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2024-03-04 23:45:56 +08:00
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Chapter2/2-4-PolyAdd/PolyAdd.cpp Normal file
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// 2-4-PolyAdd-稀疏多项式求和
// WARNING: /sdl is disabled to pass the compilation process.
#include<iostream>//cout,cin
using namespace std;
struct PolyNode // 多项式结点
{
float coef; // 系数
int exp; // 指数
PolyNode* next; // 指向下一项结点
};
void InitPoly(PolyNode*& L)
{ //创建一空多项式
L = new PolyNode;
L->next = NULL;
}
bool CreatePoly(PolyNode*& L, int n) // 尾插法创建n项多项式
{
int i;
PolyNode* p, * s;
p = L;
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
{
s = new PolyNode;
if (!s)
return false;
cout << "输入第" << i << "项系数和幂指数：";
cin >> s->coef >> s->exp;
s->next = p->next;
p->next = s;
p = s;
}
return true;
}
//显示多顶式
void DispPoly(PolyNode* L) // 通过遍历结点，输出多项式
{
PolyNode* p;
if (!L) // 空表，返回
{
cout << "空表!";
return;
}
p = L->next;
while (p && p->next)
{
cout << p->coef << "x^" << p->exp << " + ";
p = p->next;
}
cout << p->coef << "x^" << p->exp;
cout << endl;
}
//【算法2.26】 求多项式LA=LA+LB
void PolyAdd(PolyNode*& LA, PolyNode*& LB)
{
float sum;
PolyNode* pa, * pb, * qa, * qb; // 1.工作指针初始化
pa = LA;
qa = pa->next;
pb = LB;
qb = pb->next;
while (qa != NULL && qb != NULL) // 2. 两表均不空
{
if (qa->exp < qb->exp) // 2.1 LA的幂小
{ // pa、qa后移
pa = qa; qa = qa->next;
}
else if (qa->exp > qb->exp) //2.2 LA 幂大
{
pb->next = qb->next; // qb链接到pa之后
qb->next = qa;
pa->next = qb;
pa = qb;
qb = pb->next;
}
else // 2.3 LA与LB幂相同
{
sum = qa->coef + qb->coef; // 计算系数和
if (sum != 0) // 2.3.1 系数和不为0
{
qa->coef = sum; // 2.3.1.1 qa->coef←sum
pa = qa; qa = qa->next; // 2.3.1.2 pa，qa后移
pb->next = qb->next;
delete qb; // 2.3.1.3删除qb，
qb = pb->next;
}
else // 2.3.2 系数和为0
{
pa->next = qa->next;
delete qa; // 2.3.2.1 删除qa，
qa = pa->next; // 2.3.2.2 qa为pa后继；
pb->next = qb->next;
delete qb; // 2.3.2.3 删除qb
qb = pb->next; // 2.3.2.4 qb为pb的后继
}
}
}//while
if (qb != NULL) // 3. LA处理结束，LB未结束
pa->next = qb; // 3.1 qb链到qa之后
delete pb; // 3.2 删除lb头结点
LB = NULL;
}//Add
void DestroyPoly(PolyNode*& L) // 释放链表所占空间
{
PolyNode* p;
while (L) // 从头结点开始，依次释放结点
{
p = L;
L = L->next;
delete p;
}
L = NULL; // 头结点指向空
}
void SortPoly(PolyNode*& L) // 将多项式按幂升序排序
{
PolyNode* p1, * p2, * q, * r; // 采用插入排序算法
p1 = L; p2 = p1->next; // p1是p2的前驱
if (p2 == NULL || p2->next == NULL) // 空表或只有1项的多项式，不需要排序
{
cout << "不需要排序!" << endl;
return;
}
r = L->next; // 有序表表尾
q = r->next; // q为当前处理项，有序表的后一项
while (q) // 未处理完
{ // 从首元结点开始查找插入点
p1 = L; p2 = p1->next;
while (q->exp > p2->exp && p2 != q) // 当前结点幂大，插入点后移
{
p1 = p2; p2 = p2->next;
}
if (p2 == q) // 当前项无需移动
{
r = q; // 有序表表尾顺移
}
else // q插入到p2前面
{
r->next = q->next; // 摘除q结点
q->next = p1->next; // 在p1后插入结点q
p1->next = q;
}
q = r->next; // 下一个需处理的项
}
return;
}
void dispmenu()
{//显示主菜单
cout << endl;
cout << "*** 稀疏多项式求和 ***\n";
cout << "1-创建多项式A\n";
cout << "2-创建多项式B\n";
cout << "3-多项式求和A=A+B\n";
cout << "4-显示多项式\n";
cout << "0-退出\n";
}
//主函数
int main()
{
int m, n;
char c;
PolyNode* LA, * LB;
system("cls"); // 执行系统命令cls，清屏
int choice;
do
{
dispmenu(); // 显示主菜单
cout << "Enter choice(1~4,0 退出):";
cin >> choice;
switch (choice)
{
case 1: // 创建多项式A
InitPoly(LA);
cout << "请输入多项式 A 的项数： ";
cin >> m;
CreatePoly(LA, m);
cout << "创建的多项式 A 为：" << endl;
DispPoly(LA);
SortPoly(LA);
cout << "排序后多项式 A 为：" << endl;
DispPoly(LA);
break;
case 2: // 创建多项式B
InitPoly(LB);
cout << "请输入多项式B的项数： ";
cin >> n;
CreatePoly(LB, n);
cout << "创建的多项式B为：" << endl;
DispPoly(LB);
SortPoly(LB);
cout << "排序后多项式 B 为：" << endl;
DispPoly(LB);
break;
case 3: //多项式求和
cout << "A = ";
DispPoly(LA);
cout << "B = ";
DispPoly(LB);
PolyAdd(LA, LB); // 求多项式 LA=LA+LB
cout << "A + B = "; // 显示结果
DispPoly(LA);
cout << endl;
break;
case 4: // 显示多项式
cout << "选择要显示的多项式 A 或 B：" << endl;
cin >> c;
if (c == 'A' || c == 'a')
DispPoly(LA);
else if (c == 'B' || c == 'b')
DispPoly(LB);
else
cout << "选择错误！" << endl;
break;
case 5: //退出
DestroyPoly(LA);
DestroyPoly(LB);
cout << "结束运行bye-bye!" << endl;
break;
default: //非法选择
cout << "非法选择!\n";
break;
}
} while (choice != 0);
return 0;
}//end of main function