C语言实现一元多项式的表示和实现

一元多项式可以表示为： a0 + a1*x + a2*x^2 + ... + an*x^n 其中 a0, a1, ..., an 为系数，n 为最高次数，x 为未知数。 实现一元多项式可以定义一个结构体，包含系数和次数两个成员变量。具体实现如下： ```c #include <stdio.h> #include <stdlib.h> typedef struct Node *PtrToNode; typedef PtrToNode Polynomial; struct Node { int coef; // 系数 int expon; // 次数 Polynomial Next; }; Polynomial CreatePoly(); // 创建多项式 Polynomial AddPoly(Polynomial P1, Polynomial P2); // 多项式相加 void PrintPoly(Polynomial P); // 输出多项式 int main() { Polynomial P1, P2, PP; printf("创建第一个多项式：\n"); P1 = CreatePoly(); printf("第一个多项式："); PrintPoly(P1); printf("创建第二个多项式：\n"); P2 = CreatePoly(); printf("第二个多项式："); PrintPoly(P2); PP = AddPoly(P1, P2); printf("两个多项式相加的结果为："); PrintPoly(PP); return 0; } Polynomial CreatePoly() { Polynomial P, Rear, t; int c, e; P = (Polynomial)malloc(sizeof(struct Node)); P->Next = NULL; Rear = P; printf("请输入多项式系数和指数，以 -1 -1 结束\n"); scanf("%d %d", &c, &e); while (c != -1) { t = (Polynomial)malloc(sizeof(struct Node)); t->coef = c; t->expon = e; t->Next = NULL; Rear->Next = t; Rear = t; scanf("%d %d", &c, &e); } return P; } Polynomial AddPoly(Polynomial P1, Polynomial P2) { Polynomial Front, Rear, temp; int sum; Front = (Polynomial)malloc(sizeof(struct Node)); Rear = Front; P1 = P1->Next; P2 = P2->Next; while (P1 && P2) { if (P1->expon == P2->expon) { sum = P1->coef + P2->coef; if (sum) { temp = (Polynomial)malloc(sizeof(struct Node)); temp->coef = sum; temp->expon = P1->expon; Rear->Next = temp; Rear = temp; } P1 = P1->Next; P2 = P2->Next; } else if (P1->expon > P2->expon) { temp = (Polynomial)malloc(sizeof(struct Node)); temp->coef = P1->coef; temp->expon = P1->expon; Rear->Next = temp; Rear = temp; P1 = P1->Next; } else { temp = (Polynomial)malloc(sizeof(struct Node)); temp->coef = P2->coef; temp->expon = P2->expon; Rear->Next = temp; Rear = temp; P2 = P2->Next; } } while (P1) { temp = (Polynomial)malloc(sizeof(struct Node)); temp->coef = P1->coef; temp->expon = P1->expon; Rear->Next = temp; Rear = temp; P1 = P1->Next; } while (P2) { temp = (Polynomial)malloc(sizeof(struct Node)); temp->coef = P2->coef; temp->expon = P2->expon; Rear->Next = temp; Rear = temp; P2 = P2->Next; } Rear->Next = NULL; temp = Front; Front = Front->Next; free(temp); return Front; } 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"); } ``` 以上代码中，CreatePoly() 函数用于创建多项式，AddPoly() 函数用于相加两个多项式，PrintPoly() 函数用于输出多项式。 在主函数中，先分别创建两个多项式，然后将它们相加，最后输出结果。