02-线性结构2 一元多项式的乘法与加法运算

  1 #include<cstdio> 
  2 #include<cstdlib>
  3 
  4 typedef struct polynode *ptrtopolynode;
  5 typedef ptrtopolynode position;
  6 struct polynode {
  7     int c, e;
  8     position next;
  9 };
 10 typedef ptrtopolynode list;
 11 
 12 //多项式读入函数 
 13 list readpoly(){
 14     int n, c, e;
 15     scanf("%d", &n);
 16     list p = (list)malloc(sizeof(struct polynode));    
 17     p->next = NULL; 
 18     position rear = p;   
 19     while(n--){
 20         list temp = (list)malloc(sizeof(struct polynode));   
 21         scanf("%d%d", &temp->c , &temp->e);   
 22         temp->next = NULL;                   
 23         rear->next = temp;            
 24         rear = temp;             
 25     }
 26     list t=p; p=p->next; free(t);
 27     return p;
 28 }
 29 
 30 //多项式输出函数 
 31 void print(list p){
 32     int flag=0; 
 33     if(p==NULL) printf("0 0");     //零多项式特殊处理
 34     else{
 35         while(p!=NULL){
 36             if(flag==0) flag=1;
 37             else printf(" ");
 38             if(p->c==0&&p->e==0) flag=2;
 39             else printf("%d %d", p->c, p->e);
 40             p = p->next;
 41         }
 42     }
 43     printf("\n");
 44 }
 45 
 46 //根据指数的大小确定temp插入的位置 
 47 void attach(list p, list temp1){
 48     position pre=p, rear=p->next;
 49     while(rear->e>temp1->e){         //rear在第一个不大于temp指数的位置，或者链表末尾跳出循环 
 50         pre = rear;
 51         if(rear->next==NULL){
 52             rear=NULL;
 53             break;
 54         }
 55         rear = rear->next;
 56     }
 57     if(rear==NULL){                  
 58         temp1->next = NULL;
 59         pre->next = temp1;
 60     }
 61     else if(rear->e==temp1->e){      //同类项合并 
 62         rear->c += temp1->c;
 63         if(rear->c==0){
 64             pre->next = rear->next;   
 65         }
 66     }
 67     else{
 68         temp1->next = rear;
 69         pre->next = temp1;
 70     }
 71 }
 72 
 73 //多项式乘法函数 
 74 list multiply( list p1, list p2){
 75     list mult = (list)malloc(sizeof(struct polynode)); 
 76     mult->next = NULL;
 77     if(p1==NULL || p2==NULL){         //p1，p2有一个或以上为空，乘积一定为零多项式 
 78         mult=NULL;
 79     }
 80     else{                               
 81         position rear1, rear2;          
 82         rear1=p1; rear2=p2;
 83         while(rear1) {                 
 84             while(rear2){              
 85                 list temp = (list)malloc(sizeof(struct polynode));  
 86                 temp->c = rear1->c*rear2->c;
 87                 temp->e = rear1->e+rear2->e;
 88                 if(temp->c==0) temp->e=0;
 89                 if(mult->next==NULL){        //第一个节点插入到头节点之后  
 90                     temp->next =NULL;          
 91                     mult->next = temp;
 92                 }
 93                 else attach(mult, temp);
 94                 rear2 = rear2->next;
 95             }
 96             rear2 = p2;
 97             rear1 = rear1->next; 
 98         }
 99         list t = mult; mult = mult->next; free(t);
100     }
101     return mult;
102 }
103 
104 //加法实现函数 
105 list polysum(list p1, list p2){
106     list sum = (list)malloc(sizeof(struct polynode));
107     //两多项式其中之一是零多项式，则和等于另一多项式 
108     if(p1==NULL) sum->next=p2;                 
109     else if(p2==NULL) sum->next=p1;
110     else{
111         //两多项式均不为零多项式，只需要把p2逐个插入到p1中去，attach函数中已处理好同类项合并 
112         sum->next = p1;
113         for(list rear=p2; rear; rear=rear->next){ 
114             list temp = (list)malloc(sizeof(struct polynode));
115             temp->c = rear->c; temp->e = rear->e; temp->next = NULL;    
116             attach(sum, temp);
117         }
118     }
119     list t=sum; sum = sum->next; free(t);
120     return sum;
121 }
122 
123 //程序框架 
124 int main( ){   
125     list p1, p2, mult, sum;
126     p1 = readpoly();
127     p2 = readpoly();
128     mult = multiply(p1, p2);
129     sum = polysum(p1, p2);
130     print(mult);
131     print(sum);
132     return 0;
133 }