实验目的:
掌握线性表的链式存储结构设计与基本操作的实现。
实验内容与要求:
⑴定义线性表的链式存储表示;
⑵基于所设计的存储结构实现线性表的基本操作;
⑶编写一个主程序对所实现的线性表进行测试;
⑷线性表的应用:①设线性表L1和L2分别代表集合A和B,试设计算法求A和B的并集C,并用线性表L3代表集合C(无重复元素);②设线性表L1和L2中的数据元素为整数,且均已按值非递减有序排列,试设计算法对L1和L2进行合并,用线性表L3保存合并结果(无重复元素),要求L3中的数据元素也按值非递减有序排列。
⑸设计一个一元多项式计算器,要求能够:①输入并建立多项式;②输出多项式;③执行两个多项式相加;④执行两个多项式相减;⑤(选做)执行两个多项式相乘。
#include
using namespace std;
class list {
private:
class node {
public:
float coef; //多项式系数
int expn; //多项式指数
node* next;
};
node* head; //头结点
public:
//初始化
list() {
head = new node;
head->coef = 0;
head->expn = 0;
}
//创建
void create(int n) {
node* p = head; node* q = NULL;
for (int i = 0; i < n; i++) {
q = new node;
cin >> q->coef >> q->expn;
q->next = NULL;
p->next = q;
p = q;
}
}
//取值,取第i个元素的系数和指数
void get(int i, float& e1, int& e2) {
node* p = head;
for (int j = 0; j < i; j++) {
p = p->next;
}
e1 = p->coef;
e2 = p->expn;
}
//插入,前插
void insert(int i, float e1, int e2) {
node* p = head; node* q = NULL;
for (int j = 0; j < i - 1; j++) {
p = p->next;
}
q = new node;
q->coef = e1; q->expn = e2;
q->next = p->next;
p->next = q;
}
//删除,删除第i个节点
void remove(int i) {
node* p = head;
for (int j = 0; j < i - 1; j++) {
p = p->next;
}
p->next = p->next->next;
}
//无序合并
void merge(list &L1, list &L2) {
node* ptr = L1.head->next;
node* p = this->head; node* q = NULL;
while (ptr != NULL) {
//去除重复元素
node* u = L2.head;
while (u->next != NULL) {
if (u->next->expn == ptr->expn && u->next->coef == ptr->coef) {
u->next = u->next->next;
}
else {
u = u->next;
}
}
q = new node;
q->coef = ptr->coef; q->expn = ptr->expn;
q->next = NULL;
p->next = q;
p = q;
ptr = ptr->next;
}
ptr = L2.head->next;
while (ptr != NULL) {
q = new node;
q->coef = ptr->coef; q->expn = ptr->expn;
q->next = NULL;
p->next = q;
p = q;
ptr = ptr->next;
}
}
//有序合并
void merge2(list &L1, list &L2) {
node* ha = L1.head->next; node* hb = L2.head->next;
node* hc = this->head; node* q = NULL;
//去除重复元素
while (ha != NULL) {
//去除重复元素
node* u = L2.head;
while (u->next != NULL) {
if (u->next->expn == ha->expn && u->next->coef == ha->coef) {
u->next = u->next->next;
}
else {
u = u->next;
}
}
ha = ha->next;
}
ha = L1.head->next;
//有序合并
while (ha != NULL && hb != NULL) {
if (ha->expn < hb->expn) {
q = new node;
q->expn = ha->expn; q->coef = ha->coef;
q->next = NULL;
hc->next = q;
hc = q;
ha = ha->next;
}
else if (ha->expn > hb->expn) {
q = new node;
q->expn = hb->expn; q->coef = hb->coef;
q->next = NULL;
hc->next = q;
hc = q;
hb = hb->next;
}
else {
if (ha->coef < hb->coef) {
q = new node;
q->expn = ha->expn; q->coef = ha->coef;
q->next = NULL;
hc->next = q;
hc = q;
ha = ha->next;
}
else {
q = new node;
q->expn = hb->expn; q->coef = hb->coef;
q->next = NULL;
hc->next = q;
hc = q;
hb = hb->next;
}
}
}
if (ha == NULL && hb != NULL) {
while (hb != NULL) {
q = new node;
q->expn = hb->expn; q->coef = hb->coef;
q->next = NULL;
hc->next = q;
hc = q;
hb = hb->next;
}
}
if (hb == NULL && ha != NULL) {
while (ha != NULL) {
q = new node;
