一元多项式的表示及相加 【链表的应用】

#include <iostream>
#include <cstdio>
#include <stdlib.h>
using namespace std;

struct Node {
double coef;
int expn;
Node *next;
};

void CreatPolynomial(Node *&head, int n)        //生成带表头结点的单链表，除头结点外另生成n个结点
{
head = (Node *)malloc(sizeof(Node));
head->coef = 0;
head->expn = 0;
head->next = NULL;                           //初始化头结点
cout << "请输入各项系数及指数:"<< endl;
Node *p = head;
for(int i = 0; i < n; i++) {
p->next = (Node *)malloc(sizeof(Node));  //生成新结点，尾插入生成链表
p = p->next;
cin >> p->coef >> p->expn;
p->next = NULL;
}
}

void PrintPolynomial(Node *&head)
{
if(head->next == NULL)                            //结果是0时直接输出0
putchar('0');
else {
for(Node *p = head->next; p != NULL; p = p->next){
if(p != head->next && p->coef >0)        //当p非首项且指向的系数为正时才输出'+'
putchar('+');                        //之前只判定了p->coef >0

if(p->coef == 1){                       //系数为1或-1时特殊处理
if(p->expn == 0)
putchar('1');                   //判断条件不能写在一起：
}                                      //if(p->coef == 1 && p->expn == 0) putchar('1');
else if(p->coef == -1)
putchar('-');
else
cout << p->coef;

switch(p->expn){                        //指数为0或1时特殊处理

case 0:
break;

case 1:
putchar('x');
break;

default:
p->expn < 0 ? printf("x^(%d)", p->expn) : printf("x^%d", p->expn);  //  指数小于0时打括号
break;
}
}
}
cout << endl;
}

void Free(Node *&head)
{
Node *q = NULL;
for(Node *p = head; p != NULL; p = q){
q = p->next;
free(p);
}
}

char cmp(int a, int b)
{
if(a > b)
return '>';
if(a < b)
return '<';
return '=';
}

void AddPolynomial(Node *&pA, Node *&pB)        //传进两个链表的头指针
{
Node *ha = pA;
Node *hb = pB;
Node *qa = ha->next;                     //ha, hb分别跟在qa, qb的后一位置
Node *qb = hb->next;                     //qa, qb分别指向Pa, Pb中当前比较元素
while(qa && qb)
{
double sum = 0;
int a = qa->expn;
int b = qb->expn;
switch( cmp(a, b) ){

case '<':
ha = qa;
qa = qa->next;                       //非ha = ha->next;
break;

case '=':
sum = qa->coef + qb->coef;
if(sum != 0.0) {
qa->coef = sum;
ha = qa;
}
else {
if(ha->next != qa)
cout << "Error: ha->next != qa" << endl;
ha->next = ha->next->next;     //删除和为0的结点，ha不变，还在qa后一位置
free(qa);
}
if(hb->next != qb)
cout << "Error: hb->next != qb" << endl;
hb->next = hb->next->next;
free(qb);
qb = hb->next;
qa = ha->next;
break;

case '>':
hb->next = hb->next->next;         //删除qb指向的结点
qb->next = ha->next;              //将qb插入ha后qa前
ha->next = qb;

qb = hb->next;                       //not qb = ha->next
ha = ha->next;
break;

default:
cout << "Error!" << endl;
break;
}
}
if(qb)
ha->next = qb;
free(hb);
}

int main()
{                                             //freopen("cin.txt", "r", stdin);
Node *A = NULL;
Node *B = NULL;
int lenA;
int lenB;
while(cout << "请输入A的项数：" << endl, cin >> lenA) {
CreatPolynomial(A, lenA);                   //生成A链表
cout << "请输入B的项数：" << endl;         //生成B链表
cin >> lenB;
CreatPolynomial(B, lenB);

cout << " A = ";                          //输出A链表
PrintPolynomial(A);
cout << " B = ";                          //输出B链表
PrintPolynomial(B);

AddPolynomial(A, B);                        //A = A + B
cout << "A+B= ";
PrintPolynomial(A);                         //输出和
cout << endl;

Free(A);                                    //务必释放结点
}
return 0;
}