題目連接:uva 684 - Integral Determinant
題目大意:給定一個行列式,求行列式的值。
解題思路:將行列式轉化成上三角的形式,值即為對角線上元素的積。因為要消元,又是整數,所以用分數去寫了。
#include
#include
#include
using namespace std;
typedef long long type;
struct Fraction {
type member; // 分子;
type denominator; // 分母;
Fraction (type member = 0, type denominator = 1);
void operator = (type x) { this->set(x, 1); }
Fraction operator * (const Fraction& u);
Fraction operator / (const Fraction& u);
Fraction operator + (const Fraction& u);
Fraction operator - (const Fraction& u);
void set(type member, type denominator);
};
inline type gcd (type a, type b) {
return b == 0 ? (a > 0 ? a : -a) : gcd(b, a % b);
}
inline type lcm (type a, type b) {
return a / gcd(a, b) * b;
}
/*Code*/
/////////////////////////////////////////////////////
const int maxn = 105;
typedef long long ll;
int N;
Fraction A[maxn][maxn];;
/*
bool cmp (const Fraction& a, const Fraction& b) {
ll p = a.member * b.denominator;
ll q = a.denominator * b.member;
if (p < 0)
p = -p;
if (q < 0)
q = -q;
return p > q;
}
*/
inline void self_swap (Fraction& a, Fraction& b) {
Fraction tmp = a;
a = b;
b = tmp;
}
ll solve () {
int sign = 1;
Fraction ret = 1;
for (int i = 0; i < N; i++) {
// printf("%d!\n", i);
int r = i;
for (int j = i+1; j < N; j++)
if (A[j][i].member)
r = j;
if (r != i) {
for (int j = 0; j < N; j++)
self_swap(A[i][j], A[r][j]);
sign *= -1;
}
if (A[i][i].member == 0 || A[i][i].denominator == 0)
return 0;
for (int j = i + 1; j < N; j++) {
Fraction f = A[j][i] / A[i][i];
for (int k = N-1; k >= 0; k--) {
A[j][k] = A[j][k] - (A[i][k] * f);
}
}
ret = ret * A[i][i];
}
/*
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
printf("%lld/%lld ", A[i][j].member, A[i][j].denominator);
printf("\n");
}
*/
if (ret.denominator < 0)
sign *= -1;
return ret.member * sign;
}
int main () {
while (scanf("%d", &N) == 1 && N) {
ll x;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
scanf("%lld", &x);
A[i][j] = x;
}
}
printf("%lld\n", solve());
}
printf("*\n");
return 0;
}
/////////////////////////////////////////////////////
Fraction::Fraction (type member, type denominator) {
this->set(member, denominator);
}
Fraction Fraction::operator * (const Fraction& u) {
type tmp_p = gcd(member, u.denominator);
type tmp_q = gcd(u.member, denominator);
return Fraction( (member / tmp_p) * (u.member / tmp_q), (denominator / tmp_q) * (u.denominator / tmp_p) );
}
Fraction Fraction::operator / (const Fraction& u) {
type tmp_p = gcd(member, u.member);
type tmp_q = gcd(denominator, u.denominator);
return Fraction( (member / tmp_p) * (u.denominator / tmp_q), (denominator / tmp_q) * (u.member / tmp_p));
}
Fraction Fraction::operator + (const Fraction& u) {
type tmp_l = lcm (denominator, u.denominator);
return Fraction(tmp_l / denominator * member + tmp_l / u.denominator * u.member, tmp_l);
}
Fraction Fraction::operator - (const Fraction& u) {
type tmp_l = lcm (denominator, u.denominator);
return Fraction(tmp_l / denominator * member - tmp_l / u.denominator * u.member, tmp_l);
}
void Fraction::set (type member, type denominator) {
if (denominator == 0) {
denominator = 1;
member = 0;
}
type tmp_d = gcd(member, denominator);
this->member = member / tmp_d;
this->denominator = denominator / tmp_d;
}