在上一题的基础上,建立两个struct Item为结点的代数多项式单链表。计算多项式的加减运算,产生和多项式单链表、差多项式单链表,并显示这两个多项式。输入x的值,计算并显示和多项式、差多项式值。
时间: 2024-03-25 12:37:18 浏览: 21
好的,我明白了。不过在这里需要说明一下,我的语言模型只能回答和文本相关的问题,并不能直接进行程序设计和编写。我会尽力回答你的问题,但可能需要你自己进行代码实现。
针对你的问题,我可以给你一些思路和建议。你可以定义两个结构体,一个是多项式的项,一个是多项式的结点。多项式的项应该包括系数和幂次两个属性,多项式的结点应该包括一个指向多项式项的指针和一个指向下一个结点的指针。然后,你需要定义加法和减法的函数来进行多项式的运算。在计算结果时,可以通过遍历多项式链表来计算每一项的值。
具体的代码实现可以参考以下示例:
```c++
#include <iostream>
using namespace std;
struct Item {
float coefficient;
int exponent;
};
struct Node {
Item item;
Node *next;
};
Node* createPolynomial() {
Node *head = new Node();
head->next = NULL;
Node *p = head;
int n;
cout << "请输入多项式的项数:";
cin >> n;
for (int i = 0; i < n; i++) {
Item item;
cout << "请输入第" << i + 1 << "项的系数和幂次:";
cin >> item.coefficient >> item.exponent;
Node *q = new Node();
q->item = item;
q->next = NULL;
p->next = q;
p = q;
}
return head;
}
void displayPolynomial(Node *head) {
Node *p = head->next;
while (p != NULL) {
if (p->item.coefficient > 0 && p != head->next) {
cout << "+";
}
cout << p->item.coefficient << "x^" << p->item.exponent;
p = p->next;
}
cout << endl;
}
Node* addPolynomial(Node *a, Node *b) {
Node *head = new Node();
head->next = NULL;
Node *p = a->next, *q = b->next, *r = head;
while (p != NULL && q != NULL) {
if (p->item.exponent > q->item.exponent) {
r->next = p;
r = p;
p = p->next;
} else if (p->item.exponent < q->item.exponent) {
r->next = q;
r = q;
q = q->next;
} else {
Item item;
item.coefficient = p->item.coefficient + q->item.coefficient;
item.exponent = p->item.exponent;
if (item.coefficient != 0) {
Node *s = new Node();
s->item = item;
s->next = NULL;
r->next = s;
r = s;
}
p = p->next;
q = q->next;
}
}
while (p != NULL) {
r->next = p;
r = p;
p = p->next;
}
while (q != NULL) {
r->next = q;
r = q;
q = q->next;
}
r->next = NULL;
return head;
}
Node* subtractPolynomial(Node *a, Node *b) {
Node *head = new Node();
head->next = NULL;
Node *p = a->next, *q = b->next, *r = head;
while (p != NULL && q != NULL) {
if (p->item.exponent > q->item.exponent) {
r->next = p;
r = p;
p = p->next;
} else if (p->item.exponent < q->item.exponent) {
Item item;
item.coefficient = -q->item.coefficient;
item.exponent = q->item.exponent;
Node *s = new Node();
s->item = item;
s->next = NULL;
r->next = s;
r = s;
q = q->next;
} else {
Item item;
item.coefficient = p->item.coefficient - q->item.coefficient;
item.exponent = p->item.exponent;
if (item.coefficient != 0) {
Node *s = new Node();
s->item = item;
s->next = NULL;
r->next = s;
r = s;
}
p = p->next;
q = q->next;
}
}
while (p != NULL) {
r->next = p;
r = p;
p = p->next;
}
while (q != NULL) {
Item item;
item.coefficient = -q->item.coefficient;
item.exponent = q->item.exponent;
Node *s = new Node();
s->item = item;
s->next = NULL;
r->next = s;
r = s;
q = q->next;
}
r->next = NULL;
return head;
}
float evaluatePolynomial(Node *head, float x) {
float result = 0;
Node *p = head->next;
while (p != NULL) {
result += p->item.coefficient * pow(x, p->item.exponent);
p = p->next;
}
return result;
}
int main() {
cout << "请输入第一个多项式:" << endl;
Node *a = createPolynomial();
cout << "请输入第二个多项式:" << endl;
Node *b = createPolynomial();
Node *c = addPolynomial(a, b);
Node *d = subtractPolynomial(a, b);
cout << "第一个多项式为:";
displayPolynomial(a);
cout << "第二个多项式为:";
displayPolynomial(b);
cout << "和多项式为:";
displayPolynomial(c);
cout << "差多项式为:";
displayPolynomial(d);
float x;
cout << "请输入x的值:";
cin >> x;
cout << "和多项式的值为:" << evaluatePolynomial(c, x) << endl;
cout << "差多项式的值为:" << evaluatePolynomial(d, x) << endl;
return 0;
}
```
需要注意的是,这只是一个简单的示例,实际的代码实现可能需要更多的细节处理和错误检查。