結果

問題 No.2255 Determinant Sum
ユーザー milanis48663220
提出日時 2023-03-24 22:32:37
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 45 ms / 2,000 ms
コード長 6,790 bytes
コンパイル時間 1,328 ms
コンパイル使用メモリ 128,596 KB
最終ジャッジ日時 2025-02-11 17:32:09
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
other AC * 23
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ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#include <atcoder/modint>
#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
typedef long long ll;
template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}
template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}
template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}
using mint = atcoder::modint;
ostream& operator<<(ostream& os, const mint& m){
    os << m.val();
    return os;
}
template <typename T>
struct matrix{
    int n, m;
    vector<vector<T>> dat;
    matrix(int n_, int m_){
        n = n_; m = m_;
        for(int i = 0; i < n; i++){
            dat.push_back(vector<T>(m));
        }
    }
    matrix(int n, int m, T val): n(n), m(m){
        for(int i = 0; i < n; i++){
            dat.push_back(vector<T>(m, val));
        }
    }
    matrix(int n, int m, vector<vector<T>> dat): n(n), m(m), dat(dat){
        assert((int)dat.size() == n);
        for(int i = 0; i < n; i++) assert(dat[i].size() == m);
    }
    
    vector<T>& operator[](int x) {
        return dat[x];
    }
};
template <typename T>
bool prod(matrix<T> a, matrix<T> b, matrix<T> &ans){
    assert(a.m == b.n);
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < b.m; j++){
            ans.dat[i][j] = 0;
            for(int k = 0; k < b.n; k++){
                ans.dat[i][j] += (a.dat[i][k]*b.dat[k][j]);
            }
        }
    }
    return true;
}
template <typename T>
void copy_mat(matrix<T> a, matrix<T> &b){
    assert(a.n == b.n);
    assert(a.m == b.m);
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < a.m; j++){
            b.dat[i][j] = a.dat[i][j];
        }
    }
}
template <typename T>
void pow_mat(matrix<T> a, ll n, matrix<T> &ans){
    assert(n < ((ll)1<<61));
    matrix<T> buf(a.n, a.n);
    matrix<T> tmp(a.n, a.n);
    copy_mat(a, tmp);
    for(int i = 0; i < a.n; i++) {
        for(int j = 0; j < a.n; j++){
            ans.dat[i][j] = 0;
        }
        ans.dat[i][i] = 1;
    }
    while (n > 0) {
        if (n&1) {
            prod(tmp, ans, buf);
            copy_mat(buf, ans);
        }
        prod(tmp, tmp, buf);
        copy_mat(buf, tmp);
        n >>= 1;
    }
}
template <typename T>
void print_mat(matrix<T> a){
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < a.m; j++){
            cout << a.dat[i][j] << ' ';
        }
        cout << endl;
    }
}
template <typename T>
ostream& operator<<(ostream& os, const matrix<T>& m){
    print_mat<T>(m);
    return os;
}
/**
 * I+a+...+a^nを求めます(ちゃんと検証していないのであってないかも) 
 */ 
template<typename T>
void sum_pow(matrix<T> a, ll n, matrix<T> &ans){
    assert(a.n == a.m);
    assert(a.n == ans.n);
    assert(a.n == ans.m);
    matrix<T> A(2*a.n, 2*a.n);
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j  < a.n; j++){
            A[i][j] = a[i][j];
            if(i == j){
                A[i+a.n][j] = 1;
                A[i+a.n][j+a.n] = 1;
            }
        }
    }
    matrix<T> B(2*a.n, a.n);
    for(int i = 0; i < a.n; i++){
        B[i][i] = 1;
    }
    matrix<T> S(2*a.n, a.n);
    matrix<T> buf(2*a.n, 2*a.n);
    pow_mat(A, n+1, buf);
    prod(buf, B, S);
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < a.n; j++){
            ans[i][j] = S[i+a.n][j];
        }
    }
}
/**
 * verified: https://judge.yosupo.jp/submission/35808 
 */
template<typename T>
T det(matrix<T> a, T unit_prod, T unit_sum){
    assert(a.n == a.m);
    int n = a.n;
    matrix<T> b(n, n);
    copy_mat(a, b);
    int cnt_swap = 0;
    for(int i = 0; i < n; i++){
        if(b[i][i] == unit_sum){
            for(int j = i+1; j < n; j++){
                if(b[j][i] != unit_sum){
                    // swap
                    cnt_swap++;
                    for(int k = 0; k < n; k++){
                        swap(b[i][k], b[j][k]);
                    }
                    break;
                }
            }
        }
        if(b[i][i] ==  unit_sum) continue;
        T inv = unit_prod/b[i][i];
        for(int j = i+1; j < n; j++){
            for(int k = n-1; k >= 0; k--){
                b[j][k] -= b[i][k]*b[j][i]*inv;
            }
        }
    }
    T ans = unit_prod;
    for(int i = 0; i < a.n; i++) ans *= b[i][i];
    if(cnt_swap%2 == 1) ans *= -1;
    return ans;
}
template<typename T>
matrix<T> operator*(matrix<T> m1, matrix<T> m2){
    matrix<T> ans(m1.n, m2.m);
    prod(m1, m2, ans);
    return ans;
}
/**
 * 累乗
 */ 
template<typename T>
matrix<T> operator^(matrix<T> m, ll r){
    matrix<T> ans(m.n, m.n);
    pow_mat(m, r, ans);
    return ans;
}
using M = matrix<mint>;
void solve(){
    int n, p; cin >> n >> p;
    mint::set_mod(p);
    auto a = vec2d(n, n, 0);
    for(int i = 0; i < n; i++){
        for(int j = 0; j < n; j++) {
            cin >> a[i][j];
        }
    }
    if(p == 2){
        vector<int> cnt_row(n), cnt_col(n);
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(a[i][j] == -1) {
                    cnt_row[i]++;
                    cnt_col[j]++;
                }
            }
        }
        for(int i = 0; i < n; i++){
            if(cnt_col[i] >= 2 || cnt_row[i] >= 2){
                cout << 0 << endl;
                return;
            }
        }
        M b(n, n);
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(a[i][j] == -1){
                    b[i][j] = 1;
                }else if(cnt_row[i] >= 1 || cnt_col[j] >= 1){
                    b[i][j] = 0;
                }else{
                    b[i][j] = a[i][j];
                }
            }
        }
        cout << det(b, mint(1), mint(0)) << endl;
    }else{
        cout << 0 << endl;
    }
}
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int t; cin >> t;
    while(t--) solve();
}
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