数据结构多项式相加和相乘

这是数据结构的实验~~
由于某些实验要上交，所以一部分的程序的代码改为英语注释了
这是求解多项式相加和相乘的算法实现。
采用线性表就可以实现了。
代码可能有点繁杂，因为线性表的实现也包括在里面了。
   
Experiment1_1.h ，算法的实现的头文件。
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/* Experiment1_1.h */ 
    
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -    
//  实验题1.1  问题描述：    
//  有两个指数递减的一元多项式，写一程序先求这两个多项式的和，再求它们的积。   
//    
//  提示 1 ： 
//  用带表头结点的单链表作为多项式的存储表示； 
//  要建立两个单链表； 
//  多项式相加就是要把一个单链表中的结点插入到另一个单链表中去，要注意插入、删除操作中指针的正确修改。  
//  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -    
    
#include <iostream> 
using namespace std; 
    
// - - - - base constant value - - - - -  
const int OK    = 1;         
const int FAIL  = 0;         
const int EQUAL = 1;    // equal to 
const int BIG   = 2;    // bigger than 
const int LESS  = 3;    // less than 
    
    
// - - - - data structure - - - - -  
    
// element of Polynomial 
typedef struct   
{ 
    float coef; 
    int   expn; 
}term, ElemType; 
    
// node of linklist 
typedef struct LinkList   
{ 
    term e; 
    struct LinkList* next; 
}LinkList, LNode, Polynomial; 
    
    
// - - - - - - base functions - - - - - -  
    
int  InitList     (LinkList*& L); 
int  SetCurElem   (LNode*& h, const ElemType e); 
int  MakeNode     (LNode*& s, const ElemType e); 
int  InsFirst     (LNode*& q, LNode*& s); 
int  compare      (const term a, const term b); 
int  LocateElem   (LinkList* L, const ElemType e, LNode*& q); 
void CreatPolyn   (Polynomial*& P, const int m); 
void DestroyPolyn (Polynomial*& P); 
void CopyPolyn    (Polynomial*& P, const Polynomial* copy); 
int  PrintPolyn   (const Polynomial* P); 
void AddPolyn     (Polynomial*& Pa, Polynomial*& Pb); 
void MutilplyPolyn(Polynomial*& Pa, Polynomial*& Pb); 
    
    
// add pa to pb and destroy pb 
void AddPolyn(Polynomial*& Pa, Polynomial*& Pb) 
{ 
    // aCur point to the current node of pa 
    // aPrior point to the prior node of aCur 
    // bCur point to the current node of pb 
    // tmp pointer used temporary  
    LNode* aCur; 
    LNode* aPrior; 
    LNode* bCur; 
    LNode* tmp; 
    
    // initialize the pointers 
    aPrior = Pa; 
    aCur = aPrior->next; 
    bCur = Pb->next; 
    
    // result save the result of the compare function 
    // forDelete point to the node to be deleted 
    int result; 
    LNode* forDelete; 
    
    // polynomial addition 
    while (aCur && bCur) 
    { 
        result = compare(aCur->e, bCur->e); 
        switch(result) 
        { 
        // add the b's coef to a 
        case EQUAL: 
            aCur->e.coef += bCur->e.coef; 
                
            forDelete = bCur; 
            bCur = bCur->next; 
            delete forDelete; 
    
            if (aCur->e.coef == 0.0) 
            { 
                forDelete = aCur; 
                aCur = aCur->next; 
                aPrior->next = aCur; 
                delete forDelete; 
            } 
            break; 
        // aCur point to the next node 
        case BIG: 
            aPrior = aPrior->next; 
            aCur = aPrior->next; 
            break; 
        // insert bCur to aCur's prior node 
        case LESS: 
            tmp = bCur; 
            bCur = bCur->next; 
            aPrior->next = tmp; 
            tmp->next = aCur; 
            aPrior = aPrior->next; 
            break; 
        default: 
            break; 
        } 
    } 
    // if aCur=NULL then add b's rest nodes to the rear of a 
    if (!aCur) 
    { 
        aPrior->next = bCur; 
    } 
    
    delete Pb; 
} 
    
// multiply b to a, and destroy b 
void MutilplyPolyn(Polynomial*& Pa, Polynomial*& Pb) 
{ 
    // Pa = A(x) = sum(ai * x ^ aei), i=1...m; 
    // Pb = B(x) = sum(bi * x ^ bei), i=1...n; 
    // Pa*Pb = sum(bi * A(x) * x^bei) = sum( sum((aj * bi) * x^(aej+bei)), j=1...m ), i=1...n; 
    
