功能介绍：

将俩个一元多项式相加， 好了就这些。

图解：

1）.

2）.

3).

闵版代码

#include <stdio.h>
#include <malloc.h>

/**
 * Linked list of integers. The key is data. The key is sorted in non-descending order.
 */
typedef struct LinkNode{
	int cofficient;
	int exponent;
	struct LinkNode *next;
} *LinkList, *NodePtr;

/** 
 * Initialize the list with a header.
 * @return The pointer to the header.
 */
LinkList initLinkList(){
	LinkList tempHeader = (LinkList)malloc(sizeof(struct LinkNode));
	tempHeader->cofficient = 0;
	tempHeader->exponent = 0;
	tempHeader->next = NULL;
	return tempHeader;
}//Of initLinkList

/**
 * Print the list.
 * @param paraHeader The header of the list.
 */
void printList(LinkList paraHeader){
	NodePtr p = paraHeader->next;
	while(p != NULL) {
		printf("%d * 10^%d", p->cofficient, p->exponent);
		if(p->next != NULL){
			printf(" + ");
		}
		p = p->next;
	}//Of while
	printf("\r\n");
}//Of printList

/**
 * Print one node for testing.
 * @param paraPtr The pointer to the node.
 * @param paraChar The name of the node.
 */
void printNode(NodePtr paraPtr, char paraChar){
	if (paraPtr == NULL) {
		printf("NULL\n");
	} else {
		printf("The element of %c is (%d * 10^%d)\n", paraChar, paraPtr->cofficient, paraPtr->exponent);
	}//Of while
} //Of printNode

/**
 * Add an element to the tail.
 * @param paraCoefficient The coefficient of the new element.
 * @param parExponent The exponent of the new element.
 */
 
void appendElement(LinkList paraHeader, int paraCofficient, int paraExponent){
	NodePtr p, q;
	
	//Step 1.Construct a new node.
	q = (NodePtr)malloc(sizeof(struct LinkNode));
	q->cofficient = paraCofficient;
	q->exponent = paraExponent;
	q->next = NULL;
	
	//Step 2.Search to the tail.
	p = paraHeader;
	while (p->next != NULL) {
		p = p->next;
	} //Of while
	
	//Step 3.Now add/link.
	p->next = q; 
}//Of addpendElement.

/**
 * Polynomial addition.
 * @param paraList The first list.
 * @param paraList2 The second list. 
 */
void add(NodePtr paraList1, NodePtr paraList2){
	NodePtr p, q, r, s;
	//Step 1.Search to the position.
	p = paraList1->next;
	printNode(p, 'p');
	q = paraList2->next;
	printNode(q, 'q');
	r = paraList1; //Previous pointer for  inserting.
	printNode(r, 'r');
	s = paraList2; //s for free();
	free(s);
	
	//Step 2.add the two list.
	while ((p != NULL)  NULL)) {
		printf("p->exponent = %d q->exponent = %d\n", p->exponent, q->exponent);
		if (p->exponent < q->exponent) {
			//Link the current node of first list.
			printf("case 1\r\n");
			r = p;
			printNode(r, 'r');
			p = p->next;
			printNode(p, 'p');
		} else if (p->exponent > q->exponent) {
			//Link the current node of the second list.
			printf("case 2\r\n");
			r->next = q;
			r = q;
			printNode(r, 'r');
			//r->next = p;
			q = q->next;
			printNode(q, 'q');
		} else {
			printf("case 3\r\n");
			//Change the current node of the first list.
			p->cofficient = p->cofficient + q->cofficient;
			printf("The cofficient is: %d.\n", p->cofficient);
			if (p->cofficient == 0) {
				printf("case 3.1\r\n");
				s = p;
				p = p->next;
				printNode(p, 'p');
				free(s);
			} else {
				printf("case 3.2\r\n");
				r = p;
				printNode(r, 'r');
				p = p->next;
				printNode(p, 'p');
			} //Of if
			s = q;
			q = q->next;
			free(s);
		} //Of if
		printf("p = %ld q = %ld\n", p, q);
	}// Of while
	printf("End of while.\n");
	
	if (p == NULL) {
		r->next = q;
	} else {
		r->next = p;
	} //Of if
	printf("Addition ends.\r\n");
}//Of add.
/**
 * Unit test.
 */
void additionTest(){
	
	//Step 1. Initialize the first polynomial.
	LinkList tempList1 = initLinkList();
	appendElement(tempList1, 7, 0);
	appendElement(tempList1, 3, 1);
	appendElement(tempList1, 9, 8);
	appendElement(tempList1, 5, 17);
	printList(tempList1);
	
	//Step 2. Initialize the second polynomial.
	LinkList tempList2 = initLinkList();
	appendElement(tempList2, 8, 1);
	appendElement(tempList2, 22, 7);
	appendElement(tempList2, -9, 8);
	printList(tempList2);
	
	//Step 3. Add them to the first.
	add(tempList1, tempList2);
	printList(tempList1);
}//of additionTest

/**
 * The entrance.
 */
int main(){
	additionTest();
	printf("Finish.\r\n");
	return 0;
}

代码更改：

因为该相加算法，必须是按照指数从小到大排序的，那么在插入函数时应该自动排序。

另外可以增加加法函数的参数，来实现加法减法, 再把系数乘以（-1），但暂时没成功。

代码：

#include <stdio.h>
#include <malloc.h>

/**
 * Linked list of integers. The key is data. The key is sorted in non-descending order.
 */
typedef struct LinkNode{
	int cofficient;
	int exponent;
	struct LinkNode *next;
} *LinkList, *NodePtr;

/** 
 * Initialize the list with a header.
 * @return The pointer to the header.
 */
LinkList initLinkList(){
	LinkList tempHeader = (LinkList)malloc(sizeof(struct LinkNode));
	tempHeader->cofficient = 0;
	tempHeader->exponent = 0;
	tempHeader->next = NULL;
	return tempHeader;
}//Of initLinkList

/**
 * Print the list.
 * @param paraHeader The header of the list.
 */
void printList(LinkList paraHeader){
	NodePtr p = paraHeader->next;
	while(p != NULL) {
		printf("%d * 10^%d", p->cofficient, p->exponent);
		if(p->next != NULL){
			printf(" + ");
		}
		p = p->next;
	}//Of while
	printf("\r\n");
}//Of printList

/**
 * Print one node for testing.
 * @param paraPtr The pointer to the node.
 * @param paraChar The name of the node.
 */
void printNode(NodePtr paraPtr, char paraChar){
	if (paraPtr == NULL) {
		printf("NULL\n");
	} else {
		printf("The element of %c is (%d * 10^%d)\n", paraChar, paraPtr->cofficient, paraPtr->exponent);
	}//Of while
} //Of printNode

/**
 * Add an element to the tail.
 * @param paraCoefficient The coefficient of the new element.
 * @param parExponent The exponent of the new element.
 */
 
void appendElement(LinkList paraHeader, int paraCofficient, int paraExponent){
	NodePtr p, q;
	
	p = paraHeader;
	q = (NodePtr)malloc(sizeof(struct LinkNode));
	q->next = NULL;
	q->exponent = paraExponent;
	q->cofficient = paraCofficient;
	
	//第一步-判断是不是空 
	if (p->next == NULL){
		p->next = q;
	} else {
		while ((p->next->exponent < paraExponent)) {
			p = p->next;
			if(p->next == NULL){
				break;
			}
		}
		q->next = p->next;
		p->next = q;
	}
	//第二部-判断后插入 
}//Of addpendElement.

/**
 * Polynomial addition.
 * @param paraList The first list.
 * @param paraList2 The second list. 
 */
void add(NodePtr paraList1, char paraChar, NodePtr paraList2){
	
	NodePtr p, q, r, s;
	//Step 1.Search to the position.
	p = paraList1->next;
	printNode(p, 'p');
	q = paraList2->next;
	printNode(q, 'q');
	r = paraList1; //Previous pointer for  inserting.
	printNode(r, 'r');
	s = paraList2; //s for free();
	free(s);
	
	//Step 2.add the two list.
	while ((p != NULL)  NULL)) {
		printf("p->exponent = %d q->exponent = %d\n", p->exponent, q->exponent);
		if (p->exponent < q->exponent) {
			//Link the current node of first list.
			printf("case 1\r\n");
			r = p;
			printNode(r, 'r');
			p = p->next;
			printNode(p, 'p');
		} else if (p->exponent > q->exponent) {
			//Link the current node of the second list.
			printf("case 2\r\n");
			r->next = q;
			r = q;
			printNode(r, 'r');
			//r->next = p;
			q = q->next;
			printNode(q, 'q');
		} else {
			printf("case 3\r\n");
			//Change the current node of the first list.
			p->cofficient = p->cofficient + q->cofficient;
			printf("The cofficient is: %d.\n", p->cofficient);
			if (p->cofficient == 0) {
				printf("case 3.1\r\n");
				s = p;
				p = p->next;
				printNode(p, 'p');
				free(s);
			} else {
				printf("case 3.2\r\n");
				r = p;
				printNode(r, 'r');
				p = p->next;
				printNode(p, 'p');
			} //Of if
			s = q;
			q = q->next;
			free(s);
		} //Of if
		printf("p = %ld q = %ld\n", p, q);
	}// Of while
	printf("End of while.\n");
	
	if (p == NULL) {
		r->next = q;
	} else {
		r->next = p;
	} //Of if
	printf("Addition ends.\r\n");
}//Of add.
/**
 * Unit test.
 */
void additionTest(){
	printf("--- additionTest Test ----\n");
	//Step 1. Initialize the first polynomial.
	LinkList tempList1 = initLinkList();
	appendElement(tempList1, 3, 1);
	appendElement(tempList1, 7, 0);
	appendElement(tempList1, 5, 17);
	appendElement(tempList1, 9, 8);
	
	
	printList(tempList1);
	
	//Step 2. Initialize the second polynomial.
	LinkList tempList2 = initLinkList();
	appendElement(tempList2, -9, 8);
	appendElement(tempList2, 22, 7);
	appendElement(tempList2, 8, 1);
	printList(tempList2);
	
	//Step 3. Add them to the first.
	add(tempList1, '+', tempList2);
	printList(tempList1);
	
}//of additionTest


/**
 * The entrance.
 */
int main(){
	additionTest();

	printf("Finish.\r\n");
	return 0;
}