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Commit 8155c44

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lxylxy123456lxylxy123456
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allow Fraction
1 parent 8f6a8ee commit 8155c44

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+152
-10
lines changed

2 files changed

+152
-10
lines changed

‎LUPSolve.cpp

Lines changed: 141 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -30,6 +30,132 @@
3030

3131
using PT = std::vector<size_t>;
3232

33+
template <typename T>
34+
class Fraction
35+
{
36+
public:
37+
Fraction(): numerator(0), denominator(0) {}
38+
Fraction(T a): numerator(a), denominator(1) {}
39+
Fraction(T a, T b): numerator(a), denominator(b) {
40+
if (!b)
41+
throw std::invalid_argument("zero denominator");
42+
reduce_fraction();
43+
}
44+
Fraction& operator= (const Fraction& rhs) {
45+
if (&rhs == this)
46+
return *this;
47+
if (!rhs.denominator)
48+
throw std::invalid_argument("zero denominator");
49+
this->numerator = rhs.numerator;
50+
this->denominator = rhs.denominator;
51+
return *this;
52+
}
53+
const Fraction operator- () const {
54+
if (!denominator)
55+
throw std::invalid_argument("zero denominator");
56+
return Fraction(-numerator, denominator);
57+
}
58+
const Fraction operator+ (const Fraction& a) const {
59+
if (!denominator || !a.denominator)
60+
throw std::invalid_argument("zero denominator");
61+
int num = numerator * a.denominator + denominator * a.numerator;
62+
int den = denominator * a.denominator;
63+
return Fraction(num, den);
64+
}
65+
const Fraction operator- (const Fraction& a) const {
66+
if (!denominator || !a.denominator)
67+
throw std::invalid_argument("zero denominator");
68+
int num = numerator * a.denominator - denominator * a.numerator;
69+
int den = denominator * a.denominator;
70+
return Fraction(num, den);
71+
}
72+
const Fraction operator* (const Fraction& a) const {
73+
if (!denominator || !a.denominator)
74+
throw std::invalid_argument("zero denominator");
75+
int num = numerator * a.numerator;
76+
int den = denominator * a.denominator;
77+
return Fraction(num, den);
78+
}
79+
const Fraction operator/ (const Fraction& a) const {
80+
if (!denominator || !a.denominator)
81+
throw std::invalid_argument("zero denominator");
82+
int num = numerator * a.denominator;
83+
int den = denominator * a.numerator;
84+
return Fraction(num, den);
85+
}
86+
Fraction& operator+= (const Fraction& a) {
87+
if (!denominator || !a.denominator)
88+
throw std::invalid_argument("zero denominator");
89+
int num = numerator * a.denominator + denominator * a.numerator;
90+
int den = denominator * a.denominator;
91+
numerator = num;
92+
denominator = den;
93+
reduce_fraction();
94+
return *this;
95+
}
96+
Fraction& operator-= (const Fraction& a) {
97+
if (!denominator || !a.denominator)
98+
throw std::invalid_argument("zero denominator");
99+
int num = numerator * a.denominator - denominator * a.numerator;
100+
int den = denominator * a.denominator;
101+
numerator = num;
102+
denominator = den;
103+
reduce_fraction();
104+
return *this;
105+
}
106+
Fraction& operator*= (const Fraction& a) {
107+
if (!denominator || !a.denominator)
108+
throw std::invalid_argument("zero denominator");
109+
numerator *= a.numerator;
110+
denominator *= a.denominator;
111+
reduce_fraction();
112+
return *this;
113+
}
114+
Fraction& operator/= (const Fraction& a) {
115+
if (!denominator || !a.denominator)
116+
throw std::invalid_argument("zero denominator");
117+
numerator *= a.denominator;
118+
denominator *= a.numerator;
119+
reduce_fraction();
120+
return *this;
121+
}
122+
bool operator< (const Fraction& a) const {
123+
if (!denominator || !a.denominator)
124+
throw std::invalid_argument("zero denominator");
125+
return numerator * a.denominator < denominator * a.numerator;
126+
}
127+
bool operator== (const Fraction& a) const {
128+
if (!denominator || !a.denominator)
129+
throw std::invalid_argument("zero denominator");
130+
return numerator == a.numerator && denominator == a.denominator;
131+
}
132+
friend std::ostream& operator<< (std::ostream& os, const Fraction& v) {
133+
if (!v.denominator)
134+
throw std::invalid_argument("zero denominator");
135+
if (v.denominator == 1)
136+
return os << v.numerator;
137+
else
138+
return os << v.numerator << '/' << v.denominator;
139+
}
140+
T numerator;
141+
T denominator;
142+
void reduce_fraction() {
143+
// some idea from "reduce_fraction.c"
144+
T a = numerator, b = denominator, tmp;
145+
while (b) {
146+
tmp = a % b;
147+
a = b;
148+
b = tmp;
149+
}
150+
// now abs(a) == abs(gcd(a, b))
151+
if ((denominator > 0) ^ (a > 0))
152+
a = -a;
153+
// now a == abs(gcd(a, b)) * sgn(b)
154+
numerator /= a;
155+
denominator /= a;
156+
}
157+
};
158+
33159
template <typename T>
34160
Matrix<T> LUPSolve(Matrix<T>& L, Matrix<T>& U, PT& pi, Matrix<T>& b) {
35161
size_t n = L.rows;
@@ -78,13 +204,13 @@ PT LUPDecomposition(Matrix<T>& A) {
78204
T p = 0;
79205
size_t kk;
80206
for (size_t i = k; i < n; i++) {
81-
T abs = A[i][k] < 0 ? -A[i][k] : A[i][k];
82-
if (abs > p) {
207+
T abs = A[i][k] < (T) 0 ? -A[i][k] : A[i][k];
208+
if (p < abs) {
83209
p = abs;
84210
kk = i;
85211
}
86212
}
87-
if (p == 0)
213+
if (p == (T) 0)
88214
throw std::invalid_argument("singular matrix");
89215
std::swap(pi[k], pi[kk]);
90216
for (size_t i = 0; i < n; i++)
@@ -100,13 +226,11 @@ PT LUPDecomposition(Matrix<T>& A) {
100226
#endif
101227

