02-线性结构2 一元多项式的乘法与加法运算（20 分）

02-线性结构2 一元多项式的乘法与加法运算 （20 分）

设计函数分别求两个一元多项式的乘积与和。

输入格式:

输入分2行，每行分别先给出多项式非零项的个数，再以指数递降方式输入一个多项式非零项系数和指数（绝对值均为不超过1000的整数）。数字间以空格分隔。

输出格式:

输出分2行，分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。数字间以空格分隔，但结尾不能有多余空格。零多项式应输出0 0。

输入样例:

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

输出样例:

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

---

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

typedef struct Node {
	// 系数
	int coefficient;
	// 指数
	int exponent;
	struct Node *next;
}Node, *Polynomial;

// 向给定多项式末尾添加结点
void addNode(Polynomial P, Node *N) {
	Polynomial p = P;
	while (p->next){
		p = p->next;
	}
	p->next = N;
}

// 输入结点
Polynomial input() {
	int n, i;
	Polynomial resultPolynomial = (Polynomial)malloc(sizeof(Node)), temp;
	resultPolynomial->next = NULL;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		temp = (Polynomial)malloc(sizeof(Node));
		scanf("%d", &(temp->coefficient));
		scanf("%d", &(temp->exponent));
		temp->next = NULL;
		addNode(resultPolynomial, temp);
	}
	// 当非零结点数为0时，添加一个系数和指数均为0的结点
	if (n == 0) {
		temp = (Polynomial)malloc(sizeof(Node));
		temp->coefficient = 0;
		temp->exponent = 0;
		temp->next = NULL;
		addNode(resultPolynomial, temp);
	}
	return resultPolynomial;
}

// 从前到后逐个打印结点
void print(Polynomial P) {
	Polynomial p;
	// 没有结点
	if (P->next == NULL) {
		printf("0 0\n");
		return;
	}
	p = P->next;
	while (p) {
		if(p->next == NULL)
			printf("%d %d\n", p->coefficient, p->exponent);
		else
			printf("%d %d ", p->coefficient, p->exponent);
		p = p->next;
	}
}

// 多项式相加
Polynomial plus(Polynomial P1, Polynomial P2) {
	Polynomial resultPolynomial = (Polynomial)malloc(sizeof(Node)), temp, p1 = P1->next, p2 = P2->next, p1pre = P1, p2pre = P2, tempP1, tempP2, tempP1pre, tempP2pre;
	resultPolynomial->next = NULL;
	while (p1 && p2) {
		if (p1->exponent >= p2->exponent) {
			temp = (Polynomial)malloc(sizeof(Node));
			temp->exponent = p1->exponent;
			temp->coefficient = p1->coefficient;
			temp->next = NULL;
			tempP2 = p2;
			tempP2pre = p2pre;
			// 搜寻P2的相同指数结点
			while (tempP2) {
				// 如果指数相同则系数相加
				if (tempP2->exponent == temp->exponent) {
					temp->coefficient += tempP2->coefficient;
					// 删除相加结点
					if (tempP2 == p2)
						p2 = p2->next;
					tempP2pre->next = tempP2->next;
					free(tempP2);
					break;
				}
				tempP2 = tempP2->next;
				tempP2pre = tempP2pre->next;
			}
			addNode(resultPolynomial, temp);
			p1 = p1->next;
			p1pre = p1pre->next;
		}
		else {
			temp = (Polynomial)malloc(sizeof(Node));
			temp->exponent = p2->exponent;
			temp->coefficient = p2->coefficient;
			temp->next = NULL;
			tempP1 = p1;
			tempP1pre = p1pre;
			// 搜寻P1的相同指数结点
			while (tempP1) {
				// 如果指数相同则系数相加
				if (tempP1->exponent == temp->exponent) {
					temp->coefficient += tempP1->coefficient;
					// 删除相加结点
					if (tempP1 == p1)
						p1 = p1->next;
					tempP1pre->next = tempP1->next;
					free(tempP1);
					break;
				}
				tempP1 = tempP1->next;
				tempP1pre = tempP1pre->next;
			}
			addNode(resultPolynomial, temp);
			p2 = p2->next;
			p2pre = p2pre->next;
		}
	}
	while (p1){
		addNode(resultPolynomial, p1);
		p1 = p1->next;
		p1pre = p1pre->next;
	}
	while (p2) {
		addNode(resultPolynomial, p2);
		p2 = p2->next;
		p2pre = p2pre->next;
	}
	// 删除系数为0的结点
	p1 = resultPolynomial->next;
	p1pre = resultPolynomial;
	while (p1) {
		if (p1->coefficient == 0) {
			p1pre->next = p1->next;
			free(p1);
			p1 = p1pre->next;
		}
		else {
			p1 = p1->next;
			p1pre = p1pre->next;
		}
	}
	return resultPolynomial;
}

// 多项式相乘
Polynomial multiply(Polynomial P1, Polynomial P2) {
	Polynomial resultPolynomial = (Polynomial)malloc(sizeof(Node)), temp, p, pre, p1 = P1->next, p2 = P2->next;
	resultPolynomial->next = NULL;
	if (p1->exponent >= p2->exponent) {
		while (p1) {
			p2 = P2->next;
			while (p2) {
				temp = (Polynomial)malloc(sizeof(Node));
				temp->coefficient = p1->coefficient * p2->coefficient;
				temp->exponent = p1->exponent + p2->exponent;
				temp->next = NULL;
				addNode(resultPolynomial, temp);
				p2 = p2->next;
			}
			p1 = p1->next;
		}
	}
	else {
		while (p2) {
			p1 = P1->next;
			while (p1) {
				temp = (Polynomial)malloc(sizeof(Node));
				temp->coefficient = p2->coefficient * p1->coefficient;
				temp->exponent = p2->exponent + p1->exponent;
				temp->next = NULL;
				addNode(resultPolynomial, temp);
				p1 = p1->next;
			}
			p2 = p2->next;
		}
	}
	// 将指数相同的项合并
	p = resultPolynomial->next;
	pre = resultPolynomial;
	while (p && p->next) {
		p1 = p;
		p2 = p->next;
		while (p2) {
			if (p->exponent == p2->exponent) {
				p->coefficient += p2->coefficient;
				p1->next = p2->next;
				free(p2);
				p2 = p1->next;
			}
			else {
				p2 = p2->next;
				p1 = p1->next;
			}
		}
		p = p->next;
		pre = pre->next;
	}
	// 删除系数为0的结点
	p = resultPolynomial->next;
	pre = resultPolynomial;
	while (p) {
		if (p->coefficient == 0) {
			pre->next = p->next;
			free(p);
			p = pre->next;
		}
		else {
			p = p->next;
			pre = pre->next;
		}
	}
	return resultPolynomial;
}

int main(void) {
	Polynomial P1, P2;
	P1 = input();
	P2 = input();
	print(multiply(P1, P2));
	print(plus(P1, P2));
}