一元多项式的相加（单链表的应用）

Posted 2020-09-26 渔腻

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 -1



typedef 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。