一元多项式相加

描述：

对于两个一元多项式，如果需要对他们进行多项式相加操作，常见的两种思路如下：(1)对于一个多项式，保存其最高项次数HighPowder，以及一个该多项式对应次数分别为0-HighPowder的各项的系数的数组()。(2)多项式中系数不为零的每一项，保存其系数与该项的次数。下面分别用这两种思路实现一元多项式加法操作。

思路一（数组实现）：

数据结构定义：

1 typedef struct Poly
2 {
3     int CoeffArray[11];
4     int HighPower;
5 } *Polynomial;

实现：

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3
 4 typedef struct Poly
 5 {
 6     int CoeffArray[11];
 7     int HighPower;
 8 } *Polynomial;
 9
10 void ZeroPolynomial(Polynomial Poly)
11 {
12     int i;
13     for(i = 0; i < 11; i++)
14     {
15         Poly->CoeffArray[i] = 0;
16     }
17     Poly->HighPower = 0;
18 }
19
20 void AddPolynomial(Polynomial Poly1,Polynomial Poly2, Polynomial PolySum)
21 {
22     int i;
23     ZeroPolynomial(PolySum);
24     PolySum->HighPower = Poly1->HighPower > Poly2->HighPower?
25         Poly1->HighPower:Poly2->HighPower;
26     for(i = PolySum->HighPower; i >= 0 ; i--)
27     {
28         PolySum->CoeffArray[i] = Poly1->CoeffArray[i] + Poly2->CoeffArray[i];
29     }
30 }
31
32 int main(void)
33 {
34     int i,j,k;
35     Polynomial P1,P2,Sum;
36     P1 = malloc(sizeof(struct Poly));
37     P2 = malloc(sizeof(struct Poly));
38     Sum = malloc(sizeof(struct Poly));
39     //初始化
40     ZeroPolynomial(P1);
41     ZeroPolynomial(P2);
42     P1->HighPower = 10;
43     for(i = 10; i >= 0; i--)
44     {
45         P1->CoeffArray[i] = i;
46     }
47
48     P2->HighPower = 8;
49     for(j = 8; j >=0; j--)
50     {
51         P2->CoeffArray[j] = j;
52     }
53     P2->CoeffArray[8] = 8;
54     AddPolynomial(P1,P2,Sum);
55
56     printf("The high power of the Polynomial is %d\n",Sum->HighPower);
57     for(k = 0; k <= 10; k++)
58     {
59         printf("The Coeff of power %d is %d\n",k,Sum->CoeffArray[k]);
60     }
61
62     return 0;
63 }

它适合大部分项都有的稠密多项式。

思路二（单链表实现）：

数据结构定义：

1 typedef struct PolyNode *PtrToNode;
2
3 //定义链表节点，也就是多项式中的某一项；
4 typedef struct PolyNode
5 {
6     int Coeff;
7     int Exponent;
8     PtrToNode Next;
9 } PolyNode;

实现：

  1 #include <stdio.h>
  2 #include <stdlib.h>
  3
  4 typedef struct PolyNode *PtrToNode;
  5
  6 //定义链表节点，也就是多项式中的某一项；
  7 typedef struct PolyNode
  8 {
  9     int Coeff;
 10     int Exponent;
 11     PtrToNode Next;
 12 } PolyNode;
 13
 14
 15 typedef PtrToNode Polynomial;
 16
 17 /************************************************************
 18 *多项式相加的函数:
 19 *P、Q为存储两个多项式各项的单链表(含头结点)
 20 *Sum为多项式相加结果存放的单链表
 21 *
 22 ************************************************************/
 23 void AddPolynomial(Polynomial P,Polynomial Q,Polynomial Sum)
 24 {
 25     Polynomial PIndex,QIndex,SumIndex;
 26     PIndex = P->Next;
 27     QIndex = Q->Next;
 28     SumIndex = Sum;
 29     while(!(PIndex == NULL && QIndex == NULL))
 30     {
 31         if(PIndex==NULL)
 32         {
 33             SumIndex->Next = QIndex;
 34             QIndex = QIndex->Next;
 35             SumIndex = SumIndex->Next;
 36         }
 37         else if(QIndex == NULL)
 38         {
 39             SumIndex->Next = PIndex;
 40             PIndex = PIndex->Next;
 41             SumIndex = SumIndex->Next;
 42         }
 43         else
 44         {
 45             if(PIndex->Exponent > QIndex->Exponent)
 46             {
 47                 SumIndex->Next = PIndex;
 48                 PIndex = PIndex->Next;
 49                 SumIndex = SumIndex->Next;
 50                 //continue在判断下面if条件时会有异常，类似Java
 51                 //的空引用异常
 52                 continue;
 53             }
 54             if(PIndex->Exponent == QIndex->Exponent)
 55             {
 56                 Polynomial PP = malloc(sizeof(struct PolyNode));
 57                 PP->Exponent = PIndex->Exponent;
 58                 PP->Coeff = PIndex->Coeff + QIndex->Coeff;
 59                 SumIndex->Next = PP;
 60                 PIndex = PIndex->Next;
 61                 QIndex = QIndex->Next;
 62                 SumIndex = SumIndex->Next;
 63                 continue;
 64             }
 65             if(PIndex->Exponent < QIndex->Exponent)
 66             {
 67                 SumIndex->Next = QIndex;
 68                 QIndex = QIndex->Next;
 69                 SumIndex = SumIndex->Next;
 70                 continue;
 71             }
 72         }
 73     }
 74     SumIndex->Next = NULL;
 75 }
 76
 77 /************************************************************
 78 *遍历单链表(含头结点)函数:
 79 *P：待遍历的链表
 80 *************************************************************/
 81 void TraversePolynomial(Polynomial P)
 82 {
 83     Polynomial Tmp = P->Next;
 84     while(Tmp != NULL)
 85     {
 86         printf("Coeff is %d and Exponent is %d\n",Tmp->Coeff,Tmp->Exponent);
 87         Tmp = Tmp->Next;
 88     }
 89 }
 90
 91
 92
 93 int main(void)
 94 {
 95     Polynomial Poly1,Poly2,Poly3,Poly11,Poly22;
 96     int i,j;
 97     Poly1 = malloc(sizeof(struct PolyNode));
 98     Poly2 = malloc(sizeof(struct PolyNode));
 99     Poly3 = malloc(sizeof(struct PolyNode));
100     Poly11 = Poly1;
101     Poly22 = Poly2;
102
103     //创建两个链表时，需要保证是按照指数递减的方式构造的
104     for(i = 5;i >= 1;i--)
105     {
106         Polynomial Tmp  = malloc(sizeof(struct PolyNode));
107         Tmp->Coeff = i;
108         Tmp->Exponent = i;
109         Poly11->Next = Tmp;
110         Poly11 = Poly11->Next;
111     }
112     Poly11->Next = NULL;
113     for(j = 11;j >= 3;j--)
114     {
115         Polynomial Tmp  = malloc(sizeof(struct PolyNode));
116         Tmp->Coeff = j;
117         Tmp->Exponent = j;
118         Poly22->Next = Tmp;
119         Poly22 = Poly22->Next;
120     }
121     Poly22->Next = NULL;
122     TraversePolynomial(Poly1);
123     printf("*****************************************\n");
124     TraversePolynomial(Poly2);
125     AddPolynomial(Poly1,Poly2,Poly3);
126     printf("*****************************************\n");
127     TraversePolynomial(Poly3);
128     return 0;
129 }

原文链接