一元多项式的相加（单链表的应用）

来源：互联网发布：淘宝聚划算怎么报名编辑：程序博客网时间：2024/06/08 17:34

一元多项式的相加，基于单链表的结构上实现的。

单链表的结点结构定义为：

typedef struct _NODE
{
int coef;
int exp;
struct _NODE *next;
}NODE；

第一个变量指的是系数，第二个变量指的是指数，x^7系数为1，指数为7

第三个变量next指针，将结点连接起来。

比如a1 = x^5+x^4+x^2+3 a2 = x^7+x^4+x+8

a1+a2 = x^7+x^5+2x^4+x^2+x+11

list.h 里面包含了一些对单链表进行操作的方法的声明

#ifndef _LINK_LIST_H_#define _LINK_LIST_H_#define ERROR -1typedef struct _NODE{    int coef;    int exp;    struct _NODE *next;}NODE;NODE *alloc_node(int coef,int exp);NODE *init_link_list_ex();bool insert_head(NODE *phead,int coef,int exp);  //O(1)----bool is_empty(NODE *phead); //O(1)bool show(NODE *phead);//O(N)int get_length(NODE *phead); //O(N)----NODE *get_last(NODE *phead);bool insert_tail(NODE *phead,int coef,int exp); //O(N)----NODE *get_sec_last(NODE *phead);bool delete_head(NODE *phead);//O(1)----bool delete_tail(NODE *phead);//O(N)----bool destory_link_list(NODE *phead);       //O(N)----#endif

list.h

list.c里面实现了对单链表操作方法的实现。

#include "LINK_LIST.h"#include <stdio.h>#include <stdlib.h>NODE *alloc_node(int coef,int exp){    NODE *tmp = (NODE *)malloc(sizeof(NODE) * 1);    if (tmp == NULL)    {        return NULL;    }    tmp->coef = coef;    tmp->exp = exp;    tmp->next = NULL;    return tmp;}NODE *init_link_list_ex(){    NODE *phead = (NODE *)malloc(sizeof(NODE) * 1);    phead->coef = 0;    phead->exp = 0;    phead->next = NULL;    return phead;}bool insert_head(NODE *phead,int coef,int exp){    if (phead == NULL)    {        return false;    }    NODE *tmp = alloc_node(coef,exp);    tmp->next = phead->next;    phead->next = tmp;    return true;}bool is_empty(NODE *phead){    if (phead == NULL)    {        return true;//ERROR    }    return phead->next == NULL;}bool show(NODE *phead){    if (phead == NULL)    {        return false;    }    if (is_empty(phead))    {        return false;    }    NODE *p = phead->next;    while(p != NULL)    {        if (p->coef > 0)        {            printf("+%dx^%d ",p->coef,p->exp);        }        else if( p->coef == 0)        {            printf("0+");        }        else        {            printf("-%dx^%d ",p->coef,p->exp);        }        p = p->next;     }    printf("\n");    return true;}int get_length(NODE *phead){    if (phead == NULL)    {        return ERROR;    }    int count = 0;    NODE *p = phead->next;    while(p != NULL)    {        p = p->next;        count++;    }    return count;}NODE *get_last(NODE *phead){    if (phead == NULL)    {        return NULL;    }    NODE *p = phead;    while(p->next != NULL)    {        p = p->next;    }    return p;}bool insert_tail(NODE *phead,int coef,int exp){    if (phead == NULL)    {         return false;    }    get_last(phead)->next = alloc_node(coef,exp);    return true;}NODE *get_sec_last(NODE *phead){    if (phead == NULL)    {        return NULL;    }    if (is_empty(phead))    {        return NULL;    }    NODE *p = phead->next;    NODE *s = phead;    while(p->next != NULL)    {        s = p;        p = p->next;    }    return s;}bool delete_head(NODE *phead){    if (phead == NULL)    {        return false;    }    if (is_empty(phead))    {        return false;    }    NODE *p = phead->next;    phead->next = p->next;    free(p);    return true;}bool delete_tail(NODE *phead){    if (phead == NULL)    {        return false;    }    if (is_empty(phead))    {        return false;    }    NODE *p = get_sec_last(phead);    free(p->next);    p->next = NULL;    return true;}bool clear_link_list(NODE *phead){    if (phead == NULL)    {        return false;    }    while(!is_empty(phead))    {        delete_head(phead);    }    //free(phead);    return true;}bool destory_link_list(NODE *phead){    clear_link_list(phead);    free(phead);    return true;}

list.c

另外，实现了方法NODE *create_poly()生成多项式 ,

add_poly相加函数，这里我实现的是a1 = a1+a2;

NODE *create_poly()//创建好的单链表有序 {    NODE *phead = init_link_list_ex();    int coef = 0;    int exp = 0;    while(1)    {        printf("请输入系数,指数，形式如下：10,20  输入0,0结束表达式输入\n");        scanf("%d,%d",&coef, &exp);        if (coef ==0 && exp ==0)        {            printf("输入结束\n");            show(phead);            break;        }        NODE *tmp = alloc_node(coef, exp);        NODE *p = phead;        while(p->next != NULL)        {            if (p->next->exp > tmp->exp)            {                break;            }            p = p->next;        }        tmp->next = p->next;        p->next = tmp;    }    return phead;}

create_poly

NODE *add_poly(NODE *pa,NODE *pb){    NODE *p = pa->next;    NODE *s = pb->next;    NODE *m = pb->next;    while(p != NULL && s != NULL)    {        if (p->exp < s->exp)        {            //p下去            p = p->next;        }        else if (p->exp > s->exp)        {            //s下去            m = s;            p->next = m;            p = m;            s = s->next;        }        else//合并        {            if (!(p->coef+s->coef))            {                p = p->next;                s = s->next;                continue;            }            p->coef = p->coef + s->coef ;            p = p->next;            s = s->next;        }    }    while(p != NULL)    {        p = p->next;    }    while(s != NULL)    {        m = s;        p->next = m;        p = m;        s = s->next;    }    return pa;}

add_poly

最后在主函数中调用：

int main(){    NODE *pheadA = create_poly();    NODE *pheadB = create_poly();    show(pheadA);    show(pheadB);    pheadA =add_poly(pheadA,pheadB);    show(pheadA);    show(pheadB);    destory_link_list(pheadA);    destory_link_list(pheadB);    return 0;}

main

值得注意，所以结点的开辟都是在堆（heap）上进行的，所以务必要对内存进行释放，防止内存泄漏。

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