結果

問題 No.187 中華風 (Hard)
ユーザー kenti
提出日時 2024-11-14 12:45:51
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 3,574 bytes
コンパイル時間 3,998 ms
コンパイル使用メモリ 300,196 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-14 12:46:02
合計ジャッジ時間 10,679 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 11 WA * 14
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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 <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll MOD = (ll)(1e9 + 7);
template <typename T = ll>
T ext_gcd(T a, T b, T& x, T& y) {
    x = 1; y = 0;
    T x1 = 0, y1 = 1, a1 = a, b1 = b;
    while (b1) {
        T q = a1 / b1;
        tie(x, x1) = make_tuple(x1, x - q * x1);
        tie(y, y1) = make_tuple(y1, y - q * y1);
        tie(a1, b1) = make_tuple(b1, a1 - q * b1);
    }
    return a1;
}
template <typename T = ll>
vector<T> garner(vector<T> a, vector<T> m) {
    int k = a.size();
    for (int i = 0; i < k; i++) {
        a[i] = (a[i] % m[i] + m[i]) % m[i];
    }
    vector<T> x(k);
    for (int i = 0; i < k; i++) {
        x[i] = a[i];
        for (int j = 0; j < i; j++) {
            T tmp, r;
            ext_gcd(m[i], m[j], tmp, r);
            x[i] = (r * (x[i] - x[j]) % m[i] + m[i]) % m[i];
        }
    }
    return x;
}
template <typename T = ll>
bool crt_general(vector<T> a, vector<T> m, vector<T>& ans, vector<T>& radix) {
    int k = a.size();
    map<T, pair<T, T>> mp;
    for (int i = 0; i < k; i++) {
        T tmp = m[i];
        for (T j = 2; j * j <= tmp; j++) {
            if (tmp % j == 0) {
                T res = 1;
                while (tmp % j == 0) {
                    tmp /= j; res *= j;
                }
                T ap = (a[i] % res + res) % res;
                if (mp.contains(j)) {
                    if (mp[j].second < res) {
                        swap(mp[j].first, ap);
                        swap(mp[j].second, res);
                    }
                    if (mp[j].first % res != ap) {
                        return false;
                    }
                } else {
                    mp[j] = make_pair(ap, res);
                }
            }
        }
        if (tmp > 1) {
            T ap = (a[i] % tmp + tmp) % tmp;
            if (mp.contains(tmp)) {
                if ((mp[tmp].first - ap) % tmp) {
                    return false;
                }
            } else {
                mp[tmp] = make_pair(ap, tmp);
            }
        }
    }
    vector<T> na, nm;
    for (auto it = mp.begin(); it != mp.end(); it++) {
        na.push_back(it->second.first);
        nm.push_back(it->second.second);
    }
    radix = nm;
    ans = garner(na, nm);
    return true;
}
ll mod_lcm(int n, vector<ll> y) {
    map<int, ll> pfs;
    for (int i = 0; i < n; i++) {
        for (int j = 2; j * j <= y[i]; j++) {
            if (y[i] % j == 0) {
                ll pf = 1;
                while (y[i] % j == 0) {
                    y[i] /= j; pf *= j;
                }
                if (pfs.contains(j)) {
                    pfs[j] = max(pfs[j], pf);
                } else {
                    pfs[j] = pf;
                }
            }
        }
        if (y[i] > 1 && !pfs.contains(y[i])) {
            pfs[y[i]] = y[i];
        }
    }
    ll ret = 1;
    for (auto it = pfs.begin(); it != pfs.end(); it++) {
        ret = ret * it->second % MOD;
    }
    return ret;
}
int main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    int n; cin >> n;
    vector<ll> a(n), m(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i] >> m[i];
    }
    vector<ll> ans, radix;
    if (crt_general(a, m, ans, radix)) {
        ll res = 0, prod = 1;
        for (int i = 0; i < n; i++) {
            res = (res + ans[i] * prod) % MOD;
            prod = prod * radix[i] % MOD;
        }
        if (res > 0) cout << res << "\n";
        else cout << mod_lcm(n, m) << "\n";
    } else {
        cout << -1 << "\n";
    }
    return 0;
}
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