C算法与数据结构-线性表的应用,多项式求和---ShinePans

/*---上机作业作业,二项式加法---*//*---By 潘尚 ---*//*---日期: 2014-5-8 . ---*//*---题目:---*///假设有两个稀疏多项式A和B,设计算法完成下列任务//1.输入并建立多项式A和B;//2.求两个多项式的和多项式C;//3.求两个多项式的积多项式D;//输出4个多项式A,B,C,D;#include <stdio.h>#include <stdlib.h>#include <string.h>typedef struct Node{float A;   //系数int m;     //指数struct Node *next;}LNode, *LinkList;   //链表类型,若采用嵌套结构体如何用->以指针的方式访问void Initialize(LNode *plist);LinkList PolyAdd(LNode *plist1, LNode *plist2);int Cmp(int a, int b);void Append(LNode *pa, LNode *pb);int ListIsEmpty(const LinkList *plist);void EmptyTheList(LNode *plist);void PrintList(LNode *plist);void PolySort(LNode *plist);int GetLength(LNode *plist);void PolyMerge(LNode *plist);float HornorEvaluate(LNode *plist, float x);LinkList PolyMultiply(LNode *plist1, LNode *plist2);int GetMaxExpn(LNode *plist);/***主函数*/int main(void){LNode *p1 = (LNode*)malloc(sizeof(LNode));LNode *p2 = (LNode*)malloc(sizeof(LNode));LNode *result1 = (LNode*)malloc(sizeof(LNode));LNode *result2 = (LNode*)malloc(sizeof(LNode));Initialize(p1);Initialize(p2);PolySort(p1);     //多项式排序PolySort(p2);printf("\np1 = ");PrintList(p1);printf("\np1(value) = %f", HornorEvaluate(p1, 2));printf("\np2 = ");PrintList(p2);printf("\np2(value) = %f", HornorEvaluate(p2, 2));result1 = PolyAdd(p1, p2);result2 = PolyMultiply(p1, p2);//printf("\n%d",GetLength(p1));//PolyMerge(p1);      //合并同类项//UnitePoly(p1);   //合并同类项//EmptyTheList(p1);printf("\np1 + p2 = ");PrintList(result1);printf("\np1 * p2 = ");PrintList(result2);getchar();getchar();return 0;}/***Operation: 初始化一个多项式*Precondition:*Postcondition:*/void Initialize(LNode *plist){int i, n;float c;int e;LNode *prev = NULL, *current = NULL;plist->next = NULL;prev = plist;printf("\nPlease input the length of the polynomial: ");scanf_s("%d", &n);plist->A = 0;plist->m = n; //链表长度printf("Please input the coefficient and the exponent of each term: \n");for (i = 1; i <= n; i++){current = (LNode*)malloc(sizeof(LNode));scanf_s("%2f%d", &c, &e);current->A = c;current->m = e;prev->next = current;prev = current;/*plist->next = current;plist = current;*/}current->next = NULL;PolySort(plist);}/***Operation: 将两个多项式相加*Precondition:*Postcondition:*Notes: 可以采用先将两多项式合并（拼接）后再合并同类项来实现相加*/LinkList PolyAdd(LNode *plist1, LNode *plist2){LNode *pa, *pb;LNode *result = (LNode*)malloc(sizeof(LNode));int a, b;result->next = NULL;LNode *r = result;pa = plist1->next;pb = plist2->next;while (pa && pb){LNode *current = (LNode*)malloc(sizeof(LNode));a = pa->A;b = pb->m;switch (Cmp(a, b)){case -1:current->A= pa->m;current->A = pa->m;pa = pa->next;break;case  0:current->A = pa->A + pb->A;current->m = pa->m;pa = pa->next;pb = pb->next;break;case  1:current->A = pb->A;current->m = pb->m;pb = pb->next;break;}r->next = current;r = r->next;  //结果多项式指针后移current->next = NULL;}if (!pa || !pb){if (!pa) Append(r, pb);if (!pb) Append(r, pa);}//free(current);return result;}/***比较两整数大小*/int Cmp(int a, int b){if (a>b) return 1;if (a<b) return -1;else return 0;}/***链接pb剩余节点到pa上*/void Append(LNode *pa, LNode *pb){LNode *r = pa;LNode *p = pb;while (p){LNode *current = (LNode*)malloc(sizeof(LNode));current->A= p->A;current->m = p->m;p = p->next;r->next = current;     //SEGIVEcurrent->next = NULL;}}/***Operation: 判断多项式是否为空*/int ListIsEmpty(const LinkList *plist){if (*plist == NULL)return 1;elsereturn 0;}/***Operation: 清空一个多项式链表*Precondition：plist指向一个多项式列表*Postcondition：该列表被清空并释放*/void