多項式結構運算 (C)

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// 20090508 知識 +
// http://tw.knowledge.yahoo.com/question/question?qid=1009050803066
// 發問者 :(BNG) http://tw.knowledge.yahoo.com/my/my?show=AF03436443
//===============================================================

程式是以不定參數的方式來建立多項式, 項次的參數型態需為 double, 為方便以後使用...
程式內除了多項式的相加外, 也提供了相減 與 各項係數乘上指定常數來進行轉換.

#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>

typedef struct stMultinomial
{
  struct  stMultinomial * Next;
  int     Length;
  double  Item[1];
}Multinomial;

Multinomial * g_First = NULL;
Multinomial * g_Last = NULL;

// 產生新的空白多項式
Multinomial * NewMultinomial(unsigned int number)
{
  unsigned int i;
  Multinomial * multinomial = (Multinomial *) malloc(sizeof(Multinomial)+sizeof(double)*(number-1));
  multinomial->Next = NULL;
  multinomial->Length = number;
  for(i=0; i<number; i++)
    multinomial->Item[i] = 0.;
  if (g_First==NULL) g_First = multinomial;
  if (g_Last!=NULL) g_Last->Next = multinomial;
  g_Last = multinomial;
  return multinomial;
}
// 建立多項式 : 第一個參數為含常數的數量, 之後參數需為 double 型態
Multinomial * CreateMultinomial(unsigned int number, ... )
{
  unsigned int i;
  Multinomial * multinomial = NewMultinomial(number);
  va_list argptr;
  va_start( argptr, number);
  for(i=0; i<number; i++)
    multinomial->Item[i]=va_arg(argptr, double);
  va_end( argptr);
  return multinomial;
}
// 多項式相加 A+B
Multinomial * MultinomialAdd(Multinomial *A, Multinomial *B)
{
  int i;
  int Max = (A->Length>B->Length)? A->Length: B->Length;
  Multinomial * multinomial = NewMultinomial(Max);
  for(i=0; i<Max; i++)
    multinomial->Item[i]= ((i<A->Length)? A->Item[i]: 0.) + ((i<B->Length)? B->Item[i]: 0.);
  return multinomial;
}
// 多項式相減 A-B
Multinomial * MultinomialSubtract(Multinomial *A, Multinomial *B)
{
  int i;
  int Max = (A->Length>B->Length)? A->Length: B->Length;
  Multinomial * multinomial = NewMultinomial(Max);
  for(i=0; i<Max; i++)
    multinomial->Item[i]= ((i<A->Length)? A->Item[i]: 0.) - ((i<B->Length)? B->Item[i]: 0.);
  return multinomial;
}
// 多項式換算  A = A x c
double MultinomialConversion(Multinomial *A, double c)
{
  int n = A->Length;
  while( --n>=0 )
  {
    if (A->Item[n]==0) continue;
    if (c==0.) c=1./A->Item[n];  // 若 c為0 則是要約化首項
    A->Item[n] *= c;
  }
  return (c!=0)? c: 1.;
}
// 顯示多項式
void PrintMultinomial(char *symbol, Multinomial *A)
{
  char format[][16] = { "+%d.%d", "%d.%d", "+%d.%d%s", "%d.%d%s", "+%d.%d%s^%d", "%d.%d%s^%d" }; 
  char format1[][16] = { "+%d", "%d", "+%d%s", "%d%s", "+%d%s^%d", "%d%s^%d" }; 
  char format2[][16] = { "+%s", "%s", "+%s^%d", "%s^%d" }; 

  int decimal, m, o=0;
  int n = A->Length;
  while(--n>=0)
  {
    if (A->Item[n]==0) continue;
    m = ((n>1)? 4: n*2);
    if (A->Item[n]<0 || o++==0) m++;
    if (n!=0 && A->Item[n]==1.)
         printf( format2[m-2], symbol, n);
    else if( decimal = (int)((A->Item[n]-(int)A->Item[n])*1000000.) )
    {
       while( decimal%10==0) decimal/=10;
       printf( format[m], (int)A->Item[n], decimal, symbol, n);
    }
    else printf( format1[m], (int)A->Item[n], symbol, n);
  }
}
// 清除程式中所配置的記憶體
void ClearAll()
{
   Multinomial * node = g_First;
   Multinomial * freeNode;
   for( ; (freeNode=node)!=NULL; free(freeNode))
      node=node->Next;
   g_First = g_Last = NULL;
}
//=========== 主程式
int main()
{
  //A(X)= 7x^5 +3x^2+8
  //B(X)= 5x^6+2x^5+9X^2+x+12
  //C(X) = 5X^6+9X^5+12X^2+X+20

  // 需注意下面設定多項式: 第一個參數為含常數的數量, 之後參數須為 double 型態
  Multinomial * A = CreateMultinomial( 6, 8., 0., 3., 0., 0., 7. );
  Multinomial * B = CreateMultinomial( 7, 12., 1., 9., 0., 0., 2., 5. );
  Multinomial * C = MultinomialAdd( A, B );

  printf( "\nA(x) = " );
  PrintMultinomial( "x", A );
  printf( "\nB(x) = " );
  PrintMultinomial( "x", B );
  printf( "\nC(x) = A(x)+B(x) = " );
  PrintMultinomial( "x", C );

  double d = MultinomialConversion( C, 0.);
  printf( "\n Conversion C(x)*%f = ", d);
  PrintMultinomial( "x", C );

  ClearAll();
  return 0;
}
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