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425#include "frac.h"
Frac::Frac(int value, const QString &key) {
if(value != 0)
mMapPoly[key] = value;
}
Frac::Frac(int a, int b) {
if(b == 0)
throw FracError("cannot div 0");
if(a != 0)
mMapPoly[""] = a;
this->b = b;
reduct();
}
Frac::Frac(QString str, bool *ok) {
str.replace(' ', "");
int indexOfDiv = str.indexOf("/");
if(indexOfDiv == -1) {
bool ok2;
int value = str.toInt(&ok2);
if(ok2) {
mMapPoly[""] = value;
} else {
SET_PTR(ok, false);
return;
}
} else {
bool ok2;
int top = str.left(indexOfDiv).toInt(&ok2);
if(!ok2) {
SET_PTR(ok, false);
return;
}
int bottom = str.right(str.length() - indexOfDiv - 1).toInt(&ok2);
if(!ok2 || bottom == 0) {
SET_PTR(ok, false);
return;
}
mMapPoly[""] = top;
b = bottom;
}
reduct();
SET_PTR(ok, true);
}
Frac::Frac(const PlainFrac &plain) {
if(plain.a == 0)
return;
mMapPoly[""] = plain.a;
b = plain.b;
}
PlainFrac Frac::toPlain() {
int a = mMapPoly.value("", 0);
return PlainFrac(a, b);
}
//void Frac::checkZero() {
// QStringList lNeedRemoveMono;
// for(auto iter = mapPoly.begin(); iter != mapPoly.end(); ++iter)
// if(iter.value() == 0)
// lNeedRemoveMono << iter.key();
// for(QString& mono : lNeedRemoveMono)
// mapPoly.remove(mono);
// if(mapPoly.isEmpty())
// b = 1;
//}
//#define DEBUG_FRAC_SOLVINGRQUATIONS
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
#include <QDebug>
#endif
QList<Frac> Frac::SolvingEquations(const QList<Frac> &lFracs, const QStringList &lUnkNumbers, SolvingError *err) {
return SolvingEquations(lFracs, lUnkNumbers, QStringList(), err);
}
QList<Frac> Frac::SolvingEquations(QList<Frac> lFracs, const QStringList &lUnkNumbers,
const QStringList &lRemoveLetters, SolvingError *err)
{
//对于可以直接判断无解的情况，就结束该函数
if(lUnkNumbers.isEmpty()) {
SET_PTR(err, SolvingError::Unsolvable);
return QList<Frac>();
}
if(lFracs.size() < lUnkNumbers.size()) {
SET_PTR(err, SolvingError::Insufficient);
return QList<Frac>();
}
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug().noquote() << "\033[35m初始:\033[0m";
for(Frac &frac : lFracs)
qDebug().noquote() << frac.format(true, true) << "= 0";
#endif
for(const QString &remove : lRemoveLetters) {
//如果未知数中存在该字母，则跳过本次循环
if(lUnkNumbers.contains(remove))
continue;
auto iter = lFracs.end();
//查找第一个该字母出现的位置
for(auto listIter = lFracs.begin(); listIter != lFracs.end(); ++listIter) {
if((*listIter).mMapPoly.contains(remove)) {
iter = listIter;
break;
}
}
//如果无法从现有的式子中找到该字母，就跳过本次循环
if(iter == lFracs.end())
continue;
Frac paramFrac = (*iter).paramSep(remove); //分离该字母
lFracs.erase(iter); //从lFracs中移除该iter
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug().noquote() << "\n\033[35m将\033[0m " + remove + " = " + paramFrac.format(true, true) + " \033[35m代入得:\033[0m";
#endif
for(Frac &otherFrac : lFracs) { //将分离的结果代入到其他式子中
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug().noquote() << otherFrac.substitute(remove, paramFrac).format(true, true) << "= 0";
#else
otherFrac.substitute(remove, paramFrac);
#endif
}
}
QList<Frac> lRes;
for(const QString &unkNumber : lUnkNumbers) {
