数据结构严蔚敏课本40页一元多项式运算源代码

于 2022-12-24 09:03:10 发布
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分类专栏： 数据结构严蔚敏课本源代码更新 文章标签： 数据结构 链表
版权声明：本文为博主原创文章，遵循 CC 4.0 BY-SA 版权协议，转载请附上原文出处链接和本声明。
本文链接：https://blog.youkuaiyun.com/mute_sparkle/article/details/128425877
该代码实现了多项式的一系列操作，包括初始化、销毁、遍历、比较、插入、删除等。此外，还提供了多项式相加、相减和相乘的功能，所有操作均基于带有头结点的有序链表表示的多项式。用户可以输入多项式的项数及系数和指数来创建多项式，然后进行算术运算。

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1.head.h

#include<stdio.h>
#include<stdlib.h>
#define TRUE  1
#define FALSE 0
#define OK    1
#define ERROR 0
#define INFEASIBLE -1
#define OVERFLOW -2
typedef int Status;

typedef struct{ //项的表示，多项式的项作为数据元素 
    float coef; //系数 
    int expn;   //指数 
} term,ElemType; //两个类型名，term用于本ADT，ElemType为LinkList的数据对象名

typedef struct LNode{
    ElemType data;
    struct LNode *next;
} * Link, *Position;

typedef struct{
    Link head, tail;
    int len;
} LinkList;

typedef LinkList polynomail;//用带有头结点的有序链表表示多项式 

Status MakeNode(Link &p, ElemType e); 

void FreeNode(Link &p);

Status InitList(LinkList &L);

Status ClearList(LinkList &L);

Status DestroyList(LinkList &L);

Status InsFirst(LinkList &L,Link h, Link s);

Status DelFirst(LinkList &L,Link h, Link &q);

Status Append(LinkList &L, Link s);

Status Remove(LinkList &L, Link &q);

Status SetCurElem(Link &p, ElemType e);

ElemType GetCurElem(Link p);

Status ListEmpty(LinkList L);

int ListLength(LinkList L);

Position GetHead(LinkList L); 

Position PriorPos(LinkList L, Link p);

Position NextPos(LinkList L, Link p);

int compare(ElemType a,ElemType b);

Status LocateElem(LinkList L,ElemType e,Position &q,Status (*compare)(ElemType,ElemType));

void visit(ElemType e);

Status ListTraverse(LinkList L,void(*visit)(ElemType));
//遍历链表中数据并输出 
void CreatPolyn(polynomail &P,int m);
//1 输入m项的系数和指数，建立表示一元多项式的有序链表p
void DestoryPolyn(polynomail &P);
//2 销毁一元多项式p
void PrintPolyn(polynomail P);
//3 打印输出一元多项式p中的项数 
int PolynLength(polynomail P);
//4 返回一元多项式p中的项数 
int cmp(term a,term b);
//5  比较指数值 
void AddPolyn(polynomail &Pa,polynomail &Pb);
//6  完成多项式相加运算，并销毁pb
void SubtractPolyn(polynomail &Pa,polynomail &Pb);
//7 完成多项式相减运算，并销毁pb
void OrderInsert(LinkList &L,ElemType e,int (compare)(ElemType,ElemType));
//按照有序判定函数compare的约定，将值为e的结点插入到有序链表L的适当位置上 
void MultiplyPolyn(polynomail &Pa,polynomail &Pb);
//8 完成多项式相乘运算，并销毁pb

2.head.cpp

#include "head.h"

Status MakeNode(Link &p, ElemType e)
{
    p = (LNode*)malloc(1 * sizeof(LNode));
    p->data.coef= e.coef;
    p->data.expn= e.expn;
    if(p)
        return OK;
    else
        return ERROR;
}

void FreeNode(Link &p)
{
    free(p);
    p = NULL;
}

Status InitList(LinkList &L)
{
    L.head = (LNode*)malloc(1 * sizeof(LNode));
    L.head->next = NULL;
    L.tail = L.head;
    L.len = 0;
    if(L.head){
        printf("初始化成功");
        return OK;
    }else
        return ERROR;
}

Status ClearList(LinkList &L)
{
    Link p = L.head->next;
    while(p){
        L.head->next = p->next;
        free(p);
        p = NULL;
        L.len--;
        p = L.head->next;
    }
    if(L.head->next==NULL){
        return OK;
    }else
        return ERROR;
}

Status DestroyList(LinkList &L)
{
    ClearList(L);
    free(L.head);
    L.head = NULL;
    L.tail = NULL;
    if(!L.head)
        return OK;
    else
        return ERROR;
}

Status InsFirst(LinkList &L,Link h, Link s)
{
    s->next = h->next;
    h->next = s;
    if(h==L.tail)
        L.tail = h->next;
    L.len++;
    return OK;
}

Status DelFirst(LinkList &L,Link h, Link &q)
{
    q = h->next;
    if(q){
        h->next = q->next;
        if(!h->next)
            L.tail = h;
        L.len--;
        return OK;
    }else
        return ERROR;
}

