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| #include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
#define maxm 6005
#define maxn 1010
#define inf 2147483647
#define maxw 13000
#define rep(i, a, b) for(int i = a; i <= b; i++)
#define loop(i, a, b) for(int i = a; i >= b; i--)
#define sqr(x) ((x) * (x))
inline ll read() {
ll s = 0, w = 1;
char ch = getchar();
while(ch < '0' || ch > '9') {if(ch == '-') w = -1; ch = getchar();}
while(ch >= '0' && ch <= '9') {s = s * 10 + ch - '0'; ch = getchar();}
return s * w;
}
ll n;
struct frac {
ll up, down;
};
ll gcd(ll a, ll b) {
if(b == 0) return a;
return gcd(b, a % b);
}
frac add(frac a, frac b) {
ll tmp1 = a.down * b.down, tmp2 = a.up * b.down + b.up * a.down;
ll g = gcd(tmp1, tmp2);
tmp1 /= g, tmp2 /= g;
return frac{tmp2, tmp1};
}
frac subt(frac a, frac b) {
ll tmp1 = a.down * b.down, tmp2 = a.up * b.down - b.up * a.down;
ll g = gcd(tmp1, tmp2);
tmp1 /= g, tmp2 /= g;
if(tmp1 < 0) {
tmp1 = abs(tmp1);
tmp2 = -tmp2;
}
return frac{tmp2, tmp1};
}
frac mul(frac a, frac b) {
ll tmp1 = a.down * b.down, tmp2 = a.up * b.up;
ll g = gcd(tmp1, tmp2);
tmp1 /= g, tmp2 /= g;
return frac{tmp2, tmp1};
}
frac div(frac a, frac b) {
ll tmp1 = a.down * b.up, tmp2 = a.up * b.down;
ll g = gcd(tmp1, tmp2);
tmp1 /= g, tmp2 /= g;
return frac{tmp2, tmp1};
}
frac A[maxn][maxn];
ll exc = 0;
void Guass() {
rep(i, 1, n) {
ll maxx = i;
rep(j, i + 1, n) {
if(abs(A[j][i].up * A[maxx][i].down) > abs(A[maxx][i].up * A[j][i].down)) {
maxx = j;
}
}
if(maxx != i) {
cout << "Switch the " << i << "-th row with the " << maxx << "-th row" << endl;
rep(j, 1, n) {
swap(A[i][j], A[maxx][j]);
}
exc++;
rep(o, 1, n) {
rep(p, 1, n) {
cout << A[o][p].up;
if(A[o][p].down != 1) cout << "/" << A[o][p].down;
cout << " ";
}
cout << endl;
}
}
rep(j, i + 1, n) {
frac tmp = div(A[j][i] ,A[i][i]);
cout << "Subtract the " << j << "-th row with " << tmp.up << "/" << tmp.down << " times of the " << i << "-th row." << endl;
rep(k, i , n) {
A[j][k] = subt(A[j][k], mul(A[i][k], tmp));
}
}
if(i < n) {
rep(o, 1, n) {
rep(p, 1, n) {
cout << A[o][p].up;
if(A[o][p].down != 1) cout << "/" << A[o][p].down;
cout << " ";
}
cout << endl;
}
}
}
frac ans = frac{1, 1};
rep(i, 1, n) {
ans = mul(ans, A[i][i]);
}
printf("The determinant of the matrix is:\n");
if(exc % 2 == 1 && ans.up != 0) cout << "-";
cout << ans.up;
if(ans.down != 1) cout << "/" << ans.down << endl;
return;
}
void inp() {
printf("Please input the matrix(integer or fraction)\n");
rep(i, 1, n) {
rep(j, 1, n) {
bool flag = false;
string s;
cin >> s;
ll num = 0, w = 1;
rep(k, 0, s.length() - 1) {
if(s[k] == '/') {
flag = true;
A[i][j].up = w * num;
w = 1, num = 0;
}
if(s[k] == '-') w = -1;
if(s[k] >= '0' && s[k] <= '9') num = num * 10 + s[k] - '0';
}
if(flag) A[i][j].down = w * num;
else {
A[i][j].up = w * num;
A[i][j].down = 1;
}
}
}
}
int main() {
printf("Please input the matrix size(n*n)\n");
n = read();
inp();
Guass();
return 0;
}
|