    // backupPa save the copy of Pa 
    // backupPa = A(x) = sum(ai * x ^ aei), i=1...m; 
    // tmp memorize the intermediate result 
    // tmp = sum((aj * bi) * x^(aej+bei)), j=1...m 
    Polynomial* backupPa; 
    Polynomial* tmp; 
    
    // aCur point to backupPa 
    LNode* aCur; 
    LNode* bCur; 
    LNode* tmpCur; 
        
    // copy pa to backupPa and tmp 
    CopyPolyn(backupPa, Pa); 
    CopyPolyn(tmp, Pa);  
    
    // preprocessing Pa:first destroy Pa then save the first result in Pa 
    bCur = Pb->next;  
    aCur = backupPa->next; 
    tmpCur = tmp->next; 
    while (aCur) 
    { 
        tmpCur->e.coef = bCur->e.coef * aCur->e.coef; 
        tmpCur->e.expn = bCur->e.expn + aCur->e.expn; 
        aCur = aCur->next; 
        tmpCur = tmpCur->next; 
    } 
    bCur = bCur->next; 
    DestroyPolyn(Pa); 
    CopyPolyn(Pa, tmp); 
    
    // multiply the two polynomial,add tmp to Pa when finish a intermediate result 
    while (bCur) 
    { 
        CopyPolyn(tmp, Pa); 
        aCur = backupPa->next; 
        tmpCur = tmp->next; 
        while (aCur) 
        { 
            tmpCur->e.coef = bCur->e.coef * aCur->e.coef; 
            tmpCur->e.expn = bCur->e.expn + aCur->e.expn; 
            aCur = aCur->next; 
            tmpCur = tmpCur->next; 
        } 
        AddPolyn(Pa, tmp); 
        bCur = bCur->next; 
    } 
    
    DestroyPolyn(Pb); 
} 
    
// initialize the linklist 
int InitList(LinkList*& L) 
{ 
    L = new LinkList; 
    if (!L) 
    { 
        return FAIL; 
    } 
    L->next = NULL; 
    return OK; 
} 
    
// set the node h to the value e 
int SetCurElem(LNode*& h, const ElemType e) 
{    
    if (!h) 
    { 
        return FAIL; 
    } 
    else 
    { 
        h->e.coef = e.coef; 
        h->e.expn = e.expn; 
        return OK; 
    } 
} 
    
// make a node using value e, use the pointer s to point to the node 
int MakeNode(LNode*& s, const ElemType e) 
{ 
    s = new LNode; 
    if (!s) 
    { 
        return FAIL; 
    } 
    else 
    { 
        s->e.coef = e.coef; 
        s->e.expn = e.expn; 
        s->next = NULL; 
    } 
    return OK; 
} 
    
// to insert the node s after node q 
int InsFirst(LNode*& q, LNode*& s) 
{ 
    if (q == NULL || s == NULL) 
    { 
        return FAIL; 
    } 
    else 
    { 
        s->next = q->next; 
        q->next = s; 
        return OK; 
    } 
} 
    
// compare two term 
int compare(const term a, const term b) 
{ 
    if (a.expn == b.expn) 
    { 
        return EQUAL; 
    } 
    else if (a.expn > b.expn) 
    { 
        return BIG; 
    } 
    else 
    { 
        return LESS; 
    } 
} 
    
// locate the value e, if successed, return OK and q point to the position; 
// else return FAIL and q point to the position which node first less than e 
int LocateElem(LinkList* L, const ElemType e, LNode*& q) 
{ 
    LinkList* h; 
    h = L->next; 
    q = L; 
    int result; 
    while (h) 
    { 
        result = compare(h->e, e); 
        if (result == EQUAL) 
        { 
            q = h; 
            return OK; 
        } 
        else if (result == LESS) 
        { 
            return FAIL; 
        } 
        else 
        { 
            h = h->next; 
            q = q->next; 
        } 
    } 
    return FAIL; 
} 
    
