用c语言实现把任意给定的俩个一元多项式P(x),Q(x)输入计算机,计算他们的和并输出就算结果
时间: 2024-02-17 15:01:47 浏览: 27
好的,我可以帮您解决这个问题。
首先,我们需要定义一元多项式的数据结构。可以使用链表来实现,每个节点代表一项,包含系数和指数两个成员。
```c
typedef struct polyNode {
float coef;
int expn;
struct polyNode *next;
} PolyNode, *Polynomial;
```
然后,我们可以编写一个函数来输入一元多项式:
```c
Polynomial createPoly() {
Polynomial head, tail, p;
int n, i;
float c;
head = (Polynomial)malloc(sizeof(PolyNode));
head->next = NULL;
tail = head;
scanf("%d", &n);
for (i = 0; i < n; i++) {
p = (Polynomial)malloc(sizeof(PolyNode));
scanf("%f %d", &c, &p->expn);
p->coef = c;
tail->next = p;
tail = p;
}
tail->next = NULL;
return head;
}
```
该函数会读取输入的项数,然后依次读入每一项的系数和指数,构建一个一元多项式。返回值为该多项式的头节点。
接下来,我们可以编写一个函数来计算两个多项式的和:
```c
Polynomial addPoly(Polynomial P, Polynomial Q) {
Polynomial head, tail, p1, p2, tmp;
float c;
head = (Polynomial)malloc(sizeof(PolyNode));
head->next = NULL;
tail = head;
p1 = P->next;
p2 = Q->next;
while (p1 && p2) {
if (p1->expn == p2->expn) {
c = p1->coef + p2->coef;
if (c != 0) {
tmp = (Polynomial)malloc(sizeof(PolyNode));
tmp->coef = c;
tmp->expn = p1->expn;
tail->next = tmp;
tail = tmp;
}
p1 = p1->next;
p2 = p2->next;
}
else if (p1->expn > p2->expn) {
tmp = (Polynomial)malloc(sizeof(PolyNode));
tmp->coef = p1->coef;
tmp->expn = p1->expn;
tail->next = tmp;
tail = tmp;
p1 = p1->next;
}
else {
tmp = (Polynomial)malloc(sizeof(PolyNode));
tmp->coef = p2->coef;
tmp->expn = p2->expn;
tail->next = tmp;
tail = tmp;
p2 = p2->next;
}
}
while (p1) {
tmp = (Polynomial)malloc(sizeof(PolyNode));
tmp->coef = p1->coef;
tmp->expn = p1->expn;
tail->next = tmp;
tail = tmp;
p1 = p1->next;
}
while (p2) {
tmp = (Polynomial)malloc(sizeof(PolyNode));
tmp->coef = p2->coef;
tmp->expn = p2->expn;
tail->next = tmp;
tail = tmp;
p2 = p2->next;
}
tail->next = NULL;
return head;
}
```
该函数会遍历两个多项式,依次将相同指数的项相加,并将结果构建成一个新的多项式。返回值为该多项式的头节点。
最后,我们可以编写主函数来调用以上两个函数,并输出结果:
```c
int main() {
Polynomial P, Q, R;
P = createPoly();
Q = createPoly();
R = addPoly(P, Q);
while (R->next) {
R = R->next;
printf("%.1fx^%d ", R->coef, R->expn);
if (R->next && R->next->coef > 0) {
printf("+ ");
}
}
return 0;
}
```
该函数会先输入两个多项式 P 和 Q,然后调用 addPoly 函数计算它们的和,最后遍历输出结果。