6-14 Add Two Polynomials（20 point(s)）

6-14 Add Two Polynomials（20 point(s)）

Write a function to add two polynomials. Do not destroy the input. Use a linked list implementation with a dummy head node.Note: The zero polynomial is represented by an empty list with only the dummy head node.

Format of functions:

Polynomial Add( Polynomial a, Polynomial b );

where Polynomial is defined as the following:

typedef struct Node *PtrToNode;
struct Node {
    int Coefficient;
    int Exponent;
    PtrToNode Next;
};
typedef PtrToNode Polynomial;
/* Nodes are sorted in decreasing order of exponents.*/

The function Add is supposed to return a polynomial which is the sum of a and b.

Sample program of judge:

#include <stdio.h>
#include <stdlib.h>
typedef struct Node *PtrToNode;
struct Node  {
    int Coefficient;
    int Exponent;
    PtrToNode Next;
};
typedef PtrToNode Polynomial;

Polynomial Read(); /* details omitted */
void Print( Polynomial p ); /* details omitted */
Polynomial Add( Polynomial a, Polynomial b );

int main()
{
    Polynomial a, b, s;
    a = Read();
    b = Read();
    s = Add(a, b);
    Print(s);
    return 0;
}

/* Your function will be put here */

Sample Input:

4
3 4 -5 2 6 1 -2 0
3
5 20 -7 4 3 1

Sample Output:

5 20 -4 4 -5 2 9 1 -2 0

code：
Polynomial Add( Polynomial a, Polynomial b ){
  Polynomial c = (Polynomial)malloc(sizeof(struct Node));
  c->Next = NULL;//创建新链表，用来表示答案
  Polynomial tail = c;//答案链表的尾指针
  Polynomial pa,pb;
  pa = a->Next;
  pb = b->Next;//分别指向a和b的第一个有效节点
  while(pa!=NULL&&pb!=NULL){//a，b都不为空的时候循环
    if(pa->Exponent > pb->Exponent){//第一种，如果a的指数大于b直接添加a
      Polynomial newnode = (Polynomial)malloc(sizeof(struct Node));//创建新节点
      newnode->Coefficient = pa->Coefficient;
      newnode->Exponent = pa->Exponent;
      newnode->Next = NULL;
      tail->Next = newnode;
      tail = newnode;//尾指针移动到最后一个
      pa = pa->Next;//a移动到下一个节点
    }
    else if(pa->Exponent < pb->Exponent){
      Polynomial newnode = (Polynomial)malloc(sizeof(struct Node));//创建新节点
      newnode->Coefficient = pb->Coefficient;
      newnode->Exponent = pb->Exponent;
      newnode->Next = NULL;
      tail->Next = newnode;
      tail = newnode;//尾指针移动到最后一个
      pb = pb->Next;//a移动到下一个节点
    }
    else{//指数相等的时候
      if((pa->Coefficient + pb->Coefficient)!=0){//不为零才加到答案链表中去
        Polynomial newnode = (Polynomial)malloc(sizeof(struct Node));//创建新节点
        newnode->Coefficient = pa->Coefficient + pb->Coefficient;
        newnode->Exponent = pa->Exponent;
        newnode->Next = NULL;
        tail->Next = newnode;
        tail = newnode;//尾指针移动到最后一个
      }
      pa = pa->Next;
      pb = pb->Next;//ab同时往后移动
    }
  }
  //看看哪个还有剩下的，直接加到答案列表里
  if(pb==NULL){
    while(pa!=NULL){//依次加入队列
      Polynomial newnode = (Polynomial)malloc(sizeof(struct Node));//创建新节点
      newnode->Coefficient = pa->Coefficient;
      newnode->Exponent = pa->Exponent;
      newnode->Next = NULL;
      tail->Next = newnode;
      tail = newnode;//尾指针移动到最后一个
      pa = pa->Next;//a移动到下一个节点
    }
  }
  else{
    while(pb!=NULL){
      Polynomial newnode = (Polynomial)malloc(sizeof(struct Node));//创建新节点
      newnode->Coefficient = pb->Coefficient;
      newnode->Exponent = pb->Exponent;
      newnode->Next = NULL;
      tail->Next = newnode;
      tail = newnode;//尾指针移动到最后一个
      pb = pb->Next;//a移动到下一个节点
    }
  }
  return c;
}