// create the polunomial with the input value 
void CreatPolyn(Polynomial*& P, const int m) 
{ 
     InitList(P); 
    
     term e; 
     e.coef = 0.0; 
     e.expn = -1; 
     SetCurElem(P, e); 
         
     int i; 
     LNode* q; 
     LNode* s; 
     for (i=1; i<=m; i++) 
     { 
         cout<<"/ - "; 
         cin>>e.coef>>e.expn; 
         if (e.coef == 0.0) 
         { 
             continue; 
         } 
         if (LocateElem(P, e, q) == FAIL) 
         { 
            if (MakeNode(s, e)) 
            { 
                InsFirst(q, s); 
            } 
         } 
     } 
} 
    
// destroy the polynomial 
void DestroyPolyn(Polynomial*& P) 
{ 
    if (P) 
    { 
        LNode* q; 
        LNode* s; 
        q = P; 
        while (q->next) 
        { 
            s = q; 
            q = q->next; 
            delete s; 
        } 
        delete q; 
    } 
} 
    
// print the polynomial 
int PrintPolyn(const Polynomial* P) 
{ 
    if (!P) 
    { 
        return FAIL; 
    } 
    LNode* s; 
    s = P->next; 
    if (s) 
    { 
        cout<<s->e.coef<<"*X^"<<s->e.expn; 
        s = s->next; 
    } 
    while (s) 
    { 
        cout<<" + "<<s->e.coef<<"*X^"<<s->e.expn; 
        s = s->next; 
    } 
    return OK; 
} 
    
// copy the polynomial 'copy' to the polynomial p 
void CopyPolyn(Polynomial*& P, const Polynomial* copy) 
{ 
    InitList(P); 
    
    term e; 
    e.coef = 0.0; 
    e.expn = -1; 
    SetCurElem(P, e); 
    
    LNode* q; 
    LNode* r; 
    LNode* s; 
    r = P; 
    s = copy->next; 
    while (s) 
    { 
        q = new LNode; 
        q->e.coef = s->e.coef; 
        q->e.expn = s->e.expn; 
        q->next = NULL; 
        r->next = q; 
        r = r->next; 
    
        s = s->next; 
    } 
} 
   
test.cpp，应用算法完成多项式的加法和乘法
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/* test.cpp */ 
    
#include "Experiment1_1.h" 
    
void main() 
{ 
    Polynomial* P1; 
    Polynomial* P2; 
    Polynomial* backupP1; 
    Polynomial* backupP2; 
    int m1; 
    int m2; 
    
    cout<<"/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /"<<endl; 
    cout<<"/ -            实验题1.1  求两多项式的和，积              - /"<<endl; 
    cout<<"/ -                                                       - /"<<endl; 
    cout<<"/ -    输入规则：系数 指数                                - /"<<endl; 
    cout<<"/ -    例：多项式：3 * x ^ 5，输入3 5                     - /"<<endl; 
    cout<<"/ -                                                       - /"<<endl; 
    cout<<"/ -    注：各项的指数不能相同，否则会忽略相同项           - /"<<endl; 
    cout<<"/ -    注：系数不能为0，否则会忽略该项                    - /"<<endl; 
    cout<<"/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - /"<<endl; 
        
    cout<<endl; 
    cout<<"/ - 输入多项式P1的项数："; 
    cin>>m1; 
    cout<<"/ - 输入多项式的数据："<<endl; 
    CreatPolyn(P1, m1); 
    cout<<"/ - P1 = "; 
    PrintPolyn(P1); 
    cout<<endl; 
    cout<<endl; 
    
    cout<<"/ - 输入多项式P2的项数："; 
    cin>>m2; 
    cout<<"/ - 输入多项式的数据："<<endl; 
    CreatPolyn(P2, m2); 
    cout<<"/ - P2 = "; 
    PrintPolyn(P2); 
    cout<<endl; 
    cout<<endl; 
        
    CopyPolyn(backupP1, P1); 
    CopyPolyn(backupP2, P2); 
    
    cout<<"/ - P1 + P2 = "; 
    AddPolyn(P1, P2); 
    PrintPolyn(P1); 
    cout<<endl; 
    cout<<endl; 
    DestroyPolyn(P1); 
    
    cout<<"/ - P1 * P2 = "; 
    MutilplyPolyn(backupP1, backupP2); 
    PrintPolyn(backupP1); 
    cout<<endl; 
    cout<<endl; 
    
    DestroyPolyn(backupP1);