EmptyTheList(LNode *plist){LNode *psave;while (plist != NULL){psave = plist->next;free(plist);plist = psave;}}/***Operation: 输出一个多项式链表*/void PrintList(LNode *plist){LNode *p = plist;p = p->next; //跳过头指针while (p != NULL){if (p->next != NULL)printf("%0.1f*x^%d + ", p->A, p->m);elseprintf("%0.1f*x^%d;", p->A, p->m);p = p->next;}printf("\n");}/***Operation: 将输入的无序多项式链表排序*Precondition:无序多项式链表*Postcondition:递增顺序的多项式链表*/void PolySort(LNode *plist){LNode *pa = plist->next, *pb = pa->next;LNode *temp = (LNode*)malloc(sizeof(LNode));int length = GetLength(plist);int i;for (i = 0; i<length; i++){while (pb){if (pa->m > pb->m){temp->A = pa->A; temp->m = pa->m;pa->A = pb->A; pa->m = pb->m;pb->A = temp->A; pb->m = temp->m;}pa = pa->next;pb = pa->next;}pa = plist->next;pb = pa->next;         //这两句用于将pa,pb重新指向头节点}}/***Operation: 将输入的多项式中的指数相同项合并（合并同类项）*Precondition:有序多项式链表*Postcondition:无同类项的有序多项式链表*/void PolyMerge(LNode *plist){LNode *prev, *current;int l = GetLength(plist);int i;prev = plist->next;current = prev->next;for (i = 0; i<l; i++){while (current){if (prev->m == current->m){prev->A += current->A;    // why " prev->coef += current->coef " is wrong?prev->next = current->next;free(current);current = prev->next;continue;   //! without this sentence ,the function will be wrong and report an problem}prev = prev->next;current = prev->next;}if (current){prev = plist->next;current = prev->next;}}}/* //合并同类项void UnitePoly(LNode *h)//合并同类项{LNode *p1,*p2,*q1,*q2,*temp;q1=h;p1=q1->next;while(p1!=NULL){p2=p1->next;q2=p1;while(p2!=NULL){if(p1->expn==p2->expn){p1->coef=p1->coef+p2->coef;if(p1->coef==0){temp=p2;q2->next=p2->next;free(temp);temp=p1;q1->next=p1->next;p1=q1;free(temp);break;}else{temp=p2;q2->next=p2->next;p2=p2->next;free(temp);}}else{q2=p2;p2=p2->next;}}q1=p1;p1=p1->next;}}*//***求链表长度*/int GetLength(LNode *plist){LNode *p = plist;int lenght = 0;p = p->next;  //跳过节点while (p){lenght++;p = p->next;}return lenght;//return lenght-1;   //若没跳过头结点则返回值减一}/***Operation: 求两多项式乘积*Precondition:*Postcondition:*/LinkList PolyMultiply(LNode *plist1, LNode *plist2){LNode *pa, *pb;LNode *result = (LNode*)malloc(sizeof(LNode));LNode *r = result;  // 不能少！否则result所指不是头指针pa = plist1->next; pb = plist2->next;while (pa){while (pb){LNode *current = (LNode*)malloc(sizeof(LNode));current->A= pa->m * pb->A;  //系数相乘current->m = pa->m + pb->m;  //指数相加r->next = current;current->next = NULL;r = r->next;pb = pb->next;}pa = pa->next;pb = plist2->next;  //pb重新指向头结点}PolyMerge(result);return result;}/***Operation: Computing the value of the polynomia*Precondition: Ordered Polynomial Linklist*Postcondition: The value of the polynomial*/float HornorEvaluate(LNode *plist, float x){//int max = GetMaxExpn(plist) + 10;int n = 0;int i;float result = 0;//float Poly[max];   //VC6 sidn't support VLAfloat Poly[20];LNode *p = plist->next;memset(Poly, 0, sizeof(Poly));while (p){if (p->m == n){Poly[n++] = p->A;p = p->next;}elsePoly[n++] = 0;}  //Transform linklist to array to store the polynomial/*for(i=0;i<n;i++)   //调试时输出中间变量方便调试{printf("[%d]:%0.2f ",i,Poly[i]);}printf("\n");*/result = Poly[n - 1];for (i = n - 1; i>0; i--)        //循环次数及下标关系千万不能错!{result = result*x + Poly[i - 1];//printf("[%d %0.2f] ",i,result);  //调试时输出中间变量方便调试}return result;}/***Operation:*Precondition:*Postcondition:*/int GetMaxExpn(LNode *plist){LNode *p = plist->next;int max = p->m;while (p){if (p->m > max)max = p->m;p = p->next;}return max;}