auto iter = lFracs.end();
//查找第一个该未知数出现的式子
for(auto listIter = lFracs.begin(); listIter != lFracs.end(); ++listIter) {
if((*listIter).mMapPoly.contains(unkNumber)) {
iter = listIter;
break;
}
}
//如果无法从现有的式子中找到该未知数，就结束该函数
if(iter == lFracs.end()) {
SET_PTR(err, SolvingError::Insufficient);
return QList<Frac>();
}
Frac paramFrac = (*iter).paramSep(unkNumber); //分离该未知数
lRes << paramFrac; //将其加入到结果list中
lFracs.erase(iter); //从lFracs中移除该iter
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug().noquote() << "\n\033[35m将\033[0m " + unkNumber + " = " + paramFrac.format(true, true) + " \033[35m代入得:\033[0m";
#endif
for(Frac &otherFrac : lFracs) { //将分离的结果代入到其他式子中
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug().noquote() << otherFrac.substitute(unkNumber, paramFrac).format(true, true) << "= 0";
#else
otherFrac.substitute(unkNumber, paramFrac);
#endif
}
}
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug() << "\n\033[35m多余项:\033[0m";
for(Frac &frac : lFracs) {
qDebug().noquote() << frac.format(true, true) << "= 0";
}
#endif
for(Frac &frac : lFracs) { //判断是否无解(若有任何一个多余项不为0，就无解)
if(!frac.mMapPoly.isEmpty()) {
SET_PTR(err, SolvingError::Unsolvable);
return QList<Frac>();
}
}
{//往回代入，求出所有的未知数
auto iterUnkNum = lUnkNumbers.rbegin();
for(auto iterGet = lRes.rbegin(); iterGet != lRes.rend(); ++iterGet) {
Frac &cur = *iterGet;
for(auto iterSet = iterGet + 1; iterSet != lRes.rend(); ++iterSet)
(*iterSet).substitute(*iterUnkNum, cur);
++iterUnkNum;
}
}
for(Frac &frac : lRes) //将分母的负号移至分子
frac.moveNegativeToTop();
#ifdef DEBUG_FRAC_SOLVINGRQUATIONS
qDebug().noquote() << "\n\033[35m结果:\033[0m";
{
auto iterUnkNum = lUnkNumbers.begin();
for(auto iter = lRes.begin(); iter != lRes.end(); ++iter) {
qDebug().noquote() << *iterUnkNum << "=" << (*iter).format(true, true);
++iterUnkNum;
}
}
#endif
SET_PTR(err, SolvingError::NoError);
return lRes;
}
void Frac::reduct() {
// checkZero();
if(mMapPoly.isEmpty()) {
b = 1;
return;
}
while(true) {
QVector<int> vValues { b };
for(int value : mMapPoly)
vValues << value;
int divNum = j::Gcd(vValues);
if(divNum == 1 || divNum == 0)
break;
for(int &value : mMapPoly)
value /= divNum;
b /= divNum;
}
}
Frac& Frac::changeMono(const QString &before, const QString &now) {
if(before != now) {
auto iter = mMapPoly.find(before);
if(iter != mMapPoly.end()) {
mMapPoly[now] += *iter;
mMapPoly.erase(iter);
}
}
return *this;
}
Frac Frac::paramSep(const QString ¶m, bool *ok) {
// checkZero();
if(!mMapPoly.contains(param)) {
SET_PTR(ok, false);
return Frac();
}
Frac res = *this;
res.b = 1;
res.mMapPoly.remove(param);
res.div(-mMapPoly[param]);
res.reduct();
SET_PTR(ok, true);
return res;
}
Frac& Frac::substitute(const QString ¶m, int digit) {
auto iter = mMapPoly.find(param);
if(iter != mMapPoly.end()) {
int value = iter.value();
if((mMapPoly[""] += value * digit) == 0)
mMapPoly.remove("");
mMapPoly.erase(iter);
reduct();
}
return *this;
}
Frac& Frac::substitute(const QString ¶m, const Frac &other) {
auto iter = mMapPoly.find(param);
if(iter != mMapPoly.end()) {
int valueMul = iter.value();
mMapPoly.erase(iter);
