在C语言中，表示一元多项式并进行相加操作可以通过多种数据结构实现。常见的方法是使用链表，其中每个节点表示多项式中的一项。节点包含系数、指数和指向下一个节点的指针。
下面是一个简单的实现示例：
定义多项式节点结构体
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#include <stdio.h> |
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#include <stdlib.h> |
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typedef struct PolyNode { |
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int coef; // 系数 |
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int exp; // 指数 |
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struct PolyNode *next; // 指向下一个节点的指针 |
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} PolyNode, *Polynomial; |
创建多项式节点
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PolyNode* CreateNode(int coef, int exp) { |
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PolyNode* newNode = (PolyNode*)malloc(sizeof(PolyNode)); |
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if (!newNode) { |
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printf("Memory allocation failed.\n"); |
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exit(1); |
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} |
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newNode->coef = coef; |
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newNode->exp = exp; |
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newNode->next = NULL; |
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return newNode; |
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} |
插入多项式项
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void InsertTerm(Polynomial *poly, int coef, int exp) { |
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PolyNode *newNode = CreateNode(coef, exp); |
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PolyNode *current = *poly; |
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PolyNode *prev = NULL; |
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// 找到插入位置 |
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while (current != NULL && current->exp > exp) { |
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prev = current; |
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current = current->next; |
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} |
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// 插入新节点 |
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if (prev == NULL) { |
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newNode->next = *poly; |
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*poly = newNode; |
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} else { |
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prev->next = newNode; |
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newNode->next = current; |
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} |
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} |
多项式相加
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Polynomial PolyAdd(Polynomial poly1, Polynomial poly2) { |
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Polynomial result = NULL; |
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PolyNode *current1 = poly1; |
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PolyNode *current2 = poly2; |
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PolyNode *prev = NULL; |
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PolyNode *newNode; |
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while (current1 != NULL && current2 != NULL) { |
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if (current1->exp > current2->exp) { |
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newNode = CreateNode(current1->coef, current1->exp); |
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if (prev == NULL) { |
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newNode->next = result; |
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result = newNode; |
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} else { |
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prev->next = newNode; |
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newNode->next = prev->next; |
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} |
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prev = newNode; |
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current1 = current1->next; |
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} else if (current1->exp < current2->exp) { |
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newNode = CreateNode(current2->coef, current2->exp); |
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if (prev == NULL) { |
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newNode->next = result; |
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result = newNode; |
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} else { |
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prev->next = newNode; |
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newNode->next = prev->next; |
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} |
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prev = newNode; |
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current2 = current2->next; |
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} else { // 指数相同，合并系数 |
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int sumCoef = current1->coef + current2->coef; |
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if (sumCoef != 0) { // 如果系数和不为0，则创建新节点 |
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newNode = CreateNode(sumCoef, current1->exp); |
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if (prev == NULL) { |
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newNode->next = result; |
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result = newNode; |
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} else { |
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prev->next = newNode; |
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newNode->next = prev->next; |
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} |
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prev = newNode; |
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} |
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current1 = current1->next; |
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current2 = current2->next; |
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} |
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} |
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// 处理剩余节点 |
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while (current1 != NULL) { |
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newNode = CreateNode(current1->coef, current1->exp); |
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prev->next = newNode; |
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prev = newNode; |
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current1 = current1->next; |
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} |
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while (current2 != NULL) { |
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newNode = CreateNode(current2->coef, current2->exp); |
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prev->next = newNode; |
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prev = newNode; |
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current2 = current2->next; |
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} |
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return result; |
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} |
打印多项式
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void PrintPoly(Polynomial poly) { |
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PolyNode *current = poly; |
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int isFirst = 1; |
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while (current != NULL) { |
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if (!isFirst && current->coef > 0) { |
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printf("+"); |
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} |
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printf("%dx^%d", current->coef |
一元多项式在C语言中通常可以用链表来表示，其中链表的每个节点代表多项式的一个项。每个节点包含系数（coefficient）、指数（exponent）以及指向下一个节点的指针。多项式相加时，我们需要遍历两个多项式链表，对应指数的项相加或合并，处理完所有项后得到相加后的多项式。
下面是一个简单的C语言实现示例：
多项式节点的定义2
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#include <stdio.h> |
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#include <stdlib.h> |
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// 多项式项的定义 |
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typedef struct PolyNode { |
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int coef; // 系数 |
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int exp; // 指数 |
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struct PolyNode *next; // 指向下一个节点的指针 |
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} PolyNode, *Polynomial; |
创建多项式节点2
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// 创建多项式节点 |
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PolyNode* CreateNode(int coef, int exp) { |
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PolyNode* newNode = (PolyNode*)malloc(sizeof(PolyNode)); |
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if (!newNode) { |
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exit(1); // 内存分配失败 |
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} |
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newNode->coef = coef; |
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newNode->exp = exp; |
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newNode->next = NULL; |
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return newNode; |
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} |
多项式相加2
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// 多项式相加 |
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Polynomial PolyAdd(Polynomial poly1, Polynomial poly2) { |
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Polynomial result = NULL, tail = NULL; |
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PolyNode *p1 = poly1->next, *p2 = poly2->next; |
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int sum; |
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// 遍历两个多项式链表 |
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while (p1 && p2) { |
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if (p1->exp == p2->exp) { // 指数相同，系数相加 |
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sum = p1->coef + p2->coef; |
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if (sum) { // 如果系数和不为0，则创建新节点 |
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if (!result) { |
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result = tail = CreateNode(sum, p1->exp); |
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} else { |
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tail->next = CreateNode(sum, p1->exp); |
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tail = tail->next; |
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} |
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} |
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p1 = p1->next; |
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p2 = p2->next; |
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} else if (p1->exp > p2->exp) { // p1的指数大于p2的指数，将p1的节点加入结果链表 |
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if (!result) { |
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result = tail = CreateNode(p1->coef, p1->exp); |
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} else { |
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tail->next = CreateNode(p1->coef, p1->exp); |
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tail = tail->next; |
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} |
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p1 = p1->next; |
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} else { // p1的指数小于p2的指数，将p2的节点加入结果链表 |
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if (!result) { |
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result = tail = CreateNode(p2->coef, p2->exp); |
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} else { |
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tail->next = CreateNode(p2->coef, p2->exp); |
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tail = tail->next; |
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} |
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p2 = p2->next; |
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} |
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} |
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// 将剩余节点（如果有）加入结果链表 |
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while (p1) { |
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if (!result) { |
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result = tail = CreateNode(p1->coef, p1->exp); |
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} else { |
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tail->next = CreateNode(p1->coef, p1->exp); |
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tail = tail->next; |
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} |
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p1 = p1->next; |
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} |
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while (p2) { |
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if (!result) { |
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result = tail = CreateNode(p2->coef, p2->exp); |
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} else { |
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tail->next = CreateNode(p2->coef, p2->exp); |
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tail = tail->next; |
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} |
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p2 = p2->next; |
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} |
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return result; |
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} |
打印多项式2
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// 打印多项式 |
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void PrintPoly(Polynomial poly) { |
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PolyNode *p = poly->next; |
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int isFirst = 1; // 标记是否为第一个项，以决定是否打印加号 |
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while (p) { |
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if (!isFirst && p->coef > 0) { |
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printf("+"); |
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} |
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printf("%dx^%d", p->coef, p->exp); |
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isFirst = 0; |
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p = p->next; |
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} |
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printf("\n"); |
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} |
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