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;
}