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| 1 | #include <map> | |
| 2 | #include <iostream> | |
| 3 | #include <vector> | |
| 4 | #include <complex> | |
| 5 | #include <functional> | |
| 6 | ||
| 7 | using namespace std; | |
| 8 | class LINP | |
| 9 | {
| |
| 10 | - | typedef map<int/*pow*/, double/*num*/, greater<int> > value_type; |
| 10 | + | |
| 11 | typedef map<int/*Index*/, double/*Coeff*/, greater<int> > value_type; | |
| 12 | ||
| 13 | - | LINP(): cont() |
| 13 | + | |
| 14 | - | {
|
| 14 | + | LINP(): cont() {
|
| 15 | cont[1] = 1; | |
| 16 | }; | |
| 17 | - | LINP(int rhs): cont() |
| 17 | + | LINP(int rhs): cont() {
|
| 18 | - | {
|
| 18 | + | |
| 19 | }; | |
| 20 | ||
| 21 | - | LINP operator [](int rhs) const//FIXME: Use operator *() to do this |
| 21 | + | LINP operator [](int rhs) const {
|
| 22 | - | {
|
| 22 | + | |
| 23 | tmp.cont.clear(); | |
| 24 | tmp.cont[rhs] = getCoeffOfIndex(1); | |
| 25 | - | tmp.cont[rhs] = getNumOfPow(1); |
| 25 | + | |
| 26 | } | |
| 27 | ||
| 28 | - | LINP operator *(double rhs) const |
| 28 | + | LINP& operator *=(double rhs) {
|
| 29 | - | {
|
| 29 | + | for (auto& v : cont) |
| 30 | v.second *= rhs; | |
| 31 | - | for (value_type::iterator it=tmp.cont.begin(); it!=tmp.cont.end(); ++it) |
| 31 | + | return *this; |
| 32 | - | it->second *= rhs; |
| 32 | + | |
| 33 | LINP operator *(double rhs) const {
| |
| 34 | LINP tmp(*this); | |
| 35 | - | LINP operator +(const LINP& rhs) const |
| 35 | + | tmp *= rhs; |
| 36 | - | {
|
| 36 | + | |
| 37 | } | |
| 38 | - | for (value_type::const_iterator it=rhs.cont.begin(); it!=rhs.cont.end(); ++it) |
| 38 | + | |
| 39 | - | tmp.cont[it->first] += it->second; |
| 39 | + | LINP operator *=(const LINP& rhs) const {
|
| 40 | // Unimplimented | |
| 41 | } | |
| 42 | - | LINP operator -() const |
| 42 | + | LINP operator *(const LINP& rhs) const {
|
| 43 | - | {
|
| 43 | + | |
| 44 | tmp *= rhs; | |
| 45 | - | for (value_type::iterator it=tmp.cont.begin(); it!=tmp.cont.end(); ++it) |
| 45 | + | |
| 46 | - | it->second=-it->second; |
| 46 | + | |
| 47 | ||
| 48 | LINP& operator +=(const LINP& rhs) {
| |
| 49 | - | LINP operator -(const LINP& rhs) const |
| 49 | + | for (auto& v : rhs.cont) |
| 50 | - | {
|
| 50 | + | this->cont[v.first] += v.second; |
| 51 | - | return *this+(-rhs); |
| 51 | + | return *this; |
| 52 | } | |
| 53 | - | friend ostream& operator <<(ostream& os, const LINP& rhs) |
| 53 | + | |
| 54 | - | {
|
| 54 | + | LINP operator +(const LINP& rhs) const {
|
| 55 | LINP tmp(*this); | |
| 56 | - | it!=rhs.cont.end(); ++it) |
| 56 | + | tmp += rhs; |
| 57 | return tmp; | |
| 58 | } | |
| 59 | ||
| 60 | LINP& operator -=(const LINP& rhs) {
| |
| 61 | for (auto& v : rhs.cont) | |
| 62 | this->cont[v.first] -= v.second; | |
| 63 | return *this; | |
| 64 | } | |
| 65 | LINP operator -(const LINP& rhs) const {
| |
| 66 | LINP tmp(*this); | |
| 67 | tmp -= rhs; | |
| 68 | return tmp; | |
| 69 | } | |
| 70 | LINP operator -() const {
| |
| 71 | LINP tmp(*this); | |
| 72 | for (auto& v : tmp.cont) | |
| 73 | v.second = -v.second; | |
| 74 | return tmp; | |
| 75 | } | |
| 76 | ||
| 77 | friend ostream& operator <<(ostream& os, const LINP& rhs) {
