/*---上機作業作業,二項式加法---*/
/*---By 潘尚 ---*/
/*---日期: 2014-5-8 . ---*/
/*---題目:---*/
//假設有兩個稀疏多項式A和B,設計算法完成下列任務
//1.輸入並建立多項式A和B;
//2.求兩個多項式的和多項式C;
//3.求兩個多項式的積多項式D;
//輸出4個多項式A,B,C,D;
#include
#include
#include
typedef struct Node{
float A; //系數
int m; //指數
struct Node *next;
}LNode, *LinkList; //鏈表類型,若采用嵌套結構體如何用->以指針的方式訪問
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);
/**
*主函數
*/
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); //多項式排序
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); //合並同類項
//UnitePoly(p1); //合並同類項
//EmptyTheList(p1);
printf("\np1 + p2 = ");
PrintList(result1);
printf("\np1 * p2 = ");
PrintList(result2);
getchar();
getchar();
return 0;
}
/**
*Operation: 初始化一個多項式
*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; //鏈表長度
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: 將兩個多項式相加
*Precondition:
*Postcondition:
*Notes: 可以采用先將兩多項式合並（拼接）後再合並同類項來實現相加
*/
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; //結果多項式指針後移
current->next = NULL;
}
if (!pa || !pb)
{
if (!pa) Append(r, pb);
if (!pb) Append(r, pa);
}
//free(current);
return result;
}
/**
*比較兩整數大小
*/
int Cmp(int a, int b)
{
if (a>b) return 1;
if (aA= p->A;
current->m = p->m;
p = p->next;
r->next = current; //SEGIVE
current->next = NULL;
}
}
/**
*Operation: 判斷多項式是否為空
*/
int ListIsEmpty(const LinkList *plist)
{
if (*plist == NULL)
return 1;
else
return 0;
}
/**
*Operation: 清空一個多項式鏈表
*Precondition：plist指向一個多項式列表
*Postcondition：該列表被清空並釋放
*/
void EmptyTheList(LNode *plist)
{
LNode *psave;
while (plist != NULL)
{
psave = plist->next;
free(plist);
plist = psave;
}
}
/**
*Operation: 輸出一個多項式鏈表
*/
void PrintList(LNode *plist)
{
LNode *p = plist;
p = p->next; //跳過頭指針
while (p != NULL)
{
if (p->next != NULL)
printf("%0.1f*x^%d + ", p->A, p->m);
else
printf("%0.1f*x^%d;", p->A, p->m);
p = p->next;
}
printf("\n");
}
/**
*Operation: 將輸入的無序多項式鏈表排序
*Precondition:無序多項式鏈表
*Postcondition:遞增順序的多項式鏈表
*/
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; im > 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; //這兩句用於將pa,pb重新指向頭節點
}
}
/**
*Operation: 將輸入的多項式中的指數相同項合並（合並同類項）
*Precondition:有序多項式鏈表
*Postcondition:無同類項的有序多項式鏈表
*/
void PolyMerge(LNode *plist)
{
LNode *prev, *current;
int l = GetLength(plist);
int i;
prev = plist->next;
current = prev->next;
for (i = 0; im == 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;
}
}
}
/* //合並同類項
void UnitePoly(LNode *h)//合並同類項
{
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;
}
}
*/
/**
*求鏈表長度
*/
int GetLength(LNode *plist)
{
LNode *p = plist;
int lenght = 0;
p = p->next; //跳過節點
while (p)
{
lenght++;
p = p->next;
}
return lenght;
//return lenght-1; //若沒跳過頭結點則返回值減一
}
/**
*Operation: 求兩多項式乘積
*Precondition:
*Postcondition:
*/
LinkList PolyMultiply(LNode *plist1, LNode *plist2)
{
LNode *pa, *pb;
LNode *result = (LNode*)malloc(sizeof(LNode));
LNode *r = result; // 不能少！否則result所指不是頭指針
pa = plist1->next; pb = plist2->next;
while (pa)
{
while (pb)
{
LNode *current = (LNode*)malloc(sizeof(LNode));
current->A= pa->m * pb->A; //系數相乘
current->m = pa->m + pb->m; //指數相加
r->next = current;
current->next = NULL;
r = r->next;
pb = pb->next;
}
pa = pa->next;
pb = plist2->next; //pb重新指向頭結點
}
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 VLA
float Poly[20];
LNode *p = plist->next;
memset(Poly, 0, sizeof(Poly));
while (p)
{
if (p->m == n)
{
Poly[n++] = p->A;
p = p->next;
}
else
Poly[n++] = 0;
} //Transform linklist to array to store the polynomial
/*for(i=0;i0; i--) //循環次數及下標關系千萬不能錯!
{
result = result*x + Poly[i - 1];
//printf("[%d %0.2f] ",i,result); //調試時輸出中間變量方便調試
}
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;
}
