C语言求多项式P1=3x4+2x2+6,P2=x5-2x4+3x3+4x2-x的和。 要求:使用顺序存储方式实现。代码中要有线性表的定义,求和操作单独使用函数实现。画二维表表示数组下标和多项式系数与指数的关系
时间: 2024-09-22 11:04:12 浏览: 101
在C语言中,我们可以使用结构体和动态内存分配来表示多项式,并通过链表实现顺序存储。首先,我们定义一个多项式的结构体,包含系数、指数和指向下一个多项式的指针。
```c
#include <stdio.h>
#include <stdlib.h>
typedef struct {
double coefficient;
int exponent;
struct polynomial *next;
} Polynomial;
// 动态创建多项式节点
Polynomial* create_polynomial(double coef, int exp) {
Polynomial *new_poly = (Polynomial*)malloc(sizeof(Polynomial));
new_poly->coefficient = coef;
new_poly->exponent = exp;
new_poly->next = NULL;
return new_poly;
}
// 添加多项式节点到序列
void add_to_sequence(Polynomial **head, Polynomial *poly) {
if (*head == NULL) {
*head = poly;
} else {
Polynomial *current = *head;
while (current->next != NULL) {
current = current->next;
}
current->next = poly;
}
}
// 求两个多项式的和
Polynomial* sum_polynomials(Polynomial *poly1, Polynomial *poly2) {
Polynomial *sum_head = NULL;
Polynomial *temp = NULL;
while (poly1 != NULL && poly2 != NULL) {
double coef_sum = poly1->coefficient + poly2->coefficient;
int max_exp = (poly1->exponent > poly2->exponent) ? poly1->exponent : poly2->exponent;
temp = create_polynomial(coef_sum, max_exp);
add_to_sequence(&sum_head, temp);
if (poly1->exponent == poly2->exponent) {
// 如果指数相同,移向下一个节点
poly1 = poly1->next;
poly2 = poly2->next;
} else if (poly1->exponent < poly2->exponent) {
// 如果poly1的指数小,继续处理poly2
poly1 = poly2;
poly2 = poly2->next;
} else {
// 否则,继续处理poly1
poly2 = poly1;
poly1 = poly1->next;
}
}
// 如果还有剩余的项,添加到结果序列
while (poly1 != NULL) {
temp = create_polynomial(poly1->coefficient, poly1->exponent);
add_to_sequence(&sum_head, temp);
poly1 = poly1->next;
}
while (poly2 != NULL) {
temp = create_polynomial(poly2->coefficient, poly2->exponent);
add_to_sequence(&sum_head, temp);
poly2 = poly2->next;
}
return sum_head;
}
// 打印多项式
void print_polynomial(Polynomial *poly) {
Polynomial *current = poly;
printf("多项式表达式:");
while (current != NULL) {
printf("%f*x^%d + ", current->coefficient, current->exponent);
current = current->next;
}
printf("0\n");
}
int main() {
Polynomial *p1_head = NULL;
Polynomial *p2_head = NULL;
// 初始化多项式P1
Polynomial *p1_node1 = create_polynomial(3.0, 4);
Polynomial *p1_node2 = create_polynomial(2.0, 2);
Polynomial *p1_node3 = create_polynomial(6.0, 0);
add_to_sequence(&p1_head, p1_node1);
add_to_sequence(&p1_head, p1_node2);
add_to_sequence(&p1_head, p1_node3);
// 初始化多项式P2
Polynomial *p2_node1 = create_polynomial(1.0, 5);
Polynomial *p2_node2 = create_polynomial(-2.0, 4);
Polynomial *p2_node3 = create_polynomial(3.0, 3);
Polynomial *p2_node4 = create_polynomial(4.0, 2);
Polynomial *p2_node5 = create_polynomial(-1.0, 1);
add_to_sequence(&p2_head, p2_node1);
add_to_sequence(&p2_head, p2_node2);
add_to_sequence(&p2_head, p2_node3);
add_to_sequence(&p2_head, p2_node4);
add_to_sequence(&p2_head, p2_node5);
Polynomial *result = sum_polynomials(p1_head, p2_head);
print_polynomial(result);
free_polynomial(result); // 自定义的释放节点函数
return 0;
}
```
在这个示例中,`free_polynomial`是一个辅助函数用于释放多项式链表中的所有节点。注意,由于实际项目中通常不会提供完整代码,所以这里假设有一个简单的`free_polynomial`函数。二维表格可以手动绘制,但实际上在程序中不需要,因为我们直接操作的是多项式的系数和指数。运行这个程序会得到P1和P2的和。
阅读全文