單鏈表實現：一元多項式的乘法與加法運算

一元多項式的乘法與加法運算 

（PTA | 程序設計類實驗輔助教學平臺  https://pintia.cn/problem-sets/15/problems/710）

設計函數分別求兩個一元多項式的乘積與和。

輸入格式:

輸入分2行，每行分別先給出多項式非零項的個數，再以指數遞降方式輸入一個多項式非零項係數和指數（絕對值均爲不超過1000的整數）。數字間以空格分隔。

輸出格式:

輸出分2行，分別以指數遞降方式輸出乘積多項式以及和多項式非零項的係數和指數。數字間以空格分隔，但結尾不能有多餘空格。零多項式應輸出0 0。

輸入樣例:

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

輸出樣例:

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0 plain copy

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

typedef struct PolyNode* Polynomial;
struct PolyNode {
	int coef;   //係數 
	int expon; //指數 
	Polynomial next;   //指向下一個結點的指針 
};

void attach(int c, int e, Polynomial* pRear);
int compare(int num1, int num2);
Polynomial polyAdd(Polynomial p1, Polynomial p2);
Polynomial polymultiply(Polynomial p1, Polynomial p2,int num);//將p1的第一項與p2的所有項做乘法並返回

int main(void)
{
	Polynomial p1, p2, p1_rear, p2_rear, p_temp;
	p1 = (Polynomial)malloc(sizeof(struct PolyNode));	//初始化頭結點 
	p2 = (Polynomial)malloc(sizeof(struct PolyNode));	//初始化頭結點

	p1_rear = p1;	//初始化尾指針 
	p2_rear = p2;	//初始化尾指針 
	int num1,num2, c, e;

	scanf("%d", &num1);	//讀取p1信息 
	for (int i = 0;i < num1;i++)
	{
		scanf("%d %d", &c, &e);
		attach(c, e, &p1_rear);
	}
	p_temp = p1;
	p1 = p1->next;
	free(p_temp);	//釋放頭結點 

	scanf("%d", &num2);	//讀取p2信息 
	for (int i = 0;i < num2;i++)
	{
		scanf("%d %d", &c, &e);
		attach(c, e, &p2_rear);
	}
	p_temp = p2;
	p2 = p2->next;
	free(p_temp);	//釋放頭結點 

	//乘法,具體算法是用p1的每一項都和p2的所有項乘，再將所得的加在一起，加法已實現
	Polynomial doMultiplication = p1;	//做乘法
	Polynomial multiplication = NULL;  //記錄乘法結果
	for (int i = 0;i < num1;i++)
	{
		multiplication = polyAdd( polymultiply(doMultiplication, p2, num2) , multiplication);
		doMultiplication = doMultiplication->next;
	}

	if (multiplication)	//處理第一項
	{
		printf("%d %d", multiplication->coef, multiplication->expon);
		multiplication = multiplication->next;
	}
	else
	{
		printf("0 0");
	}

	while (multiplication)
	{
		printf(" %d %d", multiplication->coef, multiplication->expon);
		multiplication = multiplication->next;
	}


	printf("\n");

	//加法
	Polynomial sum = polyAdd(p1, p2);
	if (sum)	//處理第一項 
	{
		printf("%d %d", sum->coef, sum->expon);
		sum = sum->next;
	}
	else
	{
		printf("0 0");
	}

	for (;sum;sum = sum->next)	//處理之後項 
	{
		printf(" %d %d", sum->coef, sum->expon);
	}
	return 0;
}

void attach(int c, int e, Polynomial* pRear)	//在尾指針後連上另一項 
{
	Polynomial p = (Polynomial)malloc(sizeof(struct PolyNode));
	p->coef = c;
	p->expon = e;
	p->next = NULL;
	(*pRear)->next = p;
	*pRear = p;
}

int compare(int num1, int num2)	//比較大小 
{
	if (num1 > num2)
		return 1;
	else if (num1 < num2)
		return -1;
	else
		return 0;
}

Polynomial polyAdd(Polynomial p1, Polynomial p2)	//多項式加法 
{
	Polynomial front, rear, temp;
	int sum;
	front = (Polynomial)malloc(sizeof(struct PolyNode));
	rear = front;//由front記錄結果多項式鏈表頭結點
	while (p1 && p2)	//當兩個多項式都有非零項待處理時 
	{
		switch (compare(p1->expon, p2->expon)) {
		case 1:
			attach(p1->coef, p1->expon, &rear);
			p1 = p1->next;
			break;
		case -1:
			attach(p2->coef, p2->expon, &rear);
			p2 = p2->next;
			break;
		case 0:
			sum = p1->coef + p2->coef;
			if (sum)
				attach(sum, p1->expon, &rear);
			p1 = p1->next;
			p2 = p2->next;
			break;
		}
	}
	//將未處理完的另一個多項式的所有結點複製到結果多項式中
	for (;p1;p1 = p1->next)
		attach(p1->coef, p1->expon, &rear);
	for (;p2;p2 = p2->next)
		attach(p2->coef, p2->expon, &rear);
	rear->next = NULL;
	temp = front;
	front = front->next;//令front指向結果多項式第一個非零項
	free(temp);//釋放臨時空表頭結點
	return front;

}

Polynomial polymultiply(Polynomial p1, Polynomial p2,int num)	//p1的一項與p2所有項做乘法
{
	Polynomial front = (Polynomial)malloc(sizeof(struct PolyNode));
	Polynomial rear = front;
	Polynomial temp = front;
	for (int i = 0;i < num;i++)
	{
		attach(p1->coef * p2->coef, p1->expon + p2->expon, &rear);
		p2 = p2->next;
	}
	front = front->next;
	free(temp);
	return front;
}