b *= other.b;
for(int &mono : mMapPoly)
mono *= other.b;
for(auto otherIter = other.mMapPoly.begin(); otherIter != other.mMapPoly.end(); ++otherIter)
if((mMapPoly[otherIter.key()] += otherIter.value() * valueMul) == 0)
mMapPoly.remove(otherIter.key());
reduct();
}
return *this;
}
Frac& Frac::moveNegativeToTop() {
if(b < 0) {
b = -b;
for(int &mono : mMapPoly)
mono = -mono;
}
return *this;
}
QString Frac::format(bool autoSpace, bool useColor) const {
QString res;
int size = mMapPoly.size();
if(size == 0) {
res = "0";
return res;
}
if(b != 1 && size != 1)
res += "(";
bool hasPrev = false;
for(auto iter = mMapPoly.begin(); iter != mMapPoly.end(); ++iter) {
const QString& key = iter.key();
int value = iter.value();
if(hasPrev) {
res += value < 0 ? (autoSpace ? " - " : "-") : (autoSpace ? " + " : "+");
} else {
if(value < 0) res += '-';
hasPrev = true;
}
if(qAbs(value) != 1 || key.isEmpty())
res += QString::number(qAbs(value));
if(!key.isEmpty())
res += (useColor ? "\033[33m[\033[0m" : "[") + key + (useColor ? "\033[33m]\033[0m" : "]");
}
if(b != 1) {
if(size != 1)
res += ")";
res += autoSpace ? " / " : "/";
res += QString::number(b);
}
return res;
}
Frac& Frac::sum(int digit, const QString &key) {
if(digit != 0) {
digit *= b;
if((mMapPoly[key] += digit ) == 0)
mMapPoly.remove(key);
reduct();
}
return *this;
}
Frac& Frac::sub(int digit, const QString &key) {
if(digit != 0) {
digit *= b;
if((mMapPoly[key] -= digit) == 0)
mMapPoly.remove(key);
reduct();
}
return *this;
}
Frac& Frac::mul(int digit) {
if(digit == 0) {
mMapPoly.clear();
b = 1;
} else {
for(int &mono : mMapPoly)
mono *= digit;
reduct();
}
return *this;
}
Frac& Frac::div(int digit) {
if(digit == 0)
throw FracError("cannot div 0");
if(!mMapPoly.isEmpty()) {
b *= digit;
reduct();
}
return *this;
}
Frac& Frac::sum(const Frac &other) {
if(!other.mMapPoly.isEmpty()) {
int commonMulti = j::Lcm(b, other.b);
int selfMulti = commonMulti / b;
int otherMulti = commonMulti / other.b;
b = commonMulti;
for(int &mono : mMapPoly)
mono *= selfMulti;
for(QMap<QString, int>::const_iterator iter = other.mMapPoly.begin(); iter != other.mMapPoly.end(); ++iter)
if((mMapPoly[iter.key()] += iter.value() * otherMulti) == 0)
mMapPoly.remove(iter.key());
reduct();
}
return *this;
}
Frac& Frac::sub(const Frac &other) {
if(!other.mMapPoly.isEmpty()) {
int CommonMulti = j::Lcm(b, other.b);
int selfMulti = CommonMulti / b;
int otherMulti = CommonMulti / other.b;
b = CommonMulti;
for(int &mono : mMapPoly)
mono *= selfMulti;
for(QMap<QString, int>::const_iterator iter = other.mMapPoly.begin(); iter != other.mMapPoly.end(); ++iter)
if((mMapPoly[iter.key()] -= iter.value() * otherMulti) == 0)
mMapPoly.remove(iter.key());
reduct();
}
return *this;
}
Frac& Frac::mul(const PlainFrac &other) {
if(other.a == 0) {
mMapPoly.clear();
b = 1;
} else {
for(int &mono : mMapPoly)
mono *= other.a;
b *= other.b;
reduct();
}
return *this;
}
Frac& Frac::div(const PlainFrac &other) {
if(other.a == 0)
throw FracError("cannot div 0");
for(int &mono : mMapPoly)
mono *= other.b;
b *= other.a;
reduct();
return *this;
}