02线性结构2 一元多项式的乘法与加法运算

　　这道题是课上例题，不过课上没有给出完整代码，在自己实现时还是遇到了一些细节问题。

#include<stdio.h>
#include<stdlib.h>

typedef struct PolyNode *Poly;
struct PolyNode
{
    int coef;
    int expon;
    Poly Next;
};

void Attach(int c, int e, Poly *pRear)
{
    Poly tmp;
    tmp = (Poly)malloc(sizeof(struct PolyNode));
    tmp->coef = c;
    tmp->expon = e;
    tmp->Next = NULL;
    (*pRear)->Next = tmp;
    (*pRear) = tmp;
}

Poly PolyRead()
{
    Poly P, Rear, tmp;
    P = (Poly)malloc(sizeof(struct PolyNode));
    P->Next = NULL;  //创建头节点完成
    Rear = P;
    int N, c, e, i;
    scanf("%d", &N);
    for (i = 0; i < N; i++){
        scanf("%d %d", &c, &e);
        Attach(c, e, &Rear);
    }
    tmp = P;
    P = P->Next;
    free(tmp);
    return P;
}

void PolyPrint(Poly P)
{
    int flag = 0;
    if(!P){
        printf("0 0");
    }
    while(P){
        if (!flag)
            flag = 1;
        else
            printf(" ");
        printf("%d %d", P->coef, P->expon);
        P = P->Next;
    }
    printf("\n");
}

Poly PolyMult(Poly P1, Poly P2)
{
    Poly p1, p2, Rear, tmp, P;
    int c, e;
    P = (Poly)malloc(sizeof(struct PolyNode));
    P->Next = NULL;
    Rear = P;
    p1 = P1;
    p2 = P2;
    if(!p1 || !p2)
        return NULL;
    while(p2){
        c = p1->coef * p2->coef;
        e = p1->expon + p2->expon;
        if(c != 0){
            Attach(c, e, &Rear);
            p2 = p2->Next;
        }
    }
    p1 = p1->Next;
    while(p1){
        p2 = P2;
        Rear = P;
        while(p2){
            c = p1->coef * p2->coef;
            e = p1->expon + p2->expon;
            if(c != 0){

            }
            while( Rear->Next && Rear->Next->expon > e ){
                Rear = Rear->Next;
            }
            if ( Rear->Next && Rear->Next->expon == e ){
                if ( Rear->Next->coef + c )
                    Rear->Next->coef += c;
                else{
                    tmp = Rear->Next;
                    Rear->Next = tmp->Next;
                    free(tmp);
                }
            }else{
                tmp = (Poly)malloc(sizeof(struct PolyNode));
                tmp->expon = e;
                tmp->coef = c;
                tmp->Next = Rear->Next;
                Rear->Next = tmp;
                Rear = tmp;
            }
            p2 = p2->Next;
        }
        p1 = p1->Next;
    }
    tmp = P;
    P = P->Next;
    free(tmp);
    return P;
}

Poly PolyAdd(Poly P1, Poly P2)
{
    Poly p1, p2, Rear, tmp, P;
    int coefSum;
    P = (Poly)malloc(sizeof(struct PolyNode));
    P->Next = NULL;
    tmp = P;
    Rear = tmp;
    p1 = P1;
    p2 = P2;
    while(p1 && p2){
        if(p1->expon == p2->expon){
            coefSum = p1->coef + p2->coef;
            if(coefSum){
                Attach(p1->coef + p2->coef, p1->expon, &Rear);
            }
            p1 = p1->Next;
            p2 = p2->Next;
        }else if(p1->expon > p2->expon){
            Attach(p1->coef, p1->expon, &Rear);
            p1 = p1->Next;
        }else if(p1->expon < p2->expon){
            Attach(p2->coef, p2->expon, &Rear);
            p2 = p2->Next;
        }
    }
    if(p1){
        Rear->Next = p1;
    }else if(p2){
        Rear->Next = p2;
    }
    tmp = P;
    P = P->Next;
    free(tmp);
    return P;
}

int main(int argc, char const *argv[])
{
    Poly P1, P2, PMul, PAdd;
    P1 = PolyRead();
    P2 = PolyRead();
    PMul = PolyMult(P1, P2);
    PAdd = PolyAdd(P1, P2);
    PolyPrint(PMul);
    PolyPrint(PAdd);
    return 0;
}

　　实现过程中的体会有：

　　第98行需注意这里有可能出现和NULL比较的情况，所以应该用else条件，具体说来比如新接入的e一直小于当前链表中每一个expon，Rear一直指向最后一个了，再看Rear->Next->expon显然不可。

　　//之前犯下的错误有:
　　// if( Rear->Next->expon < e )，运行时直接溢出
　　// if( Rear->Next && Rear->Next->expon < e )，得出结果不全

　　另外之后链接结果时不能直接用上面构造的Attach函数; 原因是Attach仅用于接在一个链表的最后（其定义中tmp->Next = NULL）而这里是在一个链表的中间位置插入，故应重新构造并接入一个结点。