Status Append(LinkList &L, Link s)
{
    //向链表内插入数据，s以后的一个或若干个节点插入链表的尾部
    //并修改链表的tail指针
    int i = 1;
    L.tail->next = s;
    while(s->next){
        s = s->next;
        i++;
    }
    L.tail = s;
    L.len += i;
    return OK;
}

Status Remove(LinkList &L, Link &q)
{
    //删除链表尾节点元素，由q返回
    if(!L.head){
        printf("线性链表不存在");
        return ERROR;
	}
    q = L.head;
    while(q->next!=L.tail){
        q = q->next;
    }
    L.tail = q;
    q = q->next;
    L.tail->next = NULL;
    L.len--;
	free(q);
    q = NULL;
    return OK;
}

Status SetCurElem(Link &p, ElemType e)
{
    //修改当前指针p指向的元素的数据域的值为e
    p->data = e;
    return OK;
}

ElemType GetCurElem(Link p)
{
    return p->data;
}

Status ListEmpty(LinkList L)
{
    if(!L.head){
        printf("线性链表不存在");
        return ERROR;
    }
    if(L.head->next==NULL)
        return OK;
    else
        return ERROR;
}

int ListLength(LinkList L)
{
    if(!L.head){
        printf("线性链表不存在");
        return ERROR;
	}
	return L.len;
}

Position GetHead(LinkList L)
{
    if(!L.head){
        printf("线性链表不存在");
        return ERROR;
	}
	return L.head;
}

Position PriorPos(LinkList L, Link p)
{
    Link q = L.head;
    if(!L.head){
        printf("线性链表不存在");
        return ERROR;
	}
	if(p==L.head)
		return NULL;
	while(q->next!=p){
        q = q->next;
    }
	return q;
}

Position NextPos(LinkList L, Link p)
{
    if(!L.head){
        printf("线性链表不存在");
        return ERROR;
    }
	if(p==L.tail)
		return NULL;
    return p->next;
}

int compare(ElemType a,ElemType b)
{
	if(a.expn>b.expn) return 1;
	else if(a.expn<b.expn) return -1;
	else {
		if(a.coef>b.coef)  return 1;
		else if(a.coef<b.coef)  return -1;
		else return 0;
	}
}

Status LocateElem(LinkList L,ElemType e,Position &q,Status (*compare)(ElemType,ElemType))
{
    Link p = L.head, pp = p;
    p = p->next;
    while(p && (compare(p->data,e)<0)){
        pp = p;
        p = p->next;
    }
    if(!p||compare(p->data,e)>0){
        q = pp;
        return ERROR;
    }
    else{
        q = p;
        return OK;
    }
}

void visit(ElemType e)
{
    if (e.coef > 0 && e.coef != 1 && e.expn != 0)
    {
        if (e.expn > 0)
            printf("%fx^%d",e.coef,e.expn);
        else
            printf("%fx^(%d)",e.coef,e.expn);
    }
    else if (e.coef < 0 && e.expn != 0)
    {
        if (e.expn > 0)
            printf("(%f)x^%d",e.coef,e.expn);
        else
            printf("(%f)x^(%d)",e.coef,e.expn);
    }
    else if (e.coef == 1 && e.expn != 0)
    {
        if (e.expn > 0)
            printf("x^%d",e.expn);
        else
            printf("x^(%d)",e.expn);
    }
    else if (e.expn == 0 && e.coef != 0)
        printf("%f",e.coef);
    else 
        printf("");
}

Status ListTraverse(LinkList L,void(*visit)(ElemType))
{
    Link p = L.head->next;
    for (int i = 1; i <= L.len;i++)
    {
        visit(p->data);
        if(i!=L.len)
        	printf("+");
        p = p->next;
    }
    if(L.len == 0)
       printf("0");
    return OK;
}

void CreatPolyn(polynomail &P,int m)
{
    InitList(P);
    Link h = GetHead(P);
    ElemType e;
    Link q, s;
    e.coef = 0.0;
    e.expn = -1;
    SetCurElem(h, e);//设置头结点的数据元素 
    for (int i = 1; i <= m;i++){
    	printf("第%d项的系数:",i); 
    	scanf("%f",&e.coef);
        printf("第%d项的指数:",i); 
        scanf("%d",&e.expn);
        if(!LocateElem(P,e,q,cmp)){
            if(e.coef!=0)
                if(MakeNode(s,e))
                    InsFirst(P, q, s);
        }else{
            q->data.coef = q->data.coef + e.coef;
            if(q->data.coef==0)
                Remove(P, q);
        }
    }
    printf("线性链表初始化成功。\n"); 
}

void DestoryPolyn(polynomail &P)
{
    DestroyList(P);
    printf("线性链表已经销毁。"); 
}

