponent;
while (scanf("%lf,%d", &coefficient, &exponent) && coefficient!= 0 || exponent!= 0)
{
if (coefficient == 0 && exponent == 0)
{
break;
}
insertNode(&poly1, coefficient, exponent);
}
while (scanf("%lf,%d", &coefficient, &exponent) && coefficient!= 0 || exponent!= 0)
{
if (coefficient == 0 && exponent == 0)
{
break;
}
insertNode(&poly2, coefficient, exponent);
}
// 合并多项式 poly2 中的同类项
PolynomialNode* tempPoly2 = poly2;
while (tempPoly2!= NULL && tempPoly2->next!= NULL)
{
if (tempPoly2->exponent == tempPoly2->next->exponent || (tempPoly2->exponent == 1 && tempPoly2->next->exponent == 1)) {
tempPoly2->coefficient += tempPoly2->next->coefficient;
PolynomialNode* toFree = tempPoly2->next;
tempPoly2->next = tempPoly2->next->next;
free(toFree);
}
else
{
tempPoly2 = tempPoly2->next;
}
}
printPolynomial(poly1, "f(X)");
printPolynomial(poly2, "g(X)");
PolynomialNode* sum = addPolynomials(poly1, poly2);
printf("f(X)+g(X)");
if (sum == NULL)
{
printf("0.0\n");
}
else
{
printPolynomial(sum, "");
}
freePolynomial(poly1);
freePolynomial(poly2);
freePolynomial(sum);
return 0;
}