PAT数据结构_02-线性结构2 一元多项式的乘法与加法运算 (20分)

题目地址： https://pta.patest.cn/pta/test/1342/exam/4/question/19209

基于链表的实现

#include "stdio.h"
#include "stdlib.h"
#include <iostream>
using namespace std;

// 数学术语https://en.wikipedia.org/wiki/Product_(mathematics)
// Polynomial 多项式
typedef struct PolyNode *Polynomial;
struct PolyNode
{
	// 系数 coefficients
	// 指数 expon
	int coef;
	int expon;
	Polynomial next; 
};

void Attach(int c, int e, Polynomial *pRear){
	Polynomial p; 
	p = (Polynomial)malloc(sizeof(struct PolyNode));
	p->coef = c;
	p->expon = e;
	p->next = NULL;

	(*pRear)->next = p;			//传来的是地址;操作时，需要用结构体指针操作
	*pRear = p;			// *pRear = p; 或者 pRear = &p
	
	// pRear 是 Polynomial * 类型，即PolyNode **类型; 

	// pRear->next = p;		
	// error: member reference base type 'Polynomial' (aka 'PolyNode *') is not a structure or union
	// pRear = p;			
	// error: assigning to 'Polynomial *' (aka 'PolyNode **') from incompatible type 'Polynomial' (aka 'PolyNode *'); take the address with &
}


void PrintPoly(Polynomial P){
	int flag = 0;		//调整格式用，第一项前不输出空格
	
	if(!P){
		printf("0 0\n");
		return;
	}

	while (P){
		if(!flag){
			flag = 1;
		}else{
			printf(" ");
		}
		printf("%d %d", P->coef, P->expon);
		P = P->next;
	}
	printf("\n");
}


Polynomial ReadPoly(){
	Polynomial p, rear, tmp;
	int c, e, N;

	scanf("%d", &N);
	p = (Polynomial) malloc(sizeof(struct PolyNode));	//链表头空结点
	p->next = NULL;				//生成链表时，用一个临时的空结点，方便attach
	rear = p;
	while(N--){
		scanf("%d %d", &c, &e);
		Attach(c, e, &rear);		//将当前项插入多项式尾部
	}

	//删除临时生成的头结点
	tmp = p; 
	p = p->next;
	free(tmp);

	return p;
}

Polynomial Add(Polynomial P1, Polynomial P2){


	Polynomial t1 = P1; 
	Polynomial t2 = P2;

	Polynomial p, rear, tmp;
	p = (Polynomial) malloc(sizeof(struct PolyNode));
	p->next = NULL;			//合并的链表，由一个不含data的header开始
	rear = p;

	while(t1 && t2){
		// cout<<"\nt1: "<<t1->coef<<"  "<<t1->expon<<endl;
		// cout<<"\nt2: "<<t2->coef<<"  "<<t2->expon<<endl;

		if(t1->expon == t2->expon){
			int c = t1->coef + t2->coef;
			int e = t1->expon;
			if(c != 0){
				Attach(c, e, &rear);
			}
			t1 = t1->next;
			t2 = t2->next;
		}else if(t1->expon > t2->expon){
			int c = t1->coef;
			int e = t1->expon;
			Attach(c, e, &rear);
			t1 = t1->next;

		}else if(t1->expon < t2->expon){
			int c = t2->coef;
			int e = t2->expon;
			Attach(c, e, &rear);
			t2 = t2->next;
		}
	}
	while(t1){
		Attach(t1->coef, t1->expon, &rear);
		t1 = t1->next;
	}
	while(t2){
		Attach(t2->coef, t2->expon, &rear);
		t2 = t2->next;
	}

	tmp = p; p = p->next; free(tmp);		//将p指向真实的数据node

	return p;
}



Polynomial Mult(Polynomial P1, Polynomial P2){

	if(!P1 || !P2)
		return NULL;

	Polynomial t1 = P1; 
	Polynomial t2 = P2;
	int c, e;

	Polynomial p, rear, tmp;
	p = (Polynomial) malloc(sizeof(struct PolyNode));
	p->next = NULL;			//合并的链表，由一个不含data的header开始
	rear = p;
	

	// 构造初始多项式， 先用P1度第一项乘以P2，得到P
	while(t2){
		Attach(t1->coef * t2->coef, t1->expon + t2->expon, &rear);
		t2 = t2->next;
	}

	//接下来的每个 P1单项*P2， 找到合适位置插入P
	t1 = t1->next;
	while(t1){
		// cout<<"\nt1: "<<t1->coef<<"  "<<t1->expon<<endl;
		t2 = P2; 			//t1后挪后，t2重置

		rear = p;
		while(t2){		
			// cout<<"\nt2: "<<t2->coef<<"  "<<t2->expon<<endl;

			e = t1->expon + t2->expon;
			c = t1->coef * t2->coef;
			//找插入点，若下一个点的项数仍大于要插入的项，则后移rear
			while(rear->next && rear->next->expon > e){
				rear = rear->next;
			}
			//若存在对应指数，则判断相加后是否为0
			if(rear->next && rear->next->expon == e){
				if(rear->next->coef + c){
					rear->next->coef += c;
				}else{		//若相加后为0，删掉node
					tmp = rear -> next;
					rear->next = tmp->next;
					free(tmp);
				}
			}else{	
				//若不存在对应指数，生成新结点，加在rear之后，rear->next之前
				tmp = (Polynomial)malloc(sizeof(struct  PolyNode));
				tmp->coef = c;
				tmp->expon = e;
				tmp->next = rear->next;
				rear->next = tmp;
				rear = rear->next;
			}
			t2 = t2->next;
		}
		t1 = t1->next;
	}

	tmp = p; p = p->next; free(tmp);		//将p指向真实的数据node
	return p;
}


int main(){


	Polynomial p1, p2, pProduct, pSum;
	// 读入多项式1
	p1 = ReadPoly();
	// 读入多项式2
	p2 = ReadPoly();
	// PrintPoly(p1);
	// PrintPoly(p2);


	// 生成乘积多项式并输出
	// (a+b)*(c+d) = ac+ad+bc+bd
	pProduct = Mult(p1, p2);
	PrintPoly(pProduct);
	// 生成和多项式并输出
	pSum = Add(p1, p2);
	PrintPoly(pSum);

	return 0;
}