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eee102/as1/Fraction.h

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/**
* 分数运算 Fraction
*
* @category eee102-as1
* @package Fraction.h
* @copyright Copyright (c) 2019 Yimian LIU (https://iotcat.me)
* @license GNU General Public License 2.0
* @version 0.0.1
*/
#ifndef _Fraction_H_
#define _Fraction_H_
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <sstream>
#include <cmath>
using namespace std;
/**
* 分数运算
*
* @author yimian LIU
* @category eee102-as1
* @package Fraction.h
*/
class Fraction {
public:
/* 默认构造 */
Fraction(){
ini();
_bottom = 1;
};
/* 分子，分母输入构造 */
Fraction(int top, int bottom){
set(top, bottom);
};
/* 小数输入构造 */
Fraction(double d){
set(d);
};
/* 拷贝构造 */
Fraction(const Fraction& obj){
set(obj.top(), obj.bottom());
};
/* 析构 */
~Fraction(){};
/* 加法重载 */
Fraction operator +(const Fraction& obj) const{
return Fraction(this->top() * obj.bottom() + this->bottom() * obj.top(), this->bottom() * obj.bottom());
};
/* 加法重载(后) */
friend Fraction operator +(const double d, const Fraction& obj){
return obj + d;
};
/* 减法重载 */
Fraction operator -(const Fraction& obj) const{
return Fraction(this->top() * obj.bottom() - this->bottom() * obj.top(), this->bottom() * obj.bottom());
};
/* 乘法重载 */
Fraction operator *(const Fraction& obj) const{
return Fraction(this->top() * obj.top(), this->bottom() * obj.bottom());
};
/* 乘法重载(后) */
friend Fraction operator *(const double d, const Fraction& obj){
return obj * d;
};
/* 除法重载 */
Fraction operator /(const Fraction& obj) const{
return Fraction(this->top() * obj.bottom(), this->bottom() * obj.top());
};
/* 求余重载 */
Fraction operator %(const Fraction& obj) const{
return Fraction(fmod(this->val(), obj.val()));
};
/* 求余重载 */
Fraction operator %(const int t) const{
return Fraction(fmod(this->val(), t));
};
/* 求余重载 */
Fraction operator %(const double t) const{
return Fraction(fmod(this->val(), t));
};
/* 负号重载 */
Fraction operator -() const{
return Fraction(-this->top(), this->bottom());
};
/* 倒数重载 */
Fraction operator ~() const{
return Fraction(this->bottom(), this->top());
};
/* 小于号重载 */
bool operator <(const Fraction& obj) const{
return (this->val() < obj.val())? true : false;
};
/* 小于等于号重载 */
bool operator <=(const Fraction& obj) const{
return (this->val() <= obj.val())? true : false;
};
/* 大于号重载 */
bool operator >(const Fraction& obj) const{
return (this->val() > obj.val())? true : false;
};
/* 大于等于号重载 */
bool operator >=(const Fraction& obj) const{
return (this->val() >= obj.val())? true : false;
};
/* 等于号重载 */
bool operator ==(const Fraction& obj) const{
return (this->top() == obj.top() && this->bottom() == obj.bottom())? true : false;
};
/* 不等于号重载 */
bool operator !=(const Fraction& obj) const{
return (!(this->top() == obj.top() && this->bottom() == obj.bottom()))? true : false;
};
/* 前++重载 */
Fraction operator ++(){
if(_isNegative) _top -= _bottom;
else _top += _bottom;
return *this;
};
/* 后++重载 */
Fraction operator ++(int){
Fraction f = *this;
if(_isNegative) _top -= _bottom;
else _top += _bottom;
return f;
};
/* 前--重载 */
Fraction operator --(){
if(_isNegative) _top += _bottom;
else _top -= _bottom;
return *this;
};