| |
| 78 | for (value_type::const_iterator it=rhs.cont.begin(); | |
| 79 | - | int maxPow() const |
| 79 | + | it != rhs.cont.end(); ++it) |
| 80 | - | {
|
| 80 | + | |
| 81 | if (it->second != 0) | |
| 82 | {
| |
| 83 | - | int minPow() const |
| 83 | + | |
| 84 | - | {
|
| 84 | + | |
| 85 | if (it->second < 0) | |
| 86 | cout << '-'; | |
| 87 | - | double getNumOfPow(int Pow) const |
| 87 | + | |
| 88 | - | {
|
| 88 | + | |
| 89 | - | value_type::const_iterator it=cont.find(Pow); |
| 89 | + | |
| 90 | - | return it!=cont.end()? it->second : 0; |
| 90 | + | |
| 91 | {
| |
| 92 | - | vector<complex<double> > solve() const throw(exception) //Solve: *this=0 |
| 92 | + | |
| 93 | - | {
|
| 93 | + | |
| 94 | - | if (maxPow()>2 || minPow()<0) |
| 94 | + | |
| 95 | } | |
| 96 | } | |
| 97 | - | result.reserve(maxPow()); |
| 97 | + | |
| 98 | - | if (maxPow()==1) |
| 98 | + | |
| 99 | - | result.push_back(-getNumOfPow(0)/getNumOfPow(1)); |
| 99 | + | |
| 100 | return os; | |
| 101 | } | |
| 102 | - | complex<double> delta=pow(getNumOfPow(1), 2)-4*getNumOfPow(2)*getNumOfPow(0); |
| 102 | + | |
| 103 | - | result.push_back((-getNumOfPow(1)+sqrt(delta))/(2*getNumOfPow(2))); |
| 103 | + | int maxIndex() const {
|
| 104 | - | result.push_back((-getNumOfPow(1)-sqrt(delta))/(2*getNumOfPow(2))); |
| 104 | + | |
| 105 | } | |
| 106 | int minIndex() const {
| |
| 107 | return cont.rbegin()->first; | |
| 108 | } | |
| 109 | ||
| 110 | double getCoeffOfIndex(int Index) const {
| |
| 111 | value_type::const_iterator it=cont.find(Index); | |
| 112 | return it != cont.end() ? it->second : 0; | |
| 113 | } | |
| 114 | ||
| 115 | vector<complex<double> > solve() const throw(exception) {
| |
| 116 | if (maxIndex()>2 || minIndex()<0) | |
| 117 | throw std::exception(); | |
| 118 | vector<complex<double> > result; | |
| 119 | result.reserve(maxIndex()); | |
| 120 | if (maxIndex()==1) | |
| 121 | result.push_back(-getCoeffOfIndex(0)/getCoeffOfIndex(1)); | |
| 122 | else // maxPow()==2 | |
| 123 | {
| |
| 124 | complex<double> delta=pow(getCoeffOfIndex(1), 2)-4*getCoeffOfIndex(2)*getCoeffOfIndex(0); | |
| 125 | result.push_back((-getCoeffOfIndex(1)+sqrt(delta))/(2*getCoeffOfIndex(2))); | |
| 126 | result.push_back((-getCoeffOfIndex(1)-sqrt(delta))/(2*getCoeffOfIndex(2))); | |
| 127 | } | |
| 128 | return result; | |
| 129 | } | |
| 130 | ||
| 131 | private: | |
| 132 | value_type cont; | |
| 133 | }; | |
| 134 | ||
| 135 | int main() | |
| 136 | {
| |
| 137 | LINP linp=LINP()-(LINP()*0.5+1)-1; | |
| 138 | cout << linp << " = 0" << endl; | |
| 139 | cout << "X = " << linp.solve().front().real() << endl << endl; | |
| 140 | ||
| 141 | LINP linp2=LINP()[2]+LINP()*2+1; | |
| 142 | cout << linp2 << " = 0" << endl; | |
| 143 | cout << "X1 = X2 = " << linp2.solve().front().real() << endl << endl; | |
| 144 | ||
| 145 | LINP linp3=LINP()[2]+1; | |
| 146 | cout << linp3 << " = 0" << endl; | |
| 147 | vector<complex<double> > result=linp3.solve(); | |
| 148 | cout << "x1 = " << result[0].real() << " + " << result[0].imag() << 'i' << endl | |
| 149 | << "x2 = " << result[1].real() << " + " << result[1].imag() << 'i' << endl << endl; | |
| 150 | } |