//Franciszek Witt
#include<bits/stdc++.h>
using namespace std;
#define FOR(i,l,r) for(int i=(l);i<=(r);++i)
#define REP(i,n) FOR(i,0,(n)-1)
#define ssize(x) int(x.size())
template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<'('<<p.first<<", "<<p.second<<')';}
template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<'{';int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<'}';}
#ifdef DEBUG
#define debug(x...) cerr<<"["#x"]: ",[](auto...$){((cerr<<$<<"; "),...);}(x),cerr<<'\n'
#else
#define debug(...) {}
#endif
typedef long long ll;
//https://github.com/tonowak/acmlib/blob/master/code/math/determinant/main.cpp
constexpr int mod = 1000000007;
bool equal(int a, int b) {
return a == b;
}
int mul(int a, int b) {
return int((a * ll(b)) % mod);
}
int add(int a, int b) {
a += b;
return a >= mod ? a - mod : a;
}
int powi(int a, int b) {
if(b == 0)
return 1;
int x = powi(a, b / 2);
x = mul(x, x);
if(b % 2 == 1)
x = mul(x, a);
return x;
}
int inv(int x) {
return powi(x, mod - 2);
}
int divide(int a, int b) {
return mul(a, inv(b));
}
int sub(int a, int b) {
return add(a, mod - b);
}
using T = int;
T determinant(vector<vector<T>>& a) {
int n = ssize(a);
T res = 1;
REP(i, n) {
int b = i;
FOR(j, i + 1, n - 1)
if(abs(a[j][i]) > abs(a[b][i]))
b = j;
if(i != b)
swap(a[i], a[b]), res = sub(0, res);
res = mul(res, a[i][i]);
if (equal(res, 0))
return 0;
FOR(j, i + 1, n - 1) {
T v = divide(a[j][i], a[i][i]);
if (not equal(v, 0))
FOR(k, i + 1, n - 1)
a[j][k] = sub(a[j][k], mul(v, a[i][k]));
}
}
return res;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n;
cin >> n;
vector<int> v(n);
for(auto &i : v)
cin >> i;
vector vv(n, vector(n, 0));
REP(i, n) {
REP(j, i) {
if(i == j)
continue;
vv[i][j] = mod - __gcd(v[i], v[j]);
vv[j][i] = vv[i][j];
vv[i][i] = add(vv[i][i], mod - vv[i][j]);
vv[j][j] = add(vv[j][j], mod - vv[i][j]);
}
}
vv.resize(n - 1);
REP(i, n - 1)
vv[i].resize(n - 1);
cout << determinant(vv) << endl;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | //Franciszek Witt #include<bits/stdc++.h> using namespace std; #define FOR(i,l,r) for(int i=(l);i<=(r);++i) #define REP(i,n) FOR(i,0,(n)-1) #define ssize(x) int(x.size()) template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<'('<<p.first<<", "<<p.second<<')';} template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<'{';int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<'}';} #ifdef DEBUG #define debug(x...) cerr<<"["#x"]: ",[](auto...$){((cerr<<$<<"; "),...);}(x),cerr<<'\n' #else #define debug(...) {} #endif typedef long long ll; //https://github.com/tonowak/acmlib/blob/master/code/math/determinant/main.cpp constexpr int mod = 1000000007; bool equal(int a, int b) { return a == b; } int mul(int a, int b) { return int((a * ll(b)) % mod); } int add(int a, int b) { a += b; return a >= mod ? a - mod : a; } int powi(int a, int b) { if(b == 0) return 1; int x = powi(a, b / 2); x = mul(x, x); if(b % 2 == 1) x = mul(x, a); return x; } int inv(int x) { return powi(x, mod - 2); } int divide(int a, int b) { return mul(a, inv(b)); } int sub(int a, int b) { return add(a, mod - b); } using T = int; T determinant(vector<vector<T>>& a) { int n = ssize(a); T res = 1; REP(i, n) { int b = i; FOR(j, i + 1, n - 1) if(abs(a[j][i]) > abs(a[b][i])) b = j; if(i != b) swap(a[i], a[b]), res = sub(0, res); res = mul(res, a[i][i]); if (equal(res, 0)) return 0; FOR(j, i + 1, n - 1) { T v = divide(a[j][i], a[i][i]); if (not equal(v, 0)) FOR(k, i + 1, n - 1) a[j][k] = sub(a[j][k], mul(v, a[i][k])); } } return res; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n; cin >> n; vector<int> v(n); for(auto &i : v) cin >> i; vector vv(n, vector(n, 0)); REP(i, n) { REP(j, i) { if(i == j) continue; vv[i][j] = mod - __gcd(v[i], v[j]); vv[j][i] = vv[i][j]; vv[i][i] = add(vv[i][i], mod - vv[i][j]); vv[j][j] = add(vv[j][j], mod - vv[i][j]); } } vv.resize(n - 1); REP(i, n - 1) vv[i].resize(n - 1); cout << determinant(vv) << endl; } |
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