能够按照指数降序排列建立并输出多项式;能够完成两个多项式的输出、 相加、相 减,并将结果输出。 【任务】 将任意给出的 n 次多项式建成单链表结构,结点的结构为系数、指数、指针,然后 实现多项式相关运算。 良好的用户界面,对于错误的输入,要能给出信息提示。
时间: 2024-09-23 19:08:39 浏览: 61
为了实现这个功能,你需要定义一个多项式结点的数据结构,包含系数、指数以及指向下一个结点的指针。同时,你需要创建函数用于构建、操作多项式链表以及处理用户输入。
首先,定义一个多项式结点的数据结构:
```c
typedef struct PolynomialNode {
double coefficient; // 系数
int exponent; // 指数
struct PolynomialNode* next; // 指向下一个结点的指针
} Polynomial;
// 构建空多项式链表
Polynomial* buildEmptyPolynomial() {
Polynomial* head = malloc(sizeof(Polynomial));
head->coefficient = 0;
head->exponent = -1;
head->next = NULL;
return head;
}
// 根据给定的系数和指数添加结点到链表
void addTermToPolynomial(Polynomial** polynomial, double coefficient, int exponent) {
Polynomial* newNode = malloc(sizeof(Polynomial));
newNode->coefficient = coefficient;
newNode->exponent = exponent;
newNode->next = *polynomial;
*polynomial = newNode;
}
// 对多项式进行按指数降序排序
void sortPolynomialByExponentDesc(Polynomial** polynomial) {
if (*polynomial == NULL) return;
qsort(*polynomial, 1, sizeof(Polynomial), compareExponents);
}
// 比较指数函数
int compareExponents(const void* a, const void* b) {
const Polynomial* nodeA = (const Polynomial*)a;
const Polynomial* nodeB = (const Polynomial*)b;
return nodeB->exponent - nodeA->exponent;
}
// 输出多项式
void printPolynomial(const Polynomial* polynomial) {
Polynomial* current = polynomial;
printf("( ");
while (current != NULL) {
printf("%.2fX^%d ", current->coefficient, current->exponent);
current = current->next;
}
printf(")");
}
// 多项式加法和减法
Polynomial* addOrSubtractPolynomials(Polynomial* polynomial1, Polynomial* polynomial2, char operation) {
Polynomial* result = buildEmptyPolynomial();
Polynomial* current1 = polynomial1, *current2 = polynomial2;
while (current1 && current2) {
if (current1->exponent > current2->exponent) {
addTermToPolynomial(&result, current1->coefficient, current1->exponent);
current1 = current1->next;
} else if (current1->exponent < current2->exponent) {
addTermToPolynomial(&result, current2->coefficient, current2->exponent);
current2 = current2->next;
} else {
switch(operation) {
case '+':
result->coefficient += current1->coefficient;
break;
case '-':
result->coefficient -= current1->coefficient;
break;
default:
printf("Invalid operation. Please use '+' or '-' for addition or subtraction.\n");
return result;
}
current1 = current1->next;
current2 = current2->next;
}
}
while (current1) {
addTermToPolynomial(&result, current1->coefficient, current1->exponent);
current1 = current1->next;
}
while (current2) {
addTermToPolynomial(&result, current2->coefficient, current2->exponent);
current2 = current2->next;
}
return result;
}
// 用户输入处理函数
void handleUserInput() {
Polynomial* polynomial1 = buildEmptyPolynomial(), *polynomial2;
char operation;
printf("Enter the coefficients and exponents of the first polynomial separated by 'x': ");
scanf("%lf x %lf", &polynomial1->coefficient, &polynomial1->exponent);
while (scanf(" x %lf", &polynomial1->next->exponent) == 1) {
addTermToPolynomial(&polynomial1, 1, polynomial1->next->exponent);
scanf("%lf", &polynomial1->next->coefficient); // 可能需要验证非零输入
polynomial1->next = polynomial1->next->next;
}
printf("Enter operation (+/-): ");
scanf(" %c", &operation);
Polynomial* result;
if (operation == '+') {
scanf("Enter the coefficients and exponents of the second polynomial separated by 'x': ");
// 重复上述过程处理第二个多项式
polynomial2 = ...; // 处理第二个多项式的输入
result = addOrSubtractPolynomials(polynomial1, polynomial2, operation);
} else {
result = addOrSubtractPolynomials(polynomial1, NULL, operation); // 减去空多项式,相当于原地修改
}
printPolynomial(result);
}
```
这部分代码实现了多项式链表的构建、排序、输出,以及加法和减法运算。用户通过交互输入两个多项式及其对应的操作。注意,处理用户输入的部分未完全写出,你需要在`handleUserInput`函数内完善第二个多项式的输入部分。
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