学习笔记：单链表实现多项式相乘

Posted 2020-08-08 Madao东治

单链表实现多项式相乘，有这样的一个思路可以参考：

实现多项式相乘，最关键的是系数和指数的两个数据，这里命名为coef和HighPower。

最简便的办法是使用两个嵌套循环例如(3x^2+4x^1)(x^2+2x^4)用3x^2遍历另外一个括号内的数据，同时实现本身括号内的遍历。

这个想法的核心程序可归纳为以下：

while(pList!=NULL){
        while(pList2!=NULL){
            pNew=(PNODE)malloc(sizeof(NODE));
            pNew->pNext=NULL;
            pNew->coef=(pList->coef)*(pList2->coef);
            pNew->HighPower=(pList->HighPower)+(pList2->HighPower);
            pReslut=addNewItem(pReslut,pNew);
            pList2=pList2->pNext;
        }
        pList2=pHead2;
        pList=pList->pNext;
    }

这样即可实现将所有数据，输出到一个新的链表里面。

但同时这也带来了不少问题，怎样才能合并新的链表里面相同系数的参数呢？

这里可以使用这样的方法：

创捷一个新表New,新表New2，将原有的表拆分循环复制在NEW2，然后将NEW2复制给NEW,如果在NEW中有相同项，则直接相加或者相乘，如果没有，则在链表最后添加新的节点。这样即可实现合并单链表中相同系数的参数。

源码如下：

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

typedef struct node{
    int coef;
    int HighPower;
    struct node *pNext;
}NODE,*PNODE;
PNODE crateList();
void traverseLinkList(PNODE);
PNODE caculate(PNODE,PNODE);
PNODE addNewItem(PNODE ,PNODE );
PNODE total(PNODE);
PNODE ListFind(PNODE,PNODE);
int main(){
    PNODE pList,pList2,pNew;
    pList=crateList();
    getchar(); 
    pList2=crateList();
    pNew=caculate(pList,pList2);
    pNew=total(pNew);
    traverseLinkList(pNew);
    return(0);
}
PNODE crateList(){
    int a,b,c;
    PNODE pCurrent,pPre,pHead=NULL;
    pCurrent=NULL;pPre=NULL; 
    b=0,c=0;
    while(1){
        if(scanf("%d %d",&b,&c)!=2)
            break;
        pCurrent=(PNODE)malloc(sizeof(NODE));
        if(pHead==NULL)
            pHead=pCurrent;
        else
            pPre->pNext=pCurrent;
        pCurrent->pNext=NULL;
        pCurrent->coef=b;
        pCurrent->HighPower=c;
        pPre=pCurrent;
    }
    puts("input end,now next step");
    return(pHead);
}
void traverseLinkList(PNODE pList){
    PNODE pCurrent;
    pCurrent=pList;
    if(pCurrent==NULL)
        puts("No Data Record");
    else
        while(pCurrent!=NULL){
            printf("the Coef is %d,and HighPower is %d\n",pCurrent->coef,pCurrent->HighPower);
            pCurrent=pCurrent->pNext;
        }
} 
PNODE caculate(PNODE pList,PNODE pList2){
    PNODE pNew,pCurrent,pPre,pHead2=pList2,pReslut=NULL;
    if(!pList||!pList2){
        puts("wrong!");
        return(0);
    }
    while(pList!=NULL){
        while(pList2!=NULL){
            pNew=(PNODE)malloc(sizeof(NODE));
            pNew->pNext=NULL;
            pNew->coef=(pList->coef)*(pList2->coef);
            pNew->HighPower=(pList->HighPower)+(pList2->HighPower);
            pReslut=addNewItem(pReslut,pNew);
            pList2=pList2->pNext;
        }
        pList2=pHead2;
        pList=pList->pNext;
    }
    return(pReslut);
}

PNODE addNewItem(PNODE pReslut,PNODE pAdd){
    PNODE pHead=NULL,pCurrent;
    if(pReslut==NULL){
        return(pAdd);
    }
    pHead=pReslut;
    pCurrent=pReslut;
    while(pCurrent->pNext!=NULL)
        pCurrent= pCurrent->pNext;
    pCurrent->pNext=pAdd;
    pAdd->pNext=NULL;
    return(pHead);
}


PNODE  total(PNODE pNew){
    PNODE pNew3,pCurrent,pPre,pHead,pNew2=NULL;
    pCurrent=pNew;
    if(!pNew)
        return(0);
    pNew3=(PNODE)malloc(sizeof(NODE));
    pNew2=(PNODE)malloc(sizeof(NODE));
    pNew3->pNext=NULL;
    while(pCurrent!=NULL){
        pNew3->coef=pCurrent->coef;    
        pNew3->HighPower=pCurrent->HighPower;
        pNew2=ListFind(pNew2,pNew3);
        if(!pHead)
            pHead=pNew;
        pCurrent=pCurrent->pNext;
    }
    return(pHead);
}

PNODE ListFind(PNODE pNew,PNODE pList){
    PNODE pCurrent,pPre,pHead,pCurrent2;
    while(pCurrent!=NULL){
        if(pCurrent->HighPower==pList->HighPower){
            pCurrent->coef=(pCurrent->coef)*(pList->coef);
            pCurrent->HighPower=pCurrent->HighPower+pList->HighPower;
            return(pHead);
        }
        pCurrent=pCurrent->pNext;
    }
    pCurrent=(PNODE)malloc(sizeof(NODE));
    if(!pHead)
        pHead=pCurrent;
    else
        pPre->pNext=pCurrent;
    puts("ok");
    pCurrent->pNext=NULL;
    pCurrent->coef=pList->coef;
    pCurrent->HighPower=pList->HighPower;
    pPre=pCurrent;
    return(pHead);
}