# C算法与数据结构-线性表的应用,多项式求和---ShinePans

2014-05-09

*---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

```/*---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
#include
#include

typedef struct Node{
float A;   //系数
int m;     //指数
struct Node *next;

void Initialize(LNode *plist);
int Cmp(int a, int b);
void Append(LNode *pa, LNode *pb);
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);
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));

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
*/
{
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 (aA= p->A;
current->m = p->m;

p = p->next;
r->next = current;     //SEGIVE
current->next = NULL;
}

}

/**
*Operation: 判断多项式是否为空
*/
{
if (*plist == NULL)
return 1;
else
return 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);
else
printf("%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; 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;         //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; 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:
*/
{
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
*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;
}
```