完整代码实现 一元稀疏多项式计算器
时间: 2023-12-08 14:06:30 浏览: 96
根据提供的引用内容,无法确定一元稀疏多项式计算器的具体实现方式。但是,一元稀疏多项式计算器通常需要实现以下功能:
1. 输入多项式:用户可以输入多项式,例如输入 3x^2 + 2x + 1。
2. 显示多项式:用户可以查看当前输入的多项式。
3. 多项式加法:用户可以输入两个多项式,计算它们的和。
4. 多项式减法:用户可以输入两个多项式,计算它们的
相关问题
代码实现 一元稀疏多项式计算器
一元稀疏多项式计算器是一个可以对一元稀疏多项式进行加、减、乘、求导等运算的计算器。其代码实现需要使用数据结构中的链表来存储多项式的系数和指数,具体实现步骤如下:
1. 定义一个结构体来存储多项式的系数和指数,例如:
```
struct PolyNode {
int coef; // 系数
int expon; // 指数
struct PolyNode *next; // 指向下一个节点的指针
};
```
2. 定义一个链表来存储多项式,链表的每个节点都是一个PolyNode结构体,例如:
```
typedef struct PolyNode *Polynomial;
struct PolyNode {
int coef; // 系数
int expon; // 指数
struct PolyNode *next; // 指向下一个节点的指针
};
```
3. 实现多项式的输入函数,可以通过读入系数和指数来构建多项式链表,例如:
```
Polynomial ReadPoly() {
Polynomial P, rear, t;
int c, e;
P = (Polynomial)malloc(sizeof(struct PolyNode));
P->next = NULL;
rear = P;
scanf("%d %d", &c, &e);
while (c != 0) {
t = (Polynomial)malloc(sizeof(struct PolyNode));
t->coef = c;
t->expon = e;
t->next = NULL;
rear->next = t;
rear = t;
scanf("%d %d", &c, &e);
}
return P;
}
```
4. 实现多项式的输出函数,可以遍历多项式链表并输出每个节点的系数和指数,例如:
```
void PrintPoly(Polynomial P) {
int flag = 0;
if (!P) {
printf("0 0\n");
return;
}
while (P) {
if (!flag) {
flag = 1;
} else {
printf(" ");
}
printf("%d %d", P->coef, P->expon);
P = P->next;
}
printf("\n");
}
```
5. 实现多项式的加法函数,可以遍历两个多项式链表并将相同指数的项相加,例如:
```
Polynomial Add(Polynomial P1, Polynomial P2) {
Polynomial front, rear, temp;
int sum;
rear = (Polynomial)malloc(sizeof(struct PolyNode));
front = rear;
while (P1 && P2) {
if (P1->expon > P2->expon) {
temp = (Polynomial)malloc(sizeof(struct PolyNode));
temp->coef = P1->coef;
temp->expon = P1->expon;
temp->next = NULL;
rear->next = temp;
rear = temp;
P1 = P1->next;
} else if (P1->expon < P2->expon) {
temp = (Polynomial)malloc(sizeof(struct PolyNode));
temp->coef = P2->coef;
temp->expon = P2->expon;
temp->next = NULL;
rear->next = temp;
rear = temp;
P2 = P2->next;
} else {
sum = P1->coef + P2->coef;
if (sum) {
temp = (Polynomial)malloc(sizeof(struct PolyNode));
temp->coef = sum;
temp->expon = P1->expon;
temp->next = NULL;
rear->next = temp;
rear = temp;
}
P1 = P1->next;
P2 = P2->next;
}
}
while (P1) {
temp = (Polynomial)malloc(sizeof(struct PolyNode));
temp->coef = P1->coef;
temp->expon = P1->expon;
temp->next = NULL;
rear->next = temp;
rear = temp;
P1 = P1->next;
}
while (P2) {
temp = (Polynomial)malloc(sizeof(struct PolyNode));
temp->coef = P2->coef;
temp->expon = P2->expon;
temp->next = NULL;
rear->next = temp;
rear = temp;
P2 = P2->next;
}
rear->next = NULL;
temp = front;
front = front->next;
free(temp);
return front;
}
```
6. 实现多项式的乘法函数,可以遍历两个多项式链表并将每一项相乘,然后将结果插入到一个新的多项式链表中,例如:
```
Polynomial Mult(Polynomial P1, Polynomial P2) {
Polynomial P, rear, t1, t2, t;
int c, e;
if (!P1 || !P2) {
return NULL;
}
t1 = P1;
t2 = P2;
P = (Polynomial)malloc(sizeof(struct PolyNode));
P->next = NULL;
rear = P;
while (t2) {
c = t1->coef * t2->coef;
e = t1->expon + t2->expon;
t = (Polynomial)malloc(sizeof(struct PolyNode));
t->coef = c;
t->expon = e;
t->next = NULL;
rear->next = t;
rear = t;
t2 = t2->next;
}
t1 = t1->next;
while (t1) {
t2 = P2;
rear = P;
while (t2) {
e = t1->expon + t2->expon;
c = t1->coef * t2->coef;
while (rear->next && rear->next->expon > e) {
rear = rear->next;
}
if (rear->next && rear->next->expon == e) {
if (rear->next->coef + c) {
rear->next->coef += c;
} else {
t = rear->next;
rear->next = t->next;
free(t);
}
} else {
t = (Polynomial)malloc(sizeof(struct PolyNode));
t->coef = c;
t->expon = e;
t->next = rear->next;
rear->next = t;
rear = rear->next;
}
t2 = t2->next;
}
t1 = t1->next;
}
t2 = P;
P = P->next;
free(t2);
return P;
}
```
7. 实现多项式的求导函数,可以遍历多项式链表并将每一项的指数减1,然后将系数乘以指数,例如:
```
Polynomial Derivative(Polynomial P) {
Polynomial t = P;
while (t) {
t->coef *= t->expon;
t->expon--;
t = t->next;
}
return P;
}
```
c语言代码实现 一元稀疏多项式计算器
以下是C语言代码实现一元稀疏多项式计算器的步骤:
```c
#include <stdio.h>
#include <stdlib.h>
#define MAXSIZE 100
typedef struct {
float coef; // 系数
int expn; // 指数
} ElemType;
typedef struct {
ElemType data[MAXSIZE + 1]; // 存储数组,data[0]存储项数
int length; // 当前项数
} Poly;
void CreatePoly(Poly *P, int m) {
int i;
printf("请输入%d个非零项的系数和指数:\n", m);
for (i = 1; i <= m; i++) {
scanf("%f%d", &P->data[i].coef, &P->data[i].expn);
}
P->length = m;
}
void PrintPoly(Poly P) {
int i;
for (i = 1; i <= P.length; i++) {
if (i == 1) {
printf("%.2fx^%d", P.data[i].coef, P.data[i].expn);
} else {
printf(" + %.2fx^%d", P.data[i].coef, P.data[i].expn);
}
}
printf("\n");
}
void AddPoly(Poly *Pa, Poly *Pb) {
int i, j, k;
i = j = k = 1;
while (i <= Pa->length && j <= Pb->length) {
if (Pa->data[i].expn == Pb->data[j].expn) {
Pa->data[i].coef += Pb->data[j].coef;
if (Pa->data[i].coef != 0) {
i++;
}
j++;
} else if (Pa->data[i].expn < Pb->data[j].expn) {
i++;
} else {
k = Pa->length;
while (k >= i) {
Pa->data[k + 1] = Pa->data[k];
k--;
}
Pa->data[i] = Pb->data[j];
Pa->length++;
i++;
j++;
}
}
while (j <= Pb->length) {
Pa->data[++Pa->length] = Pb->data[j++];
}
}
void SubtractPoly(Poly *Pa, Poly *Pb) {
int i, j, k;
i = j = k = 1;
while (i <= Pa->length && j <= Pb->length) {
if (Pa->data[i].expn == Pb->data[j].expn) {
Pa->data[i].coef -= Pb->data[j].coef;
if (Pa->data[i].coef != 0) {
i++;
}
j++;
} else if (Pa->data[i].expn < Pb->data[j].expn) {
i++;
} else {
k = Pa->length;
while (k >= i) {
Pa->data[k + 1] = Pa->data[k];
k--;
}
Pa->data[i].coef = -Pb->data[j].coef;
Pa->data[i].expn = Pb->data[j].expn;
Pa->length++;
i++;
j++;
}
}
while (j <= Pb->length) {
Pa->data[++Pa->length].coef = -Pb->data[j].coef;
Pa->data[Pa->length].expn = Pb->data[j].expn;
j++;
}
}
void MultiplyPoly(Poly *Pa, Poly *Pb, Poly *Pc) {
int i, j, k;
for (i = 1; i <= Pa->length; i++) {
for (j = 1; j <= Pb->length; j++) {
k = Pa->data[i].expn + Pb->data[j].expn;
Pc->data[k].coef += Pa->data[i].coef * Pb->data[j].coef;
Pc->data[k].expn = k;
}
}
Pc->length = Pa->length + Pb->length - 1;
}
int main() {
Poly Pa, Pb, Pc;
int m, n;
printf("请输入多项式Pa的项数:");
scanf("%d", &m);
CreatePoly(&Pa, m);
printf("请输入多项式Pb的项数:");
scanf("%d", &n);
CreatePoly(&Pb, n);
printf("Pa = ");
PrintPoly(Pa);
printf("Pb = ");
PrintPoly(Pb);
AddPoly(&Pa, &Pb);
printf("Pa + Pb = ");
PrintPoly(Pa);
SubtractPoly(&Pa, &Pb);
printf("Pa - Pb = ");
PrintPoly(Pa);
MultiplyPoly(&Pa, &Pb, &Pc);
printf("Pa * Pb = ");
PrintPoly(Pc);
return 0;
}
```
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