102228
#ifdef MAIN_LUPSolve
103-
int main(int argc, char *argv[]) {
104-
const size_t n = get_argv(argc, argv, 1, 16);
105-
const size_t compute = get_argv(argc, argv, 2, 3);
229+
template <typename T>
230+
void main_T(const size_t n, const size_t compute) {
106231
std::vector<int> int_a, int_b;
107232
random_integers(int_a, -n, n, n * n);
108233
random_integers(int_b, -n, n, n);
109-
using T = double;
110234
std::vector<T> buf_a(n * n), buf_b(n);
111235
for (size_t i = 0; i < int_a.size(); i++)
112236
buf_a[i] = int_a[i];
@@ -144,6 +268,16 @@ int main(int argc, char *argv[]) {
144268
output_integers(ans2[i], "\t");
145269
}
146270
std::cout << std::endl;
271+
}
272+
273+
int main(int argc, char *argv[]) {
274+
const size_t type = get_argv(argc, argv, 1, 0);
275+
const size_t n = get_argv(argc, argv, 2, 5);
276+
const size_t compute = get_argv(argc, argv, 3, 3);
277+
if (!type)
278+
main_T<double>(n, compute);
279+
else
280+
main_T<Fraction<int>>(n, compute);
147281
return 0;
148282
}
149283
#endif

‎MatrixInverse.cpp

Lines changed: 11 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -44,11 +44,10 @@ Matrix<T> MatrixInverse(Matrix<T>& A) {
4444
#endif
4545

4646
#ifdef MAIN_MatrixInverse
47-
int main(int argc, char *argv[]) {
48-
const size_t n = get_argv(argc, argv, 1, 6);
47+
template <typename T>
48+
void main_T(const size_t n) {
4949
std::vector<int> int_a, int_b;
5050
random_integers(int_a, -n, n, n * n);
51-
using T = double;
5251
std::vector<T> buf_a(n * n), buf_b(n);
5352
for (size_t i = 0; i < int_a.size(); i++)
5453
buf_a[i] = int_a[i];
@@ -58,6 +57,15 @@ int main(int argc, char *argv[]) {
5857
std::cout << B << std::endl;
5958
Matrix<T> C = SquareMatrixMultiply(A, B, (T) 0);
6059
std::cout << C << std::endl;
60+
}
61+
62+
int main(int argc, char *argv[]) {
63+
const size_t type = get_argv(argc, argv, 1, 0);
64+
const size_t n = get_argv(argc, argv, 2, 5);
65+
if (!type)
66+
main_T<double>(n);
67+
else
68+
main_T<Fraction<int>>(n);
6169
return 0;
6270
}
6371
#endif

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