/* 后--重载 */
Fraction operator --(int){
Fraction f = *this;
if(_isNegative) _top += _bottom;
else _top -= _bottom;
return f;
};
/* 赋值重载 */
void operator =(const Fraction& obj){
set(obj.top(), obj.bottom());
};
/* 赋值重载 */
void operator =(const double& d){
set(d);
};
/* 加法赋值重载 */
Fraction operator +=(const Fraction& obj){
set(this->top() * obj.bottom() + this->bottom() * obj.top(), this->bottom() * obj.bottom());
return *this;
};
/* 减法赋值重载 */
Fraction operator -=(const Fraction& obj){
set(this->top() * obj.bottom() - this->bottom() * obj.top(), this->bottom() * obj.bottom());
return *this;
};
/* 乘法赋值重载 */
Fraction operator *=(const Fraction& obj){
set(this->top() * obj.top(), this->bottom() * obj.bottom());
return *this;
};
/* 除法赋值重载 */
Fraction operator /=(const Fraction& obj){
set(this->top() * obj.bottom(), this->bottom() * obj.top());
return *this;
};
/* 输出流重载 */
friend ostream &operator <<(ostream &o, Fraction f){
o << f.toStr();
return o;
};
/* 输入流重载 */
friend istream &operator >>(istream &i, Fraction &f){
string s;
stringstream ss;
i >> s;
if(s.find("/") != s.npos){
int top, bottom;
ss << s.substr(0, s.find("/"));
ss >> top;
ss.clear(); //清stream缓存
ss.str("");
ss << s.substr(s.find("/") + 1);
ss >> bottom;
f.set(top, bottom);
}else{
double val;
ss << s;
ss >> val;
f.set(val);
}
};
/* 分数形式输入配置 */
inline void set(int top = 0, int bottom = 1){
ini();
adjust_minus(top, bottom);
is_bottom_zero();
simplify();
};
/* 小数形式输入配置 */
inline void set(double d = 0){
ini();
is_double_negative(d);
if(get_long_int_length(get_double_decimals_part(d)) > 3) repeated_decimal_to_fraction(d);
if(_bottom == 0) dec_to_frac_direct(d);
simplify();
};
/* 提取小数结果 */
inline double val() const{
return (double)_top / _bottom * ((_isNegative) ? -1 : 1);
}
/* 提取string形式分数结果 */
inline string toStr(){
stringstream ss;
if(_top == 0) return "0";
ss << ((_isNegative) ? "-" : "") << _top << ((_bottom == 1)? "" : "/");
if(_bottom != 1) ss << _bottom;
return ss.str();
};
/* 提取分子 */
inline int top() const{
return ((_isNegative) ? -1 : 1) * (int) _top;
};
/* 提取分母 */
inline int bottom() const{
return (int)_bottom;
};
private:
/* 主要变量 */
unsigned int _top;
unsigned int _bottom;
bool _isNegative;
/* 初始化 */
inline void ini(){
_top = 0;
_bottom = 0;
_isNegative = false;
};
/* 处理负号 */
inline void adjust_minus(int top, int bottom){
if(top < 0 && bottom < 0){
_isNegative = false;
_top = -1 * top;
_bottom = -1 * bottom;
return;
}
if(bottom < 0){
_isNegative = true;
_top = top;
_bottom = -1 * bottom;
return;
}
if(top < 0){
_isNegative = true;
_top = (-1 * top);
_bottom = bottom;
return;
}
_top = top;
_bottom = bottom;
};
/* 处理分母为0 */
inline void is_bottom_zero() const{
if(_bottom == 0){
throw "Division by zero condition!";
}
};
/* 通分，找最大公约数 */
int get_common_divisor() const;
/* 分数化简 */
inline void simplify(){
int t_divisor = get_common_divisor();
_top /= t_divisor;
_bottom /= t_divisor;
};
/* 针对double处理负号 */
inline void is_double_negative(double& d){
if(d < 0){
d *= -1;
_isNegative = true;
}else{
_isNegative = false;
}
};
/* 去除空格 */
void remove_space(string& s) const{
while(1){
size_t pos = s.find(" ");
if(pos == string::npos) return;
s.erase(pos, 1);
}
};
/* 小数强制转分数 */
