結果

問題 No.2446 完全列
ユーザー 👑 AngrySadEight
提出日時 2023-07-14 20:49:11
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,178 bytes
コンパイル時間 19,725 ms
コンパイル使用メモリ 265,960 KB
最終ジャッジ日時 2025-02-15 10:24:40
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>
using mint = modint998244353;
template <typename T>
void debug(T e) {
    cerr << e << endl;
}
template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}
template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}
template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}
template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}
template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}
template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}
double EPS = 0.000000001;
int GaussJordan(vector<vector<double>> &A) {
    int M = A.size();
    int N = A[0].size();
    int rank = 0;
    for (int col = 0; col < N; col++) {
        int pivot = -1;
        double ma = EPS;
        for (int row = rank; row < M; row++) {
            if (abs(A[row][col]) > ma) {
                ma = abs(A[row][col]);
                pivot = row;
            }
        }
        if (pivot == -1) {
            continue;
        }
        swap(A[pivot], A[rank]);
        double fac = A[rank][col];
        for (int col2 = 0; col2 < N; col2++) {
            A[rank][col2] /= fac;
        }
        for (int row = 0; row < M; row++) {
            if (row != rank && abs(A[row][col]) > EPS) {
                double fac = A[row][col];
                for (int col2 = 0; col2 < N; col2++) {
                    A[row][col2] -= A[rank][col2] * fac;
                }
            }
        }
        rank++;
    }
    return rank;
}
int main() {
    int L, M, N;
    cin >> L >> M >> N;
    assert(L >= 1);
    assert(M >= 1);
    assert(N >= 1);
    assert(L * M <= 15);
    assert(M * N <= 15);
    vector<vector<int>> A(L, vector<int>(M));
    for (int i = 0; i < L; i++) {
        for (int j = 0; j < M; j++) {
            cin >> A[i][j];
            assert(A[i][j] >= -6 && A[i][j] <= 6);
        }
    }
    vector<vector<int>> B(M, vector<int>(N));
    for (int i = 0; i < M; i++) {
        for (int j = 0; j < N; j++) {
            cin >> B[i][j];
            assert(B[i][j] >= -6 && B[i][j] <= 6);
        }
    }
    vector<vector<int>> C(L, vector<int>(N, 0));
    for (int i = 0; i < L; i++) {
        for (int j = 0; j < M; j++) {
            for (int k = 0; k < N; k++) {
                C[i][k] += A[i][j] * B[j][k];
            }
        }
    }
    // debug(C);
    bool ans = true;
    for (int i = 0; i < L; i++) {
        for (int j = 0; j < N; j++) {
            if (C[i][j] != 0) {
                ans = false;
            }
        }
    }
    vector<vector<double>> dA(L, vector<double>(M));
    for (int i = 0; i < L; i++) {
        for (int j = 0; j < M; j++) {
            dA[i][j] = (double)A[i][j];
        }
    }
    vector<vector<double>> dB(M, vector<double>(N));
    for (int i = 0; i < M; i++) {
        for (int j = 0; j < N; j++) {
            dB[i][j] = (double)B[i][j];
        }
    }
    // debug(GaussJordan(dB));
    // debug(GaussJordan(dA));
    if (GaussJordan(dB) != M - GaussJordan(dA)) {
        ans = false;
    }
    if (ans) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
}
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