02-线性结构2 一元多项式的乘法与加法运算

Posted 2020-10-27 biankun

　　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。

  1 #include<stdio.h>
  2 #include<stdlib.h>
  3 
  4 typedef struct PolyNode *Poly;
  5 struct PolyNode
  6 {
  7     int coef;
  8     int expon;
  9     Poly Next;
 10 };
 11 
 12 void Attach(int c, int e, Poly *pRear)
 13 {
 14     Poly tmp;
 15     tmp = (Poly)malloc(sizeof(struct PolyNode));
 16     tmp->coef = c;
 17     tmp->expon = e;
 18     tmp->Next = NULL;
 19     (*pRear)->Next = tmp;
 20     (*pRear) = tmp;
 21 }
 22 
 23 Poly PolyRead()
 24 {
 25     Poly P, Rear, tmp;
 26     P = (Poly)malloc(sizeof(struct PolyNode));
 27     P->Next = NULL;  //创建头节点完成
 28     Rear = P;
 29     int N, c, e, i;
 30     scanf("%d", &N);
 31     for (i = 0; i < N; i++){
 32         scanf("%d %d", &c, &e);
 33         Attach(c, e, &Rear);
 34     }
 35     tmp = P;
 36     P = P->Next;
 37     free(tmp);
 38     return P;
 39 }
 40 
 41 void PolyPrint(Poly P)
 42 {
 43     int flag = 0;
 44     if(!P){
 45         printf("0 0");
 46     }
 47     while(P){
 48         if (!flag)
 49             flag = 1;
 50         else
 51             printf(" ");
 52         printf("%d %d", P->coef, P->expon);
 53         P = P->Next;
 54     }
 55     printf("\n");
 56 }
 57 
 58 Poly PolyMult(Poly P1, Poly P2)
 59 {
 60     Poly p1, p2, Rear, tmp, P;
 61     int c, e;
 62     P = (Poly)malloc(sizeof(struct PolyNode));
 63     P->Next = NULL;
 64     Rear = P;
 65     p1 = P1;
 66     p2 = P2;
 67     if(!p1 || !p2)
 68         return NULL;
 69     while(p2){
 70         c = p1->coef * p2->coef;
 71         e = p1->expon + p2->expon;
 72         if(c != 0){
 73             Attach(c, e, &Rear);
 74             p2 = p2->Next;
 75         }
 76     }
 77     p1 = p1->Next;
 78     while(p1){
 79         p2 = P2;
 80         Rear = P;
 81         while(p2){
 82             c = p1->coef * p2->coef;
 83             e = p1->expon + p2->expon;
 84             if(c != 0){
 85 
 86             }
 87             while( Rear->Next && Rear->Next->expon > e ){
 88                 Rear = Rear->Next;
 89             }
 90             if ( Rear->Next && Rear->Next->expon == e ){
 91                 if ( Rear->Next->coef + c )
 92                     Rear->Next->coef += c;
 93                 else{
 94                     tmp = Rear->Next;
 95                     Rear->Next = tmp->Next;
 96                     free(tmp);
 97                 }
 98             }else{
 99                 tmp = (Poly)malloc(sizeof(struct PolyNode));
100                 tmp->expon = e;
101                 tmp->coef = c;
102                 tmp->Next = Rear->Next;
103                 Rear->Next = tmp;
104                 Rear = tmp;
105             }
106             p2 = p2->Next;
107         }
108         p1 = p1->Next;
109     }
110     tmp = P;
111     P = P->Next;
112     free(tmp);
113     return P;
114 }
115 
116 Poly PolyAdd(Poly P1, Poly P2)
117 {
118     Poly p1, p2, Rear, tmp, P;
119     int coefSum;
120     P = (Poly)malloc(sizeof(struct PolyNode));
121     P->Next = NULL;
122     tmp = P;
123     Rear = tmp;
124     p1 = P1;
125     p2 = P2;
126     while(p1 && p2){
127         if(p1->expon == p2->expon){
128             coefSum = p1->coef + p2->coef;
129             if(coefSum){
130                 Attach(p1->coef + p2->coef, p1->expon, &Rear);
131             }
132             p1 = p1->Next;
133             p2 = p2->Next;
134         }else if(p1->expon > p2->expon){
135             Attach(p1->coef, p1->expon, &Rear);
136             p1 = p1->Next;
137         }else if(p1->expon < p2->expon){
138             Attach(p2->coef, p2->expon, &Rear);
139             p2 = p2->Next;
140         }
141     }
142     if(p1){
143         Rear->Next = p1;
144     }else if(p2){
145         Rear->Next = p2;
146     }
147     tmp = P;
148     P = P->Next;
149     free(tmp);
150     return P;
151 }
152 
153 int main(int argc, char const *argv[])
154 {
155     Poly P1, P2, PMul, PAdd;
156     P1 = PolyRead();
157     P2 = PolyRead();
158     PMul = PolyMult(P1, P2);
159     PAdd = PolyAdd(P1, P2);
160     PolyPrint(PMul);
161     PolyPrint(PAdd);
162     return 0;
163 }

　　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。