数据结构-多项式

实现了多项式输入，输出，加法，乘法等4个基本操作。

采用的算法：

加法：归并

乘法：1。两个多项式项两两相乘保存在数组中，2。对数组进行排序 3。顺序遍历数组，合并同类项计算结果

/*  Author : Moyiii *  Mail:  [e-mail] *  多项式的ADT实现，实现了加法和乘法 *  因为怕出现一些莫名错误，所以加法乘法都写成了静态成员函数 *  仅作学习之用，当然如果 *  你想拿去用，随你好啦。 *  如果发现BUG，或你有更好的想法，欢迎反馈给我*/#include <iostream>using namespace std;class PolyNode{public:    PolyNode(int co = 0, int ex = -1):coef(co),exp(ex)    {        ;    }    int coef;    int exp;    PolyNode* next;};class Polynomal{public:    Polynomal();    ~Polynomal();    void input();    void output();    void clear();    static void addPoly(Polynomal &polya,Polynomal &polyb, Polynomal &polyc);    static void multiPoly(Polynomal &polya,Polynomal &polyb, Polynomal &polyc);private:    PolyNode * head;    PolyNode * tail;    int length;    void insNode(int coef, int exp);};Polynomal :: Polynomal(){    head = new PolyNode();    tail = head;    head->next = NULL;    length = 0;}//尾插法，跟链表的操作是一样的void Polynomal :: insNode(int coef, int exp){    if(coef != 0)    {        PolyNode *node = new PolyNode(coef, exp);        node->next = tail->next;        tail->next = node;        tail = node;        length++;    }    return;}//输入一个多项式void Polynomal :: input(){    cout << "请安升序顺序输入系数和指数,以-1 -1结束" << endl;    int e,c;    cin >> c >> e;    while(e > 0)    {        insNode(c,e);        cin >> c >> e;    }    cout << "您本次输入的多项式为:" << endl;    output();}//输出一个多项式，做了一些格式处理void Polynomal :: output(){    PolyNode *p = head->next;    bool first = false;    while(p != NULL)    {        if(!first)        {            first = true;        }        else        {            if(p->coef > 0)            {                cout << "+";            }        }        if(p->coef == 1)        {            ;        }        else if(p->coef == -1)        {            cout << "-";        }        else        {            cout << p->coef;        }        cout << "X";        if(p->exp != 1)        {            cout << "^" << p->exp;        }        p = p->next;    }    cout << endl;    return;}Polynomal :: ~Polynomal(){    while(head != NULL)    {        PolyNode *p = head;        head = head->next;        delete p;    }}//清除一个多项式void Polynomal :: clear(){    PolyNode *p = head->next;    while(p != NULL)    {        head->next = p->next;        delete p;        p = head->next;    }    length = 0;}/*有些算法书采用计算两个多项式最大项相乘的结果max，然后建立一个0~max数组，将  相乘的结果分别映射在这max个数组中，这样的数组开销非常大。特别是碰到一些高次幂  因此本设计将直接计算两两项相乘结果，保存在数组中，然后对数组进行排序，最后  合并相同项建表。*/void swapNode(int &a, int &b){    int temp = a;    a = b;    b = temp;    return;}void Polynomal :: multiPoly(Polynomal &polya,Polynomal &polyb, Polynomal &polyc){    int len = polya.length * polyb.length;    int *coefs = new int[len + 1];    int *exps = new int[len + 1];    int index = 0;    //获得所有项    for(PolyNode *ha = polya.head->next; ha != NULL; ha = ha->next)    {        for(PolyNode *hb = polyb.head->next; hb != NULL; hb = hb->next)        {            coefs[index] = ha->coef * hb->coef;            exps[index] = ha->exp + hb->exp;            index++;        }    }    //后续处理方便    exps[index] = -1;    //对项进行冒泡排序    for(int i = 1; i <= index - 1; ++i)    {        for(int j = 0; j < index - i; ++j)        {            if(exps[j] > exps[j+1])            {                swapNode(exps[j],exps[j+1]);                swapNode(coefs[j],coefs[j+1]);            }        }    }    //合并最终结果并建项    int cur = 0;    int count = coefs[cur];    Polynomal temp;    //在处理最后一个项时，会越界，此时前边增加的一个无用项就起到作用了    //因为系数是-1，所以不会与之前有任何冲突，而且不会被计算到结果里。    while(cur < index)    {        //相同指数，系数相加保存        if(exps[cur] == exps[cur+1])        {            cur++;            count = count + coefs[cur];        }        else        {            //指数不同，从新计算系数并向项中加入一个节点            temp.insNode(count,exps[cur]);            cur++;            count = coefs[cur];        }    }    //同加法，把结果传递给PC    polyc.clear();    PolyNode *p = temp.head;    while(p != NULL)    {        polyc.insNode(p->coef, p->exp);        p = p->next;    }    return;}//采用归并的算法思想，思路比较简单,看不懂的轻去看归并排序。void  Polynomal :: addPoly(Polynomal &polya,Polynomal &polyb, Polynomal &polyc){    Polynomal temp;    PolyNode *ha = polya.head->next;    PolyNode *hb = polyb.head->next;    while(ha != NULL && hb != NULL)    {        if(ha->exp < hb->exp)        {            temp.insNode(ha->coef, ha->exp);            ha = ha->next;        }        else if(hb->exp < ha->exp)        {            temp.insNode(hb->coef, hb->exp);            hb = hb->next;        }        else        {            temp.insNode(ha->coef + hb->coef, ha->exp);            ha = ha->next;            hb = hb->next;        }    }    while(ha != NULL)    {        temp.insNode(ha->coef, ha->exp);        ha = ha->next;    }    while(hb != NULL)    {        temp.insNode(hb->coef, hb->exp);        hb = hb->next;    }    polyc.clear();    PolyNode *p = temp.head;    while(p != NULL)    {        polyc.insNode(p->coef, p->exp);        p = p->next;    }    return;}int main(){    Polynomal pa,pb,pc,pd;    pa.input();    pb.input();    Polynomal :: addPoly(pa, pb, pc);    pc.output();    Polynomal :: multiPoly(pa, pb, pd);    pd.output();    return 0;}