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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#318521#7612. Matrix InverseHaccerKatTL 3ms35308kbC++204.9kb2024-01-31 13:04:142024-01-31 13:04:15

Judging History

你现在查看的是最新测评结果

  • [2024-01-31 13:04:15]
  • 评测
  • 测评结果:TL
  • 用时:3ms
  • 内存:35308kb
  • [2024-01-31 13:04:14]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
constexpr int mod = 1e9 + 7;
template <class T>
T qpow(T x, int p) {
    T res = 1;
    for (; p; p >>= 1, x *= x) {
        if (p & 1) res *= x;    
    }
    
    return res;
}

struct Mint {
    int x;
    Mint() : x(0) {}
    Mint(ll x) : x((x % mod + mod) % mod) {}
    Mint& operator += (const Mint &rhs) {
        x += rhs.x;
        if (x >= mod) x -= mod;
        return *this;
    }
    
    Mint& operator -= (const Mint &rhs) {
        x -= rhs.x;
        if (x < 0) x += mod;
        return *this;
    }
    
    Mint& operator *= (const Mint &rhs) {
        x = (ll)x * rhs.x % mod;
        return *this;
    }
    
    Mint& operator /= (const Mint &rhs) {
        return (*this *= qpow(rhs, mod - 2));
    }
};

Mint operator + (Mint lhs, const Mint &rhs) {return lhs += rhs;}
Mint operator - (Mint lhs, const Mint &rhs) {return lhs -= rhs;}
Mint operator * (Mint lhs, const Mint &rhs) {return lhs *= rhs;}
Mint operator / (Mint lhs, const Mint &rhs) {return lhs /= rhs;}

int gauss(vector<vector<Mint>> a, vector<Mint> &ans) {
    int n = a.size(), m = a[0].size() - 1;
    vector<int> where(m, -1);
    for (int r = 0, c = 0; r < n && c < m; c++) {
        int sel = r;
        for (int i = r; i < n; i++) {
            if (a[i][c].x != 0) sel = i;
        }
        
        if (a[sel][c].x == 0) continue;
        swap(a[sel], a[r]);
        where[c] = r;
        for (int i = 0; i < n; i++) {
            if (i != r) {
                Mint mul = a[i][c] / a[r][c];
                for (int j = c; j <= m; j++) {
                    a[i][j] -= mul * a[r][j];
                }
            }    
        }
        
        r++;
    }
    
    ans = vector<Mint>(m);
    bool free = false;
    for (int i = 0; i < m; i++) {
        if (where[i] != -1) {
            ans[i] = a[where[i]][m] / a[where[i]][i];
        }
        
        else free = true;
    }
    
    for (int i = 0; i < n; i++) {
        Mint sum = 0;
        for (int j = 0; j < m; j++) {
            sum += ans[j] * a[i][j];
        }
        
        if (sum.x != a[i][m].x) return 0;
    }
    
    return (free ? 2 : 1);
}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int l, int r) {
    return uniform_int_distribution<int>(l, r)(rng);    
}

const int N = 2005;
int n;
Mint A[N][N], C[N][N], a[N], b[N];
int usedc[N], usedr[N], I[N][N], on[N];
int temp;
void solve() {
    cin >> n;    
    for (int i = 0; i < n; i++) {
        I[i][i] = 1;
        for (int j = 0; j < n; j++) {
            cin >> temp;
            A[i][j] = temp;
        }
    }
    
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cin >> temp;
            C[i][j] = temp;
        }
    }
            
    vector<int> rows, cols;
    for (int iter = 0; iter < 20; iter++) {
        for (int i = 0; i < n; i++) {
            a[i] = b[i] = 0;    
        }
        
        for (int i = 0; i < n; i++) {
            on[i] = rnd(0, 1);
            if (!on[i]) continue;
            for (int j = 0; j < n; j++) {
                a[i] += A[i][j], b[i] += A[j][i];
            }
        }
        
        for (int i = 0; i < n; i++) {
            Mint x = 0, y = 0;
            for (int j = 0; j < n; j++) {
                x += a[j] * C[j][i];
                y += C[i][j] * b[j];
                if (on[j]) {
                    x -= C[j][i], y -= C[i][j];
                }
            }
            
            if (x.x != 0 && !usedc[i]) {
                usedc[i] = 1, cols.push_back(i);
            }
            
            if (y.x != 0 && !usedr[i]) {
                usedr[i] = 1, rows.push_back(i);
            }
        }
    }
    
    sort(rows.begin(), rows.end());
    sort(cols.begin(), cols.end());
    vector<array<int, 3>> out;
    for (int y : cols) {
        int sz = rows.size();
        vector<vector<Mint>> M(n, vector<Mint>(sz + 1));
        vector<Mint> ans(sz);
        for (int i = 0; i < n; i++) {
            int cur = 0;
            for (int j = 0; j < n; j++) {
                if (usedr[j]) {
                    M[i][cur++] = A[i][j];
                }
                
                else {
                    M[i][sz] -= A[i][j] * C[j][y];
                }
            }
            
            M[i][sz] += I[i][y];
        }
        
        gauss(M, ans);
        for (int i = 0; i < sz; i++) {
            int x = rows[i];
            if (C[x][y].x != ans[i].x) {
                out.push_back({x, y, ans[i].x});
            }
        }
    }
    
    sort(out.begin(), out.end());
    cout << out.size() << "\n";
    for (auto [x, y, z] : out) {
        cout << x + 1 << " " << y + 1 << " " << z << "\n";
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    solve();
}

Details

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Test #1:

score: 100
Accepted
time: 3ms
memory: 35308kb

input:

1
953176428
107682094

output:

0

result:

ok single line: '0'

Test #2:

score: -100
Time Limit Exceeded

input:

1995
586309310 548144807 578573993 437893403 641164340 712256053 172321263 108058526 768610920 123320669 762746291 856047593 979279376 29067913 309867338 292286426 45124325 239705174 675003623 213743652 620561338 116308277 695369179 669459894 682522334 846995555 159510341 999359657 645579085 7499563...

output:


result: