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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#370979#7612. Matrix Inverseideograph_advantageWA 550ms66268kbC++204.0kb2024-03-29 20:32:032024-03-29 20:32:04

Judging History

你现在查看的是最新测评结果

  • [2024-03-29 20:32:04]
  • 评测
  • 测评结果:WA
  • 用时:550ms
  • 内存:66268kb
  • [2024-03-29 20:32:03]
  • 提交

answer

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

#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0);
#define iter(a) a.begin(), a.end()
#define pb emplace_back
#define ff first
#define ss second
#define SZ(a) int(a.size())

using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#ifdef zisk
void debug(){cerr << "\n";}
template<class T, class ... U> void debug(T a, U ... b){cerr << a << " ", debug(b...);}
template<class T> void pary(T l, T r) {
	while (l != r) cerr << *l << " ", l++;
	cerr << "\n";
}
#else
#define debug(...) void()
#define pary(...) void()
#endif

template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
    return o << '(' << p.ff << ',' << p.ss << ')';
}

const ll MOD = 1000000007;
using matrix = vector<vector<ll>>;

matrix operator*(const matrix &a, const matrix &b){
    matrix c(SZ(a), vector<ll>(SZ(b[0])));
    for(int i = 0; i < SZ(a); i++)
        for(int j = 0; j < SZ(b[0]); j++)
            for(int k = 0; k < SZ(b); k++){
                c[i][j] += a[i][k] * b[k][j] % MOD;
                c[i][j] %= MOD;
            }
    return c;
}

ll inv(ll a){
    ll b = MOD - 2;
    ll ans = 1;
    while(b){
        if(b & 1) ans = ans * a % MOD;
        b >>= 1;
        a = a * a % MOD;
    }
    return ans;
}

void topos(ll &a){
    a = (a % MOD + MOD) % MOD;
}


void debug_matrix(const matrix &mat){
    debug("matrix");
    for(auto &i : mat) pary(iter(i));
}

void gauss(matrix &mat){
    //debug("gauss");
    //debug_matrix(mat);
    int n = SZ(mat);
    for(int i = 0; i < n; i++){
        for(int j = i; j < n; j++)
            if(mat[j][i] != 0){
                mat[i].swap(mat[j]);
                break;
            }
        ll t = inv(mat[i][i]);
        for(int j = i; j <= n; j++)
            mat[i][j] = mat[i][j] * t % MOD;
        for(int j = 0; j < n; j++){
            if(i == j) continue;
            t = mat[j][i];
            for(int k = i; k <= n; k++){
                mat[j][k] -= t * mat[i][k] % MOD;
                topos(mat[j][k]);
            }
        }
        //debug("ok row", i);
        //debug_matrix(mat);
    }
}

int main(){
    StarBurstStream;
    mt19937 rng(880301);

    int n;
    cin >> n;
    matrix a(n, vector<ll>(n));
    matrix c(n, vector<ll>(n));
    for(int i = 0; i < n; i++)
        for(int j = 0; j < n; j++)
            cin >> a[i][j];
    for(int i = 0; i < n; i++)
        for(int j = 0; j < n; j++)
            cin >> c[i][j];
    
    matrix v(n, vector<ll>(1));
    for(int i = 0; i < n; i++) v[i][0] = rng() % MOD;

    matrix tmp = c * (a * v);
    //debug_matrix(v);
    //debug_matrix(tmp);
    vector<int> bad_row, bad_col;
    vector<bool> col(n);
    for(int i = 0; i < n; i++){
        if(tmp[i][0] != v[i][0]) bad_row.pb(i);
    }

    v = matrix(1, vector<ll>(n));
    //debug_matrix(v);
    //debug_matrix(tmp);
    for(int i = 0; i < n; i++) v[0][i] = rng() % MOD;
    tmp = v * a * c;
    for(int i = 0; i < n; i++){
        if(tmp[0][i] != v[0][i]) bad_col.pb(i), col[i] = true;
    }

    //pary(iter(bad_row));
    //pary(iter(bad_col));
    
    vector<pair<pii, ll>> sol;
    for(int i : bad_row){
        //debug("bad row", i);
        vector<vector<ll>> mat;
        for(int j = 0; j < SZ(bad_col); j++){
            mat.pb();
            ll sum = 0;
            for(int k = 0; k < n; k++){
                if(col[k]) mat.back().pb(a[k][j]);
                else sum += c[i][k] * a[k][j];
            }
            mat.back().pb(-sum + (i == j));
            //debug("ok", i, j, sum);
        }
        //debug_matrix(mat);
        gauss(mat);
        //debug_matrix(mat);
        for(int j = 0; j < SZ(bad_col); j++){
            if(mat[j].back() != c[i][bad_col[j]])
                sol.pb(make_pair(pii(i + 1, bad_col[j] + 1), mat[j].back()));
        }
    }

    cout << SZ(sol) << "\n";
    for(auto [p, val] : sol) cout << p.ff << " " << p.ss << " " << val << "\n";

}

Details

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Test #1:

score: 100
Accepted
time: 0ms
memory: 3564kb

input:

1
953176428
107682094

output:

0

result:

ok single line: '0'

Test #2:

score: -100
Wrong Answer
time: 550ms
memory: 66268kb

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:

4
827 238 548234094
827 499 92853578
1466 238 193910055
1466 499 34647985

result:

wrong answer 1st lines differ - expected: '2', found: '4'