void dec_to_frac_direct(double d);
/* 无限循环小数转分数 - 补丁 */
unsigned long int transfer_double_decimals_to_unsigned_long_int_for_single(const double& d) const;
/* 转换double小数部分到长整型 */
unsigned long int transfer_double_decimals_to_unsigned_long_int(const double& d);
/* 获取double小数整数部分 */
inline unsigned long int get_double_integer_part(const double& d) const{
return (unsigned long int)floor(fabs(d));
};
/* 获取double小数部分 */
inline unsigned long int get_double_decimals_part(const double& d){
double t;
return transfer_double_decimals_to_unsigned_long_int(fabs(d) - floor(fabs(d)));
};
/* 获取小数部分的某一位 */
inline unsigned short get_one_decimal(const unsigned long int& t, unsigned short point) const{
return (t / (unsigned int)pow(10, point - 1)) % 10;
};
/* 获取 int 长度 */
unsigned short get_long_int_length(long int t) const;
/* 获取循环小数循环体 */
unsigned int get_repeat_part(const unsigned long int& t);
/* 检查循环体顺序 */
void confirm_repeat_part(const unsigned long int& t, unsigned int& repeat, unsigned short& start);
/* 循环小数转分数 */
void repeated_decimal_to_fraction(double d);
};
/**
* 小数强制转分数
*
* @access private
* @param double d 要转换的值
* @return void
*/
void Fraction::dec_to_frac_direct(double d)
{
unsigned short t = get_long_int_length(get_double_decimals_part(d));
//cout << t << endl;
_top = d * (int)pow(10, t);
_bottom = (unsigned int)pow(10, t);
}
/**
* 找最大公约数
*
* @access private
* @param void
* @return int 最大公约数
*/
int Fraction::get_common_divisor() const
{
int t_top = _top;
int t_bottom = _bottom;
/* ensure that t_top is not smaller than t_buttom */
if(t_top < t_bottom){
t_top ^= t_bottom;
t_bottom = t_top ^ t_bottom;
t_top ^= t_bottom;
}
for(int tmp; t_bottom != 0;){
tmp = t_top % t_bottom;
t_top = t_bottom;
t_bottom = tmp;
}
return t_top;
}
/**
* 无限循环小数转分数 - 补丁
*
* @access private
* @param double d 需要过滤的数
* @return unsigned long int 转换结果
*/
unsigned long int Fraction::transfer_double_decimals_to_unsigned_long_int_for_single(const double& d) const
{
if(d > 0.09999999999 && d < 0.100000000001) return 1;
if(d > 0.19999999999 && d < 0.200000000001) return 2;
if(d > 0.29999999999 && d < 0.300000000001) return 3;
if(d > 0.39999999999 && d < 0.400000000001) return 4;
if(d > 0.49999999999 && d < 0.500000000001) return 5;
if(d > 0.59999999999 && d < 0.600000000001) return 6;
if(d > 0.69999999999 && d < 0.700000000001) return 7;
if(d > 0.79999999999 && d < 0.800000000001) return 8;
if(d > 0.89999999999 && d < 0.900000000001) return 9;
return 0;
}
/**
* 转换double小数部分到长整型
*
* @access private
* @param double d 需要转换的数
* @return unsigned long int 转换结果
*/
unsigned long int Fraction::transfer_double_decimals_to_unsigned_long_int(const double& d)
{
if(transfer_double_decimals_to_unsigned_long_int_for_single(d)) return transfer_double_decimals_to_unsigned_long_int_for_single(d);
unsigned long int t = (unsigned long int)(d*(1000000000));
while(d != 0 && (t % (t/10) == 0 || t % (t/10) == 9) && t > 100) t /= 10;
//if((unsigned long int)(d*(1000000000)) % 1000 == 999) return ++t;
return t;
}
/**
* 获取 int 长度
*
* @access private
* @param long int t 需要测量的数
* @return unsigned short 测量长度
*/
unsigned short Fraction::get_long_int_length(long int t) const
{
int count = 0;
