02-线性结构2 一元多项式的乘法与加法运算

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           

例子输入与输出：

序号	输入	输出
1	4 3 4 -5 2 6 1 -2 0  3 5 20 -7 4 3 1	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
2	2 1 2 1 0 2 1 2 -1 0	1 4 -1 0 2 2
3	2 -1000 1000 1000 0 2 1000 1000 -1000 0	-1000000 2000 2000000 1000 -1000000 0 0 0
4	1 999 1000	999 1000

/*!
 * \file 02-线性结构2 一元多项式的乘法与加法运算.cpp
 *
 * \author ranjiewen
 * \date 2017/03/19 16:11
 *
 * 
 */
   

//动态数组实现较好

//用链表设计

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

typedef struct PolyNode* Polynomial;

struct PolyNode{
    int coef;
    int expon;
    Polynomial next;
};

Polynomial ReadPoly();
Polynomial Mult(Polynomial P1,Polynomial P2);
void PrintPoly(Polynomial PP);
Polynomial Add(Polynomial P1,Polynomial P2);

int main() //程序框架搭建
{
    Polynomial P1, P2, PP, PS;
    P1 = ReadPoly();
    P2 = ReadPoly();

    PP = Mult(P1, P2);
    PrintPoly(PP);

    PS = Add(P1, P2);
    PrintPoly(PS);

    return 0;
}

//对Rear指针的处理：1.初值为NULL,根据是否为空做不同处理；2.指向一个空节点
//*pRear当前结果表达式尾项指针的指针
//函数实现在pRear后面插入节点
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;
    *pRear = P;
}

Polynomial ReadPoly()
{
    Polynomial P, Rear, t;
    int c, e, N;
    scanf("%d", &N);
    P = (Polynomial)malloc(sizeof(struct PolyNode)); //链表头空节点
    P->next = NULL;
    Rear = P; 
    while (N--)
    {
        scanf("%d %d", &c, &e);
        if (c != 0)  
           Attach(c, e, &Rear); //将当前项插入多项式尾部
    }
    t = P;
    P = P->next;
    free(t); //删除临时生成的头结点
    return P;
}

Polynomial Add(Polynomial P1, Polynomial P2)
{
    Polynomial t1, t2;
    t1 = P1;
    t2 = P2;
    //生成新的头结点
    Polynomial P,t;
    P = (Polynomial)malloc(sizeof(struct PolyNode));
    P->next = NULL;
    Polynomial Rear;
    Rear = P;
    while (t1&&t2)
    {
        if (t1->expon==t2->expon)
        {
            if (t1->coef+t2->coef)  //系数和为0时不添加到尾节点上  /*考虑周全*/
            {
                Attach(t1->coef + t2->coef, t1->expon, &Rear);
            }
            t1 = t1->next;
            t2 = t2->next;
        }
        else if (t1->expon>t2->expon)
        {
            Attach(t1->coef, t1->expon, &Rear);
            t1=t1->next;
        }else 
        {
            Attach(t2->coef, t2->expon, &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;
    }
    t = P;
    P = P->next;
    free(t);
    return P;
}

//多项式乘法方法：
//1. 将乘法运算转换为加法运算，让P1的每一项和P2相乘，在加到结果多项式中
//2. 逐项插入，将P1当前项乘P2当前项，在插入到结果表达式中，关键是要找到插入的位置

Polynomial Mult(Polynomial P1, Polynomial P2)
{
    Polynomial P, Rear;
    Polynomial t1, t2, t;
    if (!P1||!P2)
    {
        return NULL;
    }
    t1 = P1;
    t2 = P2;
    P = (Polynomial)malloc(sizeof(struct PolyNode));
    Rear = P;
    while (t2)
    {
        //先用P1的第一项乘以P2,得到初始结果多项式
        Attach(t1->coef*t2->coef, t1->expon + t2->expon, &Rear);
        t2 = t2->next;
    }
    t1 = t1->next;
    while (t1)
    {
        t2 = P2;
        Rear = P; //将尾节点置到头结点来
        while (t2)
        {
            int e = t1->expon + t2->expon;
            int c = t1->coef * t2->coef;   //以后的每一项相乘的结果
            while (Rear->next&&Rear->next->expon>e) //找插入位置
            {
                Rear = Rear->next;
            }
            if (Rear->next&&Rear->next->expon==e)
            {
                if (Rear->next->coef+c) //判系数是否为0
                {
                    Rear->next->coef += c;
                }
                else  //为0删除节点
                {
                    t = Rear->next;
                    Rear->next = t->next;
                    free(t);
                }
            }
            else  //插入位置
            {
                t = (Polynomial)malloc(sizeof(struct PolyNode));
                t->coef = c;
                t->expon = e;
                t->next = Rear->next;
                Rear->next = t;

                Rear = Rear->next;
            }
            t2 = t2->next;
        }
        t1 = t1->next;
    }
    t2 = P;
    P = P->next;
    free(t2);

    return P;
}

void PrintPoly(Polynomial P)
{
    int flag = 0;//辅助调整输出格式
    if (!P)
    {
        printf("0 0\n"); /*格式*/
        return;
    }
    while (P)
    {
        if (!flag) //第一次
        {
            flag = 1;
        }
        else
        {
            printf(" ");
        }
        printf("%d %d", P->coef, P->expon);
        P = P->next;
    }
    printf("\n");
}      

reference：[PAT] 02-线性结构2 一元多项式的乘法与加法运算

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