数据结构练习题 2-1 Add Two Polynomials (20分)

2-1 Add Two Polynomials (20分)（求两个多项式的和）

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.*/  

coefficient——系数
exponent——指数

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

这是一波提示：

1. 传入的链表的头指针里不含数据，数据在下一个结点内开始存储
2. tmp需要在循环内每次分配一个新空间
3. 如果指数相等时，系数和为零，则不需要进行存储，直接跳过进行下一次循环
4. 一个链表为空后，若另一个链表还不为空，直接将不为空链表内数据顺序输出

AC代码：

Polynomial Add( Polynomial a, Polynomial b ){
    if(a == NULL) return b;if(b == NULL) return a;	//如果有多项式为空，直接返回另一个多项式a = a->Next;	//a是头指针，a->Next指实际存储的数据 b = b->Next;	//b是头指针，b->Next指实际存储的数据 Polynomial head, tmp, prior; //head作为返回时直接返回的头结点, prior指向tmp的前一个结点，起到连接每个tmp结点的作用 prior = (Polynomial)malloc(sizeof(Polynomial));head = prior;//将最初的prior的值赋给head while(a != NULL && b != NULL){
    		//有一个多项式结束就停止循环 tmp = (Polynomial)malloc(sizeof(Polynomial));if(a->Exponent == b->Exponent){
    tmp->Exponent = a->Exponent;tmp->Coefficient = a->Coefficient + b->Coefficient;a = a->Next;b = b->Next;if(tmp->Coefficient == 0){
    continue;	//系数和为0的结点存储没有意义，直接跳过进行下一次循环 } }else if(a->Exponent > b->Exponent){
    tmp->Exponent = a->Exponent;tmp->Coefficient = a->Coefficient;a = a->Next;}else{
    tmp->Exponent = b->Exponent;tmp->Coefficient = b->Coefficient;b = b->Next;}prior->Next = tmp;prior = tmp;}if(a) prior->Next = a;else prior->Next = b;return head;
}