一、實驗內容及要求

1.任務描述：

實驗內容：
設有一元多項式Am(x)和Bn(X)，編程實現多項式Am(x)和Bn(x)的加法、減法和乘法運算。其中多項式描述為：
Am(x)=A0+A1x1+A2x2+A3x3+….+Amxm；
Bn(x)=B0+B1x1+B2x2+B3x3+….+Bnxn。
輸入和輸出：
（1）輸入：

• 從鍵盤輸入運算指令（相加、相減、相乘），根據運算指令進行相應運算；
• 從鍵盤輸入兩個多項式的系數和指數；
• 系數和指數采用int類型，運算結果不超出int取值范圍。
  （2）輸出：
• 每種運算結果以多項式形式輸出，要輸出升冪和降冪兩種情況。
• 結果多項式中無重復階項、無零系數項，輸出多項式時請采用如下易讀形式（一元多項式，總變元為x）：　x^4 - 3 x^2 + 5
  實驗要求：
• 實現一個簡單的交互式界面，包括系統菜單、輸入提示等。
• 多項式運算前首先判定多項式特點，根據多項式是否稀疏來選用合適的存儲結構；
• 根據多項式不同的運算要求選擇合適的存儲結構；
• 上機編輯、調試出完整正確的程序，包括相加、相減、相乘運算。

2.主要數據類型與變量

struct PolyNode {
int coef;
int expon;
PolyNode* link;
};
typedef PolyNode* Polynomial;

3.算法或程序模塊

讀多項式模塊：
Polynomial ReadPoly()
多項式乘法模塊：
Polynomial Mult(Polynomial p1, Polynomial p2)
多項式加法模塊：
Polynomial Add(Polynomial p1, Polynomial p2)
多項式減法模塊：
Polynomial Reduce(Polynomial p1, Polynomial p2)
輸出多項式模塊：
void PrintPoly(Polynomial p)

二、測試

1、 方案
輸入兩個多項式分別為：
3 4 -5 2 6 1 -2 0
5 20 -7 4 3 1
2、 結果

三、代碼

#include<cstdio> #include<cstdlib> using namespace std;struct PolyNode {int coef;int expon;PolyNode* link; }; typedef PolyNode* Polynomial;void Attach(int c, int e, Polynomial* prear) {PolyNode* node = new PolyNode();node->coef = c;node->expon = e;(*prear)->link = node;*prear = node; }Polynomial ReadPoly() {int c, e;Polynomial p, rear, temp;p = new PolyNode();rear = p;while(scanf("%d%d", &c, &e)){Attach(c,e,&rear);char ch = getchar(); if(ch == '\n')break;}temp = p; p = p->link; free(temp);return p; }Polynomial Mult(Polynomial p1, Polynomial p2) {if (!p1||!p2) return NULL;Polynomial p, rear, t1, t2, temp;p = new PolyNode();rear = p;t1 = p1; t2 = p2;int c, e;while (t2){c = t1->coef * t2->coef;e = t1->expon + t2->expon;Attach(c, e, &rear);t2 = t2->link;} t1 = t1->link;while (t1){t2 = p2; rear = p;while (t2){c = t1->coef * t2->coef;e = t1->expon + t2->expon;while (rear->link && rear->link->expon > e){rear = rear->link;}if (rear->link && rear->link->expon == e){if (rear->link->coef + c){rear->link->coef += c;}else{Polynomial temp = rear->link;rear->link = temp->link;free(temp);}}else{PolyNode* node = new PolyNode();node->coef = c;node->expon = e;node->link = rear->link;rear->link = node;rear = rear->link;}t2 = t2->link;}t1 = t1->link; }temp = p; p = p->link; free(temp);return p; }Polynomial Add(Polynomial p1, Polynomial p2) {Polynomial p, rear, t1, t2, temp;p = new PolyNode();rear = p;t1 = p1; t2 = p2;while (t1 && t2){if (t1->expon == t2->expon){if (t1->coef + t2->coef != 0) Attach(t1->coef + t2->coef, t1->expon, &rear);t1 = t1->link;t2 = t2->link;}else if(t1->expon > t2->expon){Attach(t1->coef, t1->expon, &rear);t1 = t1->link;}else{Attach(t2->coef, t2->expon, &rear);t2 = t2->link;}}for (; t1; t1 = t1->link) Attach(t1->coef, t1->expon, &rear);for (; t2; t2 = t2->link) Attach(t2->coef, t2->expon, &rear);temp = p; p = p->link; free(temp);return p; } Polynomial Reduce(Polynomial p1, Polynomial p2) {Polynomial p, rear, t1, t2, temp;p = new PolyNode();rear = p;t1 = p1; t2 = p2;while (t1 && t2){if (t1->expon == t2->expon){if (t1->coef - t2->coef != 0) Attach(t1->coef - t2->coef, t1->expon, &rear);t1 = t1->link;t2 = t2->link;}else if(t1->expon > t2->expon){Attach(t1->coef, t1->expon, &rear);t1 = t1->link;}else{Attach(-t2->coef, t2->expon, &rear);t2 = t2->link;}}for (; t1; t1 = t1->link) Attach(t1->coef, t1->expon, &rear);for (; t2; t2 = t2->link) Attach(-t2->coef, t2->expon, &rear);temp = p; p = p->link; free(temp);return p; } void PrintPoly(Polynomial p) {if (!p){printf("0\n");return;}int flag = 0;while (p){int a=p->coef;int b=p->expon;if (!flag) {flag = 1;if(b==0)printf("%d",a);else printf("%dx^%d",a,b);}else{if(a>0){if(b==0) printf("+%d",a);else if(b==1) printf("+%dx",a);else printf("+%dx^%d", a, b);} else {if(b==0) printf("%d",a);else if(b==1) printf("%dx",a);else printf("%dx^%d", a, b);}}p = p->link;}printf("\n"); }int main() {Polynomial p1, p2, pm, ps,pr;p1 = ReadPoly();p2 = ReadPoly();pm = Mult(p1, p2);PrintPoly(pm);ps = Add(p1, p2);PrintPoly(ps);pr=Reduce(p1,p2);PrintPoly(pr); }

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