程序实现高次幂一元多项式乘法

1.题目描述

给定两个高次幂一元多项式，求其乘积和和。

示例：

其乘积、和的结果分别为

则规定标准输入为每一个多项式的项数加系数和指数。输入对应的乘积、和的系数指数，并在乘积后回车

###输入样例：

4 3 4 -5 2 6 1 -2 0

3 5 20 -7 4 3 1

###输出样例

15 24 -25 22 30 21 -10 20 -21 8 35 6 -35 6 -33 5 14 4 -15 3 18 2 -6 1

5 20 -4 4 -5 2 9 1 -2 0

由于涉及已知数组的大小，动态数组解题的方法比较简单。为了训练链表的使用，顾本题采用链表的方法：

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解题：

1.P1用链表表示

2.P2用链表表示

//链表实现多项式加法和乘法#include    <stdio.h>#define     LIST_OK0#define     LIST_ERROR-1typedef struct polynomiallist{int factor;//系数int power;//幂struct polynomiallist* next;//下一节点}List;//初始化链表，第一个节点不用来存储数据int init_list(List** list){if( NULL!=*list ){printf("链表初始化失败！/n");return LIST_ERROR;}*list=(List*)malloc( sizeof(List) );if( NULL==*list ){printf("分配内存出错！/n");return LIST_ERROR;}(*list)->next=NULL;printf("链表初始化完毕！/n");return LIST_OK;}//向链表中输入节点int insert_node(List* list, List* node){if( NULL==list ){printf("链表还没有初始化，无法插入节点！/n");return LIST_ERROR;}while( NULL!=list->next ){list=list->next;}list->next=(List*)malloc(sizeof(List));if( NULL==list ){printf("分配内存出错！/n");return LIST_ERROR;}list=list->next;list->factor=node->factor;list->power=node->power;list->next=NULL;printf("插入节点成功！/n");return LIST_OK;}//从链表中删除节点int delete_node(List* list, List* node){List* tmp=NULL;if( NULL==list ){printf("链表还没有初始化，无法删除节点！/n");return LIST_ERROR;}while( NULL!=list->next ){if( (node->factor==list->next->factor) && (node->power==list->next->power) ){tmp=list->next;list->next=list->next->next;free(tmp);printf("删除节点成功！/n");return LIST_OK;}list=list->next;}printf("没有找到你要删除的节点！/n");return LIST_ERROR;}//删除链表int delete_list(List** list){List* tmp=NULL;while( NULL!=*list ){tmp=*list;*list=(*list)->next;free(tmp);}printf("删除链表成功！/n");return LIST_OK;}//求链表元素个数int list_cnt(List* list){int i=0;if( NULL==list ){return 0;}while( NULL!=list ){i++;list=list->next;}return i-1;//首个节点不存储数据}//链表排序，幂数相同的项，系数合并int sort_list(List* list){//标记元素是否排序int sorted=0;List* node;List*tmp;List* const head=list;if( NULL==list ){printf("链表没有初始化，无法排序！/n");return LIST_ERROR;}//如果链表中的元素个数小于2个，就不需要排序if( list_cnt(list)<2 ){return LIST_OK;}node=head->next;head->next=NULL;while( NULL!=node ){sorted=0;list=head;while( NULL!=list->next ){//如果是幂数相同，则合并系数if( node->power==list->next->power ){list->next->factor+=node->factor;node=node->next;sorted=1;break;}else if(node->power>list->next->power){tmp=node;node=node->next;tmp->next=list->next;list->next=tmp;sorted=1;break;}list=list->next;}//如果node的幂数最小，插入链表最后if( 0==sorted ){tmp=node;node=node->next;list->next=tmp;tmp->next=NULL;}}return LIST_OK;}//多项式加法运算，结果保存在dest链表中int add_poly(List* dest, List** src){List* head=dest;if( 0==list_cnt(dest) || 0==list_cnt(*src)){printf("无法进行多项式加法运算！/n");return LIST_ERROR;}while( NULL!=dest->next ){dest=dest->next;}dest->next=(*src)->next;//销毁*src的头节点，并置NULLfree(*src);*src=NULL;sort_list(head);return LIST_OK;}//多项式相乘运算，结果保存在dest链表中。int mul_poly(List** dest, List** src){List data;//构造新链表存储乘法运算结果List* pNew=NULL;List* head1=*dest;List* head2=*src;init_list(&pNew);if( 0==list_cnt(*dest) || 0==list_cnt(*src) ){printf("无法进行多项式的乘法运算！/n");return LIST_ERROR;}while( NULL!=(*dest)->next ){while( NULL!=(*src)->next ){data.factor=((*dest)->next->factor)*((*src)->next->factor);data.power=((*dest)->next->power)+((*src)->next->power);data.next=NULL;insert_node(pNew, &data);*src=(*src)->next;}*src=head2;*dest=(*dest)->next;}sort_list(pNew);delete_list(&head1);delete_list(&head2);*dest=pNew;return LIST_OK;}int display_poly(List* list){if( 0==list_cnt(list) ){printf("链表中没有元素，无法输出！/n");return LIST_ERROR;}if( 0!=list->next->power ){printf("%dX^%d", list->next->factor, list->next->power);}else{printf("%d", list->next->factor);}list=list->next;while( NULL!=list->next ){if( list->next->factor>0 ){if( 0==list->next->power ){printf("+%d", list->next->factor);}else{printf("+%dX^%d", list->next->factor, list->next->power);}}else if( list->next->factor<0 ){if( 0==list->next->power ){if( 0!=list->next->factor ){printf("%d", list->next->factor);}}else{printf("%dX^%d", list->next->factor, list->next->power);}}list=list->next;}//printf("/n");return LIST_OK;}int main(int argc, char *argv[]){int i;int n;List data;List* dest=NULL;List* src=NULL;init_list(&dest);init_list(&src);printf("多项式1有多少项：/n");scanf("%d",&n);printf("请分别输入多项式1的系数和幂数，中间用空格隔开：/n");for( i=0; i<n; i++){scanf("%d%d", &data.factor, &data.power);insert_node(dest, &data);}printf("多项式2有多少项：/n");scanf("%d",&n);printf("请分别输入多项式2的系数和幂数，中间用空格隔开：/n");for( i=0; i<n; i++){scanf("%d%d", &data.factor, &data.power); insert_node(src, &data);}printf("请输入你要进行什么类型的运算？1为加法，2为乘法：/n");scanf("%d",&n);switch ( n ){case 1 :printf("(");display_poly(dest);printf(")/n+/n(");display_poly(src);printf(")/n=/n");add_poly(dest, &src);display_poly(dest);printf("/n");break;case 2 :printf("(");display_poly(dest);printf(")/n*/n(");display_poly(src);printf(")/n=/n");mul_poly(&dest, &src);display_poly(dest);printf("/n");break;default :break;}delete_list(&dest);return 0;}