q->expn = ha->expn; q->coef = ha->coef;
q->next = NULL;
hc->next = q;
hc = q;
ha = ha->next;
}
}
}
//两个多项式相加,结果集为Lc
void add(list La, list Lb) {
node* ha = La.head->next; node* hb = Lb.head->next;
node* hc = this->head; node* q = NULL;
while (ha != NULL && hb != NULL) {
if (ha->expn == hb->expn) {
q = new node;
q->expn = ha->expn; q->coef = ha->coef + hb->coef;
q->next = NULL;
hc->next = q;
hc = q;
ha = ha->next;
hb = hb->next;
}
else if (ha->expn < hb->expn) {
q = new node;
q->expn = ha->expn; q->coef = ha->coef;
q->next = NULL;
hc->next = q;
hc = q;
ha = ha->next;
}
else if(ha->expn > hb->expn){
q = new node;
q->expn = hb->expn; q->coef = hb->coef;
q->next = NULL;
hc->next = q;
hc = q;
hb = hb->next;
}
}
if (ha == NULL && hb != NULL) {
while (hb != NULL) {
q = new node;
q->expn = hb->expn; q->coef = hb->coef;
q->next = NULL;
hc->next = q;
hc = q;
hb = hb->next;
}
}
if (hb == NULL && ha != NULL) {
while (ha != NULL) {
q = new node;
q->expn = ha->expn; q->coef = ha->coef;
q->next = NULL;
hc->next = q;
hc = q;
ha = ha->next;
}
}
}
//两个多项式相乘,结果集为Lc
void multiply(list La, list Lb) {
node* hc = this->head;
node* q = NULL;
node* ha = La.head->next; node* hb = Lb.head->next;
//交叉相乘,列出所有项
while (ha != NULL) {
while (hb != NULL) {
q = new node;
q->coef = ha->coef * hb->coef;
q->expn = ha->expn + hb->expn;
q->next = NULL;
hc->next = q;
hc = q;
hb = hb->next;
}
hb = Lb.head->next;
ha = ha->next;
}
//合并同类项
node* p = this->head; node* p2 = NULL;
while (p->next != NULL) {
p2 = p->next;
while (p2->next != NULL) {
if (p->next->expn == p2->next->expn) {
p->next->coef = p->next->coef + p2->next->coef;
p2->next = p2->next->next;
}
else {
p2 = p2->next;
}
}
p = p->next;
}
}
//排序,将多项式按指数排序
void sort() {
node* p = NULL; node* p2 = head->next;
node* q = NULL;
//中转介质
float temp1; int temp2;
while (p2 != NULL) {
p = this->head->next;
q = p->next;
while (q != NULL) {
if (p->expn > q->expn) {
//交换指数
temp2 = p->expn;
p->expn = q->expn;
q->expn = temp2;
//交换系数
temp1 = p->coef;
p->coef = q->coef;
q->coef = temp1;
}
p = p->next;
q = q->next;
}
p2 = p2->next;
}
}
//遍历,以多项式形式输出
void print() {
//去除系数为0的项
node* a = head;
while (a->next != NULL) {
if (a->next->coef == 0) {
a->next = a->next->next;
}
else {
a = a->next;
}
}
a->next = 0;
//遍历输出
node *ptr = head->next;
cout << "F(x) = ";
if (ptr->expn == 0) {
cout << ptr->coef;
}
else if (ptr->coef == 1 || ptr->coef == -1) {
if (ptr->coef < 0)cout << "-";
cout << "X^" << ptr->expn;
}
else {
cout << ptr->coef << "X^" << ptr->expn;
}
cout << " ";
ptr = ptr->next;
while (ptr != NULL) {
if (ptr->expn == 0) {
if (ptr->coef > 0)cout << "+";
cout << ptr->coef;
}
else if (ptr->coef == 1 || ptr->coef == -1) {
if (ptr->coef > 0)cout << "+";
if (ptr->coef < 0)cout << "-";
cout << "X^" << ptr->expn;
}
else {
if (ptr->coef > 0)cout << "+";
cout << ptr->coef << "X^" << ptr->expn;
}
cout << " ";
ptr = ptr->next;
}
}
};
void show1() {
cout << "---链表创建多项式---" << endl;
