多项式的和，积（优化版）

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/******************************************************************************************求多项式的和，积(改进版)*核心思想：输入的多项式先排序，再运算*多项式(p1,p2)求和算法： 1.多项式排序O(logMN);  *                        2.求和过程，简化成了计算p1∪p2 : O(max(M,N)); ***多项式(p1,p2)求积算法:  1.新建一个M*N项的单链表p3保存积: O(M*N);*                        2.排序p3:O(logMN);* 3.合并p3中的同类项*author；fangchang*time:   2016/04/03  22:13******************************************************************************************/#include<stdio.h>#include<stdlib.h>typedef struct polyNode {            //多项式的结构体int coef;                        //系数int exp;                         //指数struct polyNode * next;}*ppolyNode;typedef ppolyNode poly;poly createPoly();                                       //新建一个多项式  void sortPoly(poly head,poly tail);                      //排序多项式链表void uniquePoly(poly head);                              //有序多项式合并同类项void printPoly(poly head);                               //打印一个多项式void addPoly();                                          //计算2个多项式相加void multPoly();                                          //计算2个多项相乘int main () {printf("M+N:\n");addPoly();printf("M*N:\n");multPoly();fflush(stdin);getchar();return 1;}poly createPoly() {                                   //新建一个多项式 (单链表)int i,j;poly head = (poly)malloc(sizeof(struct polyNode));poly pre,cur;if(! head) {printf("createPoly malloc failed.\n");return NULL;}head->coef=0;head->exp=0;head->next=NULL;pre=head;printf("please input coef and exp ,input 0 end input:\n");while(scanf("%d%d",&i,&j) && i!=0) {                            //输入0 0 结束cur =  (poly)malloc(sizeof(struct polyNode));if(! cur) {printf("createPoly malloc failed.\n");return NULL;}cur->coef = i;cur->exp  = j;cur->next =NULL;pre->next = cur;pre = cur;}return head;}void printPoly(poly head) {                             //打印多项式(单链表)if(!head || ! head->next) {return ;}poly p = head->next;while(p) {printf("%d  %d\n",p->coef,p->exp);p=p->next;}} void sortPoly(poly head,poly tail) {                              //单链表排序(快排: log(MN))if ( head->next == tail || head->next->next == tail )          return;      poly mid = head->next;      poly p = head;      poly q = mid;  int pivot = mid->exp;      poly t = mid->next;            while ( t != tail )      {  if ( t->exp < pivot )              p = p->next = t;          else              q = q->next = t;          t = t->next;      }      p->next = mid;      q->next = tail;        sortPoly( head, mid );      sortPoly( mid, tail );  }void uniquePoly(poly head) {                          //有序多项式合并同类项if(!head  || !head->next || !head->next->next) {return ;}poly p0,p1,p2,p3;p0=head;p1=p0->next;p2=p1->next;while(p1 && p2) {if(p2->exp == p1->exp) {p1->coef+=p2->coef;p3=p2->next;p1->next=p3;free(p2);p2=p3;}p1=p2;p2=p2->next;}p0=head;                 p1=p0->next;while(p1) {if(0==p1->coef) {                     //删除系数为0的项p2=p1->next;p0->next=p2;free(p1);p1=p2;}else {p0=p1;p1=p1->next;}}}void addPoly() {printf("please input poly1:\n");poly poly1= createPoly();printf("please input poly2:\n");poly poly2= createPoly();poly p1,p2;int tmp;if(!poly1->next && poly2->next) {printPoly(poly2);return;}if(!poly2->next && poly1->next) {printPoly(poly1);return;}sortPoly(poly1,NULL);                   //p1,p2的指数(exp)均有序，计算p1+p2变成了计算p1∪p2sortPoly(poly2,NULL);p1=poly1->next;p2=poly2->next;while(p1 && p2) {                                            //计算p1∪p2if(p1->exp==p2->exp) {if(0!=p1->coef + p2->coef) {                          //合并同类型printf("%d   %d\n",(p1->coef + p2->coef),p1->exp); }p1=p1->next;p2=p2->next;}else if(p1->exp>p2->exp) {printf("%d   %d\n",p2->coef,p2->exp);p2=p2->next;}else {printf("%d   %d\n",p1->coef,p1->exp);p1=p1->next;}}while(p1) {printf("%d   %d\n",p1->coef,p1->exp);p1=p1->next;}while(p2) {printf("%d   %d\n",p2->coef,p2->exp);p2=p2->next;}}void multPoly() {printf("please input poly1:\n");poly poly1= createPoly();printf("please input poly2:\n");poly poly2= createPoly();poly p1,p2;poly poly3,pre,cur;int coef,exp;if(!poly1->next || !poly2->next) {printf("the result is 0.\n");return ;}poly3=(poly)malloc(sizeof(struct polyNode));if(!poly3) {return ;}poly3->coef=0;poly3->exp=0;poly3->next=NULL;pre= poly3;for(p1=poly1->next;p1;p1=p1->next) {                     //新建单链表保存M*Nfor(p2=poly2->next;p2;p2=p2->next) {coef=p1->coef * p2->coef ;exp = p1->exp + p2->exp ;cur = (poly)malloc(sizeof(struct polyNode));cur->coef =coef;cur ->exp = exp;cur->next = NULL;pre->next = cur;pre= cur;}}sortPoly(poly3,NULL);         //排序uniquePoly(poly3);       //去重，合并同类项printPoly(poly3);        //打印}
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