program.c

数据结构是编程的基础

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

//----- 有理数四则运算的实现 -----
Status QuotientInit(QuotientPtr &Q, int numerator, int denominator)
{
	if (denominator == 0) {	//合法性检查
	printf("Invalid denominator, it should be a non-zero integer.\n");
	return ERROR;
	}
	Q = (QuotientPtr)malloc(sizeof(Quotient)); 
	if (!Q) exit(OVERFLOW);	//存储分配失败
	Q->numerator = numerator;
	Q->denominator = denominator;

	QuotientReduction(Q);

	return OK;
}

Status QuotientDestroy(QuotientPtr &Q)
{
	if (Q) free(Q);		//合法性检查
	Q = NULL;

	return OK;
}

//得到分子
Status GetNumerator(QuotientPtr Q, int &numerator)
{
	if (!Q) return ERROR;

	numerator = Q->numerator;
	return OK;
}

//得到分母
Status GetDenominator(QuotientPtr Q, int &denominator)
{
	if (!Q) return ERROR;

	denominator = Q->denominator;
	return OK;
}

//有理数加法
Status QuotientAddition(QuotientPtr &Q, QuotientPtr Q1, QuotientPtr Q2)
{
	if (!Q || !Q1 || !Q2) return ERROR; //合法性检查
	Q->numerator = Q1->numerator * Q2->denominator + Q2->numerator * Q1->denominator;
	Q->denominator = Q1->denominator * Q2->denominator;

	QuotientReduction(Q);

	return OK;
}

//有理数减法
Status QuotientSubtraction(QuotientPtr &Q, QuotientPtr Q1, QuotientPtr Q2)
{
	if (!Q || !Q1 || !Q2) return ERROR; //合法性检查
	Q->numerator = Q1->numerator * Q2->denominator - Q2->numerator * Q1->denominator;
	Q->denominator = Q1->denominator * Q2->denominator;

	QuotientReduction(Q);

	return OK;
}

//有理数乘法
Status QuotientMultiplication(QuotientPtr &Q, QuotientPtr Q1, QuotientPtr Q2)
{
	if (!Q || !Q1 || !Q2) return ERROR; //合法性检查
	Q->numerator = Q1->numerator * Q2->numerator;
	Q->denominator = Q1->denominator * Q2->denominator;

	QuotientReduction(Q);

	return OK;
}

//有理数除法
Status QuotientDivision(QuotientPtr &Q, QuotientPtr Q1, QuotientPtr Q2)
{
	Quotient q;			// 避免在 Q = Q1 或 Q = Q2 的情形出错;

	if (!Q || !Q1 || !Q2) return ERROR; //合法性检查
	if (Q2->numerator == 0) {
	printf("Divide 0 error.\n");
	return ERROR;
	}

	q.numerator = Q1->numerator * Q2->denominator; //存放中间结果
	q.denominator = Q1->denominator * Q2->numerator; //存放中间结果
	Q->numerator = q.numerator;	
	Q->denominator = q.denominator;

	QuotientReduction(Q);

	return OK;
}

//有理数的约分及化简
Status QuotientReduction(QuotientPtr &Q)
{
	int gcd;

	if (!Q) return ERROR;		//合法性检查
	gcd = FindGCD(Q->numerator, Q->denominator); //求分子、分母的最大公因子
	Q->numerator = Q->numerator / gcd;
	Q->denominator = Q->denominator / gcd;

	//assure that the denominator always is positive.
	if( Q->denominator<0 )
	{
		Q->numerator = -(Q->numerator);
		Q->denominator = -(Q->denominator);
	}

	return OK;
}

//求最大公约数
int FindGCD(int m, int n)
{
	int r;
	r = m % n;
	m = m / n;
	while(r)
	{
	  m = n;
	  n = r;
	  r = m % n;
	}

	return n;
}