cout << "---1.多项式的实现" << endl;
cout << "---2.多项式的无序合并" << endl;
cout << "---3.多项式的有序合并" << endl;
cout << "---4.多项式的相加和相乘" << endl;
cout << "---5.退出" << endl;
cout << endl;
}
void show2() {
cout << "---1.创建多项式;" << endl;
cout << "---2.取值;" << endl;
cout << "---3.插入;" << endl;
cout << "---4.删除;" << endl;
cout << "---5.遍历;" << endl;
cout << "---6.返回上一级;" << endl;
cout << endl;
}
int main() {
int m = 1; int n; char ch, ch2;
list L3;
while (1) {
//主界面
if (m == 1) {
system("cls");
show1();
cin >> n;
if (n == 1)m = 2;
if (n == 2)m = 4;
if (n == 3)m = 5;
if (n == 4)m = 3;
if (n == 5)break;
}
//多项式的实现
if (m == 2) {
system("cls ");
show2();
cin >> n;
int i; float e1; int e2;
if (n == 1) {
cout << "创建多项式项数:";
cin >> i;
cout << "依次输入每一项的系数和指数:";
L3.create(i);
cout << endl << "创建成功!";
}
if (n == 2) {
cout << "输入取值位置:";
cin >> i;
L3.get(i, e1, e2);
cout << endl << "第" << i << "项的系数为:" << e1 << ",指数为:" << e2;
}
if (n == 3) {
cout << "输入插入位置、插入项的系数和指数(前插):";
cin >> i >> e1 >> e2;
L3.insert(i, e1, e2);
cout << endl << "插入成功!";
}
if (n == 4) {
cout << "输入删除位置:";
cin >> i;
L3.remove(i);
cout << endl << "删除成功!";
}
if (n == 5) {
L3.print();
cout << endl << "遍历成功!";
}
if (n == 6)m = 1;
cout << endl << endl << "按下回车健执行下一步";
ch = cin.get();
ch2 = cin.get();
}
//多项式的相乘相加
if (m == 3) {
system("cls ");
show1();
list L, L1, L2; int i1, i2;
cout << "创建多项式一" << endl;
cout << "输入项数:";
cin >> i1;
cout << "依次输入每一项的系数和指数:";
L1.create(i1);
cout << endl;
L1.sort();
L1.print();
cout << endl << endl;
cout << "创建多项式二" << endl;
cout << "输入项数:";
cin >> i2;
cout << "依次输入每一项的系数和指数:";
L2.create(i2);
cout << endl;
L2.sort();
L2.print();
cout << endl << endl;
cout << "两个多项式相加的结果为:";
L.add(L1, L2);
L.sort();
L.print();
cout << endl << endl;
cout << "两个多项式相乘的结果为:";
L.multiply(L1, L2);
L.sort();
L.print();
cout << endl << endl << "按下回车健执行下一步";
m = 1;
ch = cin.get();
ch2 = cin.get();
}
//多项式无序合并
if (m == 4) {
system("cls ");
show1();
list L, L1, L2; int i1, i2;
cout << "创建多项式一" << endl;
cout << "输入项数:";
cin >> i1;
cout << "依次输入每一项的系数和指数:";
L1.create(i1);
cout << endl;
L1.print();
cout << endl << endl;
cout << "创建多项式二" << endl;
cout << "输入项数:";
cin >> i2;
cout << "依次输入每一项的系数和指数:";
L2.create(i2);
cout << endl;
L2.print();
cout << endl << endl;
cout << "两个多项式无序合并的结果为:";
L.merge(L1, L2);
L.print();
cout << endl << endl << "按下回车健执行下一步";
m = 1;
ch = cin.get();
ch2 = cin.get();
}
//多项式有序合并
if (m == 5) {
system("cls ");
show1();
list L, L1, L2; int i1, i2;
cout << "创建多项式一" << endl;
cout << "输入项数:";
cin >> i1;
cout << "依次输入每一项的系数和指数(按指数排好序):";
L1.create(i1);
cout << endl;
L1.sort();
L1.print();
cout << endl << endl;
cout << "创建多项式二" << endl;
cout << "输入项数:";
cin >> i2;
cout << "依次输入每一项的系数和指数(按指数排好序):";
L2.create(i2);
cout << endl;
L2.sort();
L2.print();
cout << endl << endl;
cout << "优先比较指数,其次比较系数" << endl;
cout << "两个多项式有序合并的结果为:";
L.merge2(L1, L2);
L.print();
cout << endl << endl << "按下回车健执行下一步";
m = 1;
ch = cin.get();
ch2 = cin.get();
}
}
}