void PrintPolyn(polynomail P)
{
    ListTraverse(P, visit);
}

int PolynLength(polynomail P)
{
    return ListLength(P);
}

int cmp(term a,term b)
{
    if (a.expn == b.expn)
        return 0;
    else if(a.expn> b.expn)
        return 1;
	else
	    return -1;
}

void AddPolyn(polynomail &Pa,polynomail &Pb)
{
    Link ha, hb, qa=NULL, qb=NULL;
    ElemType a, b;
    ha = GetHead(Pa); hb = GetHead(Pb);
    if (Pa.len != 0 && Pb.len != 0)
    {
        qa = NextPos(Pa, ha);
        qb = NextPos(Pb, hb);
        while (qa && qb)
        {
            a = GetCurElem(qa);
            b = GetCurElem(qb);
            float sum;
            switch (cmp(a, b))
            {
            case -1:
                ha = qa;
                qa = NextPos(Pa, ha);
                break;
            case 0:
                sum = a.coef + b.coef;
                if (sum != 0){
                    qa->data.coef = sum;
                    ha = qa;
                }
                else{
                    DelFirst(Pa ,ha, qa);
                    FreeNode(qa);
                }
                DelFirst(Pb ,hb, qb);
                qb = NextPos(Pb, hb);
                qa = NextPos(Pa, ha);
                break;
            case 1:
                DelFirst(Pb ,hb, qb);
                InsFirst(Pa ,ha, qb);
                qb = NextPos(Pb, hb);
                qa = NextPos(Pa, ha);
                break;
            }
        }
        if (!ListEmpty(Pb))
            Append(Pa, qb);
        FreeNode(hb);
    }
    if (Pa.len == 0){
        Pa = Pb;
    }
}

void SubtractPolyn(polynomail &Pa,polynomail &Pb)
{
    Link p;
    p = Pb.head;
    while (p->next)
    {
        p = p->next;
        p->data.coef *= -1;
    }
    AddPolyn(Pa, Pb);
}

void OrderInsert(LinkList &L,ElemType e,int (compare)(ElemType,ElemType))
{
    Link q, s;
    if(LocateElem(L,e,q,compare)){
        q->data.coef += e.coef;
        if (!q->data.coef){ //系数为0，删除多项式中当前节点
            s = PriorPos(L, q);
            if(!s)//q无前驱
                s = L.head;
            DelFirst(L, s, q);
            FreeNode(q);
        }
    }else{//生成并插入
        MakeNode(s, e);
        InsFirst(L, q, s);
    }
}

void MultiplyPolyn(polynomail &Pa,polynomail &Pb)
{
    Link qa = GetHead(Pa);
    Link qb = NULL;
    polynomail Pc;
    ElemType a, b, c;
    InitList(Pc);
    if (Pa.len != 0 && Pb.len != 0){
        qa = qa->next;
        while(qa){
            a = GetCurElem(qa);
            qb = GetHead(Pb);
            qb = qb->next;
            while(qb){
                b = GetCurElem(qb);
                c.coef = a.coef * b.coef;
                c.expn = a.expn + b.expn;
                OrderInsert(Pc, c, cmp);
                qb = qb->next;
            }
            qa = qa->next;
        }
        DestoryPolyn(Pb);
        ClearList(Pa);
        Pa.head = Pc.head;
        Pa.tail = Pc.tail;
        Pa.len = Pc.len;
    }
    else if(Pb.len==0){
        Pa = Pb;
    }
}

3.main.cpp

#include "head.h"

int main()
{
	polynomail A, B;
	printf("请输入第一个多项式的项数为："); 
    int length;
    scanf("%d",&length);
    CreatPolyn(A, length);
    printf("PA(x)的项数为: ");
    int lena= PolynLength(A);
    printf("%d",lena);
    printf("PA(x) = ");
    PrintPolyn(A);
    printf("\n");
    //DestoryPolyn(A);
    printf("请输入第二个多项式的项数为："); 
    scanf("%d",&length);
    CreatPolyn(B, length);
    printf("PB(x) = ");
    PrintPolyn(B);
    printf("\n");

    char m;
    printf("请输入运算符号:");
    getchar();
    scanf("%c",&m); 
    switch (m){
        case '+':
            AddPolyn(A, B);
            printf("PA(x)+PB(x) = ");
            ListTraverse(A, visit);
            printf("\n");
            break;
        case '-':
            SubtractPolyn(A, B);
            printf("PA(x)-PB(x) = ");
            ListTraverse(A, visit);
            printf("\n");
            break;
        case '*':
            MultiplyPolyn(A, B);
            printf("PA(x)*PB(x) = ");
            ListTraverse(A, visit);
            printf("\n");
            break;
        default:
            printf("请输入正确符号");
    }
    ElemType a,b;
	printf("请输入a的系数和指数：");
	scanf("%f %d",&a.coef,&a.expn);
	printf("请输入b的系数和指数：");
	scanf("%f %d",&b.coef,&b.expn);
	printf("%d 如果为1表示a>b,如果为-1表示a<b,如果为0表示a=b。",cmp(a,b));	 
	return 0;
}

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