while(t){
t /= 10;
count++;
}
return count;
}
/**
* 获取循环小数循环体
*
* @access private
* @param unsigned long int t 长整型的小数部分
* @return unsigned int 循环体
*/
unsigned int Fraction::get_repeat_part(const unsigned long int& t)
{
unsigned short i = 1;
unsigned short len = get_long_int_length(t);
while(i < len){
unsigned short count = 0;
while(i < len && get_one_decimal(t, ++i) != get_one_decimal(t, 1));
for(unsigned short j = 1; j < i; j++){
if(get_one_decimal(t, j) == get_one_decimal(t, j + i - 1)) count++;
}
//cout << "iii" << i << endl;
if(count == i - 1) return t % (unsigned int)pow(10, i - 1);
}
return 0;
}
/**
* 检查循环体顺序
*
* @access private
* @param unsigned long int t 长整型的小数部分
* @param unsigned short& repeat 循环体部分 引用
* @param unsigned short& start 循环起始位置 引用
* @return void
*/
void Fraction::confirm_repeat_part(const unsigned long int& t, unsigned int& repeat, unsigned short& start)
{
unsigned short len = get_long_int_length(repeat);
for(unsigned short i = get_long_int_length(t); i > len; i--){
bool k = false;
if(len == 1 && get_one_decimal(t, i) == get_one_decimal(repeat, 1)) k = true;
if(len == 2 && ((get_one_decimal(t, i) == get_one_decimal(repeat, 1) && get_one_decimal(t, i+1) == get_one_decimal(repeat, 2)) || (get_one_decimal(t, i+1) == get_one_decimal(repeat, 1) && get_one_decimal(t, i) == get_one_decimal(repeat, 2)))) k = true;
if(len == 3 && ((get_one_decimal(t, i) == get_one_decimal(repeat, 1) && get_one_decimal(t, i+1) == get_one_decimal(repeat, 2) && get_one_decimal(t, i+2) == get_one_decimal(repeat, 3)) || (get_one_decimal(t, i+1) == get_one_decimal(repeat, 1) && get_one_decimal(t, i+2) == get_one_decimal(repeat, 2) && get_one_decimal(t, i) == get_one_decimal(repeat, 3)) || (get_one_decimal(t, i+2) == get_one_decimal(repeat, 1) && get_one_decimal(t, i) == get_one_decimal(repeat, 2) && get_one_decimal(t, i+1) == get_one_decimal(repeat, 3)))) k = true;
if(k){
unsigned short t_repeat = t / (unsigned int)pow(10, i -1 - len) - (t / (unsigned int)pow(10, i - 1)) * (unsigned int)pow(10, len);
if(t_repeat == repeat && repeat < 10) start = i;
else if(t_repeat == repeat && repeat < 100) start = i + 1;
else if(t_repeat == repeat && repeat < 1000) start = i + 2;
else start = i;
repeat = t_repeat;
return;
}
}
}
/**
* 循环小数转分数
*
* @access private
* @param double d 待转小数
* @return void
*/
void Fraction::repeated_decimal_to_fraction(double d)
{
unsigned long int t = get_double_decimals_part(d);
unsigned short start = 0;
unsigned int up, down = 0;
unsigned int repeat = get_repeat_part(t);
//cout << repeat << endl;
confirm_repeat_part(t, repeat, start);
//cout << repeat << endl;
for(int i = 0; i < get_long_int_length(repeat); i++){
down += 9 * (unsigned int)pow(10, i);
}//cout << "sds" << down << " " << (get_long_int_length(t) - start) << endl;
down *= (get_long_int_length(t) - start > 0)? (unsigned int)pow(10, (get_long_int_length(t) - start)) : 1;
//cout << down << endl;
up = t % (unsigned int)pow(10, get_long_int_length(repeat)) + (t / (unsigned int)pow(10, start)) * ((unsigned int)pow(10, get_long_int_length(repeat)) - 1);
up = up + get_double_integer_part(d) * down;
//cout << up << endl;
_top = up;
_bottom = down;
}
#endif