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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#426230#7612. Matrix Inversereal_sigma_team#RE 0ms0kbC++204.5kb2024-05-30 23:28:422024-05-30 23:28:42

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你现在查看的是最新测评结果

  • [2024-05-30 23:28:42]
  • 评测
  • 测评结果:RE
  • 用时:0ms
  • 内存:0kb
  • [2024-05-30 23:28:42]
  • 提交

answer

#include<bits/stdc++.h>

using namespace std;

const int mod = 1e9 + 7;

struct mint {
    int x = 0;

    mint() = default;

    mint(int x_) : x(x_) {
        if (x >= mod) x -= mod;
        if (x >= mod) x %= mod;
    }

    int power(int b) {
        int res = 1;
        for (; b; b >>= 1, x = 1ll * x * x % mod) if (b & 1) res = 1ll * res * x % mod;
        return res;
    }

    int inv() {
        return power(mod - 2);
    }
};

int abs(mint x) {
    return x.x;
}

mint operator+(mint a, mint b) {
    int ret = a.x + b.x;
    if (ret >= mod) ret -= mod;
    return mint(ret);
}

mint operator-(mint a, mint b) {
    int ret = a.x - b.x;
    if (ret < 0) ret += mod;
    return mint(ret);
}

mint operator*(mint a, mint b) {
    return mint(1ll * a.x * b.x % mod);
}

mint operator/(mint a, mint b) {
    return mint(1ll * a.x * b.inv() % mod);
}
int gauss (vector < vector<mint> > a, vector<mint> & ans) {
    int n = (int) a.size();
    int m = (int) a[0].size() - 1;

    vector<int> where (m, -1);
    for (int col=0, row=0; col<m && row<n; ++col) {
        int sel = row;
        for (int i=row; i<n; ++i)
            if (abs (a[i][col]) > abs (a[sel][col]))
                sel = i;
        if (abs (a[sel][col]) == 0)
            continue;
        for (int i=col; i<=m; ++i)
            swap (a[sel][i], a[row][i]);
        where[col] = row;

        for (int i=0; i<n; ++i)
            if (i != row) {
                mint c = a[i][col] / a[row][col];
                for (int j=col; j<=m; ++j)
                    a[i][j] = a[i][j] - a[row][j] * c;
            }
        ++row;
    }

    ans.assign (m, 0);
    for (int i=0; i<m; ++i)
        if (where[i] != -1)
            ans[i] = a[where[i]][m] / a[where[i]][i];
    for (int i=0; i<n; ++i) {
        mint sum = 0;
        for (int j=0; j<m; ++j)
            sum = sum + ans[j] * a[i][j];
        if (abs (sum - a[i][m]) != 0)
            return 0;
    }

    for (int i=0; i<m; ++i)
        if (where[i] == -1)
            return 1e9;
    return 1;
}

mt19937 rng(time(0));

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);

    int n;
    cin >> n;
    vector<vector<mint>> a(n, vector<mint>(n));
    auto c = a;
    for (auto &i: a) {
        for (auto &j: i) cin >> j.x;
    }
    for (auto &i: c) {
        for (auto &j: i) cin >> j.x;
    }
    int ptr = 0;
    vector<vector<mint>> sle;
    vector<pair<int, int>> pos;
    vector<mint> ret;
    for (int j = 0; j < n; ++j) {
        if (n <= 0) {
            for (int i = 0; i < n; ++i) {
                sle.emplace_back(ptr + n, mint(0));
                for (int l = 0; l < n; ++l) {
                    if (pos.size() < ptr + n) pos.emplace_back(l, j);
                    sle.back()[ptr + l] = a[i][l];
                }
                ret.emplace_back(i == j);
            }
            ptr += n;
        } else {
            bool bad = false;
            for (int iter = 0; iter < 10; ++iter) {
                int i = rng() % n;
                mint q(0);
                for (int l = 0; l < n; ++l) {
                    q = q + a[i][l] * c[l][j];
                }
                sle.emplace_back(ptr + n, mint(0));
                for (int l = 0; l < n; ++l) {
                    if (pos.size() < ptr + n) pos.emplace_back(l, j);
                    sle.back()[ptr + l] = a[i][l];
                }
                ret.emplace_back(i == j);
//                cout << i << ' ' << j << ' ' << q.x << endl;
                if (q.x != (i == j)) {
                    bad = true;
                }
            }
            if (!bad) {
                for (int i = 0; i < n; ++i) pos.pop_back();
                for (int iter = 0; iter < 10; ++iter) sle.pop_back(), ret.pop_back();
            }
            ptr = pos.size();
        }
    }
//    cout << ptr << endl;
    for (auto &x: sle) {
        while (x.size() < ptr) x.emplace_back(0);
    }
    for (int i = 0; i < sle.size(); ++i) {
        sle[i].push_back(ret[i]);
    }
//    for (auto i : sle) {
//        for (auto j : i) cout << j.x << ' ';
//        cout << endl;
//    }
    vector<mint> ans;
    gauss(sle, ans);
    vector<tuple<int, int, mint>> res;
    for (int i = 0; i < ans.size(); ++i) {
        if (ans[i].x != c[pos[i].first][pos[i].second].x) {
            res.emplace_back(pos[i].first, pos[i].second, ans[i]);
        }
    }
    cout << res.size() << '\n';
    for (auto [x, y, z]: res) cout << x + 1 << ' ' << y + 1 << ' ' << z.x << '\n';
}

Details

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Test #1:

score: 0
Runtime Error

input:

1
953176428
107682094

output:


result: