0x00数据结构——C语言实现（多项式）

0x00数据结构——C语言实现（多项式）

/*filename:polynomial*/
#ifndef POLYNOMIAL
#define POLYNOMIAL

//一元多项式的表示

//Pn(x)=p0 + p1*x + p2*x^2 + ... + pn*x^n
/*
基本操作：
    创建一个有m项系数和指数的一元多项式p
    销毁一元多项式p
    打印输出
    返回项数
    完成一元多项式的相加
    完成一元多项式的相减
    完成一元多项式的相乘

*/


struct term;
typedef struct term term;
typedef term *polyn;

typedef enum {
    false = 0,
    true
} BOOL;

    //初始化一个一元多项式p
polyn init_polynomial(void);

    //在多项式p中插入一个系数为c，指数为e的项
polyn insert_term(int c, int e, polyn p);

/*
    //创建一个有m项系数和指数的一元多项式p
polyn creat_polynomial(int m);
*/

    //销毁一元多项式p
BOOL destroy_polyn(polyn p);

    //打印输出
void print_polyn(polyn p);

    //返回项数
int polyn_length(polyn p);

    //完成一元多项式的相加
polyn add_polyn(polyn p1, polyn p2);

    //完成一元多项式的相减
polyn sub_polyn(polyn p1, polyn p2);

    //完成一元多项式的相乘
polyn mutiply_polyn(polyn p1, polyn p2);


#endif

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

#include "polynomial.h"

/*
typedef struct term{
    float coef; //系数
    int expn;   //指数
    struct term *next;
} term, *polyn;
*/

struct term {
    float coef; //系数
    int expn;   //指数
    struct term *next;
};

//初始化一个一元多项式p
polyn init_polynomial(void)
{
    term *head = NULL;
    head = (term*)malloc(sizeof(term));
    if(head!=NULL){
        head->coef = 0;
        head->expn = -1;
        head->next = NULL;
    }
    return head;
}

    //在多项式p中加入一个系数为c，指数为e的项
polyn insert_term(int c, int e, polyn p)
{
    if(c==0) {
        return p;
    } else {
        term *tmp = p->next, *pre = p;
        while(tmp != NULL && tmp->expn != e && tmp->expn < e) {
            pre = tmp;
            tmp = tmp->next;
        }
        if(tmp == NULL) {
            pre->next = (term*)malloc(sizeof(term));
            if(pre->next != NULL) {
                pre->next->coef = c;
                pre->next->expn = e;
                pre->next->next = NULL;
            }
        } else if(tmp->expn == e) {
            tmp->coef += c;
            if(tmp->coef == 0) {
                pre->next = tmp->next;
                free(tmp);
            }
        } else if(tmp->expn > e) {
            pre->next = (term*)malloc(sizeof(term));
            if(pre->next != NULL) {
                pre->next->coef = c;
                pre->next->expn = e;
                pre->next->next = tmp;
            }
        }
    }
    return p;
}

/*
    //创建一个有m项系数和指数的一元多项式p，带头节点
polyn creat_polynomial(int m)
{
    term *head = NULL, *tmp = NULL, *tmp_p = NULL;
    tmp = (term*)malloc(sizeof(term));
    tmp->coef = 0;
    tmp->expn = -1;
    tmp->next = NULL;
    head = tmp;
    while(m){
        tmp_p = (term *)malloc(sizeof(term));
        tmp_p->next = NULL;
        tmp->next = tmp_p;
        tmp = tmp_p;
        m--;
    }
    return head;
}
*/

    //销毁一元多项式p
BOOL destroy_polyn(polyn p)
{
    term *tmp;
    p = p->next;
    while(p != NULL){
        tmp = p;
        p = p->next;
        free(tmp);
        tmp = NULL;
    }
    return true;
}

    //打印输出
void print_polyn(polyn p)
{
    p = p->next;
    if(p!=NULL) {
        if(p->expn == 0){//考虑第一项
            printf("%g", p->coef);
            p = p->next;
            if(p!=NULL){
                if(p->expn == 1){//考虑第二项
                    p->coef>0? printf("+%gX", p->coef):printf("%gX", p->coef);
                } else {
                     p->coef>0?printf("+%gX^%d", p->coef, p->expn):printf("%gX^%d", p->coef, p->expn);
                }
                p = p->next;
            }
        } else if(p->expn == 1){//考虑第一项
            if(p->coef != 1) {
                printf("%gX", p->coef);
            } else {
                printf("X");
            }
            p = p->next;
        } else if(p->expn > 1){

            if(p->coef != 1) {
                printf("%gX^%d", p->coef, p->expn);
            } else {
                printf("X^%d", p->expn);
            }
            p = p->next;
        }
        while(p!=NULL){
            p->coef>0?printf("+%gX^%d", p->coef, p->expn):printf("%gX^%d", p->coef, p->expn);
            p = p->next;
        }
    }
    printf("\n");
}

    //返回项数
int polyn_length(polyn p)
{
    int n = 0;
    while(p->next != NULL){
        n++;
        p = p->next;
    }
    return n;
}

    //完成一元多项式的相加
polyn add_polyn(polyn p1, polyn p2)
{
    term *tmp = p1, *tmp1 = p1->next, *tmp2 = p2->next;
    while(tmp1!=NULL && tmp2!=NULL){
        //指数相等的情况
        if(tmp1->expn == tmp2->expn){
            tmp1->coef += tmp2->coef;
            if(tmp1->coef == 0){
                p1->next = tmp1->next;
                p2->next = tmp2->next;
                free(tmp1);
                free(tmp2);
                //相加为0则物理删除该项；
            } else {
                p1 = p1->next;
                p2 = p2->next;
            }
            tmp1 = p1->next;
            tmp2 = p2->next;
        } else if(tmp1->expn < tmp2->expn){
            //指数1小于指数2，p1向后比较
            p1 = p1->next;
            tmp1 = p1->next;
        } else if(tmp2->expn < tmp1->expn){
            //指数1大于指数2，将指数2项插到指数1前面
            //逻辑删除p2中指数2对应项
            p2->next = tmp2->next;

            //插出入到p1中指数1对应项前面
            tmp2->next = tmp1;
            p1->next = tmp2;

            //指针移动
            p1 = p1->next;
            tmp2 = p2->next;
        }
    }
    if(tmp1 == NULL){
        p1->next = tmp2;
    }

    free(p2);
    p2 = NULL;
    return tmp;
}

    //完成一元多项式的相减
polyn sub_polyn(polyn p1, polyn p2)
{
    term *tmp = p1, *tmp1 = p1->next, *tmp2 = p2->next;
    while(tmp1!=NULL && tmp2!=NULL){
        //指数相等的情况
        if(tmp1->expn == tmp2->expn){
            tmp1->coef -= tmp2->coef;
            if(tmp1->coef == 0){
                p1->next = tmp1->next;
                p2->next = tmp2->next;
                free(tmp1);
                free(tmp2);
                //相减为0则物理删除该项；
            } else {
                p1 = p1->next;
                p2 = p2->next;
            }
            tmp1 = p1->next;
            tmp2 = p2->next;
        } else if(tmp1->expn < tmp2->expn){
            //指数1小于指数2，p1向后比较
            p1 = p1->next;
            tmp1 = p1->next;
        } else if(tmp2->expn < tmp1->expn){
            //指数1大于指数2，将指数2项插到指数1前面
            //逻辑删除p2中指数2对应项
            tmp2->coef *= -1;
            p2->next = tmp2->next;

            //插出入到p1中指数1对应项前面
            tmp2->next = tmp1;
            p1->next = tmp2;

            //指针移动
            p1 = p1->next;
            tmp2 = p2->next;
        }
    }
    if(tmp1 == NULL){
        p1->next = tmp2;
    }

    free(p2);
    p2 = NULL;
    return tmp;
}

    //完成一元多项式的相乘
polyn mutiply_polyn(polyn p1, polyn p2)
{
    polyn tmp_res = (polyn)malloc(sizeof(term));
    tmp_res->next = NULL;
    term *cur1 = p1->next, *cur2 = p2->next;
    while(cur1!=NULL){
        polyn tmp_p2 = (polyn)malloc(sizeof(term));
        term *cur_p2 = tmp_p2;
        cur2 = p2->next;
        while(cur2!=NULL){
            cur_p2->next = (term *)malloc(sizeof(term));
            cur_p2 = cur_p2->next;
            cur_p2->coef = cur1->coef * cur2->coef;
            cur_p2->expn = cur1->expn + cur2->expn;

            cur2 = cur2->next;
        }
        cur_p2->next = NULL;
        //print_polyn(tmp_p2);
        if(tmp_res->next == NULL){
            free(tmp_res);
            tmp_res = tmp_p2;
        } else{
            add_polyn(tmp_res, tmp_p2);
        }
        //print_polyn(tmp_res);
        cur1 = cur1->next;
        //free(p1->next);
        //p1->next = cur1;
    }
    destroy_polyn(p1);
    destroy_polyn(p2);
    p1->next = tmp_res->next;
    return tmp_res;
}