242 lines
5.6 KiB
C++
242 lines
5.6 KiB
C++
// 2-4-PolyAdd-稀疏多项式求和
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// WARNING: /sdl is disabled to pass the compilation process.
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#include<iostream>//cout,cin
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using namespace std;
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struct PolyNode // 多项式结点
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{
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float coef; // 系数
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int exp; // 指数
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PolyNode* next; // 指向下一项结点
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};
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void InitPoly(PolyNode*& L)
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{ //创建一空多项式
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L = new PolyNode;
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L->next = NULL;
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}
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bool CreatePoly(PolyNode*& L, int n) // 尾插法创建n项多项式
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{
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int i;
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PolyNode* p, * s;
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p = L;
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for (i = 1; i <= n; i++) // 按幂升序依次输入多项式各项系数与幂指数
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{
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s = new PolyNode;
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if (!s)
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return false;
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cout << "输入第" << i << "项系数和幂指数：";
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cin >> s->coef >> s->exp;
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s->next = p->next;
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p->next = s;
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p = s;
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}
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return true;
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}
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//显示多顶式
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void DispPoly(PolyNode* L) // 通过遍历结点，输出多项式
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{
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PolyNode* p;
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if (!L) // 空表，返回
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{
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cout << "空表!";
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return;
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}
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p = L->next;
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while (p && p->next)
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{
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cout << p->coef << "x^" << p->exp << " + ";
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p = p->next;
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}
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cout << p->coef << "x^" << p->exp;
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cout << endl;
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}
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//【算法2.26】 求多项式LA=LA+LB
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void PolyAdd(PolyNode*& LA, PolyNode*& LB)
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{
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float sum;
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PolyNode* pa, * pb, * qa, * qb; // 1.工作指针初始化
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pa = LA;
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qa = pa->next;
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pb = LB;
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qb = pb->next;
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while (qa != NULL && qb != NULL) // 2. 两表均不空
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{
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if (qa->exp < qb->exp) // 2.1 LA的幂小
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{ // pa、qa后移
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pa = qa; qa = qa->next;
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}
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else if (qa->exp > qb->exp) //2.2 LA 幂大
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{
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pb->next = qb->next; // qb链接到pa之后
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qb->next = qa;
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pa->next = qb;
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pa = qb;
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qb = pb->next;
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}
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else // 2.3 LA与LB幂相同
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{
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sum = qa->coef + qb->coef; // 计算系数和
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if (sum != 0) // 2.3.1 系数和不为0
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{
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qa->coef = sum; // 2.3.1.1 qa->coef←sum
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pa = qa; qa = qa->next; // 2.3.1.2 pa，qa后移
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pb->next = qb->next;
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delete qb; // 2.3.1.3删除qb，
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qb = pb->next;
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}
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else // 2.3.2 系数和为0
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{
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pa->next = qa->next;
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delete qa; // 2.3.2.1 删除qa，
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qa = pa->next; // 2.3.2.2 qa为pa后继；
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pb->next = qb->next;
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delete qb; // 2.3.2.3 删除qb
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qb = pb->next; // 2.3.2.4 qb为pb的后继
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}
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}
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}//while
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if (qb != NULL) // 3. LA处理结束，LB未结束
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pa->next = qb; // 3.1 qb链到qa之后
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delete pb; // 3.2 删除lb头结点
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LB = NULL;
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}//Add
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void DestroyPoly(PolyNode*& L) // 释放链表所占空间
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{
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PolyNode* p;
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while (L) // 从头结点开始，依次释放结点
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{
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p = L;
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L = L->next;
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delete p;
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}
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L = NULL; // 头结点指向空
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}
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void SortPoly(PolyNode*& L) // 将多项式按幂升序排序
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{
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PolyNode* p1, * p2, * q, * r; // 采用插入排序算法
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p1 = L; p2 = p1->next; // p1是p2的前驱
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if (p2 == NULL || p2->next == NULL) // 空表或只有1项的多项式，不需要排序
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{
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cout << "不需要排序!" << endl;
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return;
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}
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r = L->next; // 有序表表尾
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q = r->next; // q为当前处理项，有序表的后一项
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while (q) // 未处理完
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{ // 从首元结点开始查找插入点
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p1 = L; p2 = p1->next;
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while (q->exp > p2->exp && p2 != q) // 当前结点幂大，插入点后移
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{
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p1 = p2; p2 = p2->next;
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}
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if (p2 == q) // 当前项无需移动
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{
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r = q; // 有序表表尾顺移
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}
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else // q插入到p2前面
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{
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r->next = q->next; // 摘除q结点
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q->next = p1->next; // 在p1后插入结点q
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p1->next = q;
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}
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q = r->next; // 下一个需处理的项
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}
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return;
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}
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void dispmenu()
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{//显示主菜单
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cout << endl;
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cout << "*** 稀疏多项式求和 ***\n";
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cout << "1-创建多项式A\n";
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cout << "2-创建多项式B\n";
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cout << "3-多项式求和A=A+B\n";
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cout << "4-显示多项式\n";
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cout << "0-退出\n";
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}
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//主函数
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int main()
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{
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int m, n;
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char c;
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PolyNode* LA, * LB;
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system("cls"); // 执行系统命令cls，清屏
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int choice;
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do
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{
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dispmenu(); // 显示主菜单
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cout << "Enter choice(1~4,0 退出):";
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cin >> choice;
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switch (choice)
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{
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case 1: // 创建多项式A
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InitPoly(LA);
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cout << "请输入多项式 A 的项数： ";
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cin >> m;
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CreatePoly(LA, m);
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cout << "创建的多项式 A 为：" << endl;
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DispPoly(LA);
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SortPoly(LA);
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cout << "排序后多项式 A 为：" << endl;
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DispPoly(LA);
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break;
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case 2: // 创建多项式B
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InitPoly(LB);
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cout << "请输入多项式B的项数： ";
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cin >> n;
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CreatePoly(LB, n);
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cout << "创建的多项式B为：" << endl;
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DispPoly(LB);
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SortPoly(LB);
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cout << "排序后多项式 B 为：" << endl;
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DispPoly(LB);
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break;
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case 3: //多项式求和
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cout << "A = ";
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DispPoly(LA);
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cout << "B = ";
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DispPoly(LB);
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PolyAdd(LA, LB); // 求多项式 LA=LA+LB
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cout << "A + B = "; // 显示结果
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DispPoly(LA);
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cout << endl;
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break;
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case 4: // 显示多项式
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cout << "选择要显示的多项式 A 或 B：" << endl;
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cin >> c;
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if (c == 'A' || c == 'a')
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DispPoly(LA);
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else if (c == 'B' || c == 'b')
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DispPoly(LB);
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else
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cout << "选择错误！" << endl;
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break;
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case 5: //退出
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DestroyPoly(LA);
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DestroyPoly(LB);
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cout << "结束运行bye-bye!" << endl;
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break;
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default: //非法选择
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cout << "非法选择!\n";
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break;
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}
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} while (choice != 0);
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return 0;
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}//end of main function
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