#407966 (C++17) No.950 行列累乗

提出ソース

結果

問題	No.950 行列累乗
ユーザー	yosupot
提出日時	2019-12-13 01:02:06
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	212 ms / 2,000 ms
コード長	7,835 bytes
コンパイル時間	1,502 ms
コンパイル使用メモリ	123,048 KB
実行使用メモリ	11,404 KB
最終ジャッジ日時	2024-06-27 03:50:52
合計ジャッジ時間	7,170 ms
ジャッジサーバーID （参考情報）	judge2 / judge1

このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	72 ms 11,264 KB
testcase_01	AC	170 ms 11,264 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	49 ms 8,456 KB
testcase_06	AC	69 ms 6,944 KB
testcase_07	AC	9 ms 6,944 KB
testcase_08	AC	9 ms 6,940 KB
testcase_09	AC	43 ms 6,940 KB
testcase_10	AC	5 ms 6,944 KB
testcase_11	AC	9 ms 6,944 KB
testcase_12	AC	6 ms 6,944 KB
testcase_13	AC	33 ms 6,940 KB
testcase_14	AC	35 ms 6,940 KB
testcase_15	AC	5 ms 6,944 KB
testcase_16	AC	26 ms 6,940 KB
testcase_17	AC	22 ms 6,940 KB
testcase_18	AC	70 ms 6,944 KB
testcase_19	AC	23 ms 6,940 KB
testcase_20	AC	23 ms 6,944 KB
testcase_21	AC	28 ms 7,828 KB
testcase_22	AC	120 ms 11,144 KB
testcase_23	AC	49 ms 8,968 KB
testcase_24	AC	212 ms 11,400 KB
testcase_25	AC	51 ms 8,840 KB
testcase_26	AC	51 ms 8,840 KB
testcase_27	AC	28 ms 7,948 KB
testcase_28	AC	120 ms 11,272 KB
testcase_29	AC	117 ms 11,272 KB
testcase_30	AC	212 ms 11,272 KB
testcase_31	AC	99 ms 11,272 KB
testcase_32	AC	103 ms 11,144 KB
testcase_33	AC	180 ms 11,268 KB
testcase_34	AC	101 ms 11,268 KB
testcase_35	AC	102 ms 11,404 KB
testcase_36	AC	165 ms 11,264 KB
testcase_37	AC	77 ms 11,392 KB
testcase_38	AC	69 ms 11,136 KB
testcase_39	AC	159 ms 11,264 KB
testcase_40	AC	48 ms 8,584 KB
testcase_41	AC	50 ms 8,972 KB
testcase_42	AC	29 ms 7,952 KB
testcase_43	AC	118 ms 11,268 KB
testcase_44	AC	119 ms 11,148 KB
testcase_45	AC	209 ms 11,148 KB
testcase_46	AC	127 ms 11,272 KB
testcase_47	AC	2 ms 6,940 KB
testcase_48	AC	127 ms 11,272 KB
testcase_49	AC	138 ms 11,272 KB
testcase_50	AC	115 ms 11,404 KB
testcase_51	AC	114 ms 11,148 KB
testcase_52	AC	82 ms 11,264 KB
testcase_53	AC	78 ms 11,264 KB
testcase_54	AC	2 ms 6,940 KB
testcase_55	AC	2 ms 6,944 KB
testcase_56	AC	86 ms 11,264 KB
testcase_57	AC	27 ms 7,952 KB
testcase_58	AC	2 ms 6,940 KB
testcase_59	AC	2 ms 6,944 KB
testcase_60	AC	2 ms 6,940 KB

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

raw source code

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL
       
       
#include <algorithm>
       
#include <cassert>
       
#include <cstdio>
       
#include <cstring>
       
#include <iostream>
       
#include <map>
       
#include <queue>
       
#include <set>
       
#include <string>
       
#include <unordered_map>
       
#include <unordered_set>
       
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    return os << "P(" << p.first << ", " << p.second << ")";
}
template <class T> ostream& operator<<(ostream& os, const V<T>& v) {
    os << "[";
    for (auto d : v) os << d << ", ";
    return os << "]";
}
/*
int main() {
    Scanner sc = Scanner(stdin);
    Printer pr = Printer(stdout);
    return 0;
}
*/
       
struct Scanner {
    FILE* fp = nullptr;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += fread(line + ed, 1, (1 << 15) - ed, fp);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) reread();
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        while (true) {
            succ();
            size_t sz = 1;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (st != ed) break;
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] - '0');
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(V<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    Scanner(FILE* _fp) : fp(_fp) {}
};
struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }
    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }
  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    void write_single(const T& val) {
        for (char c : val) write_single(c);
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char('0' + (val % 10));
            val /= 10;
        }
        reverse(small, small + len);
        memcpy(line + pos, small, len);
        pos += len;
    }
    template <class T> void write_single(const V<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};
       
#include <array>
Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);
using M = array<array<ll, 2>, 2>;
ll md;
M e() {
    M m = M{};
    m[0][0] = m[1][1] = 1;
    return m;
}
ll det(M a) {
    ll x = (a[0][0] * a[1][1] - a[0][1] * a[1][0]);
    return (x % md + md) % md;
}
M mul(M a, M b) {
    M c = M();
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 2; j++) {
            for (int k = 0; k < 2; k++) {
                c[i][j] += a[i][k] * b[k][j];
            }
            c[i][j] %= md;
        }
    }
    return c;
}
M pow_mod(M x, ll n) {
    M r = e();
    while (n) {
        if (n & 1) r = mul(r, x);
        x = mul(x, x);
        n >>= 1;
    }
    return r;
}
const ll STEP = TEN(5);
ll discrete_logarithm_inside(M start, M x, M y) {
    if (start == y) return 0;
    map<M, ll> mp;
    M big = e(); // x^m
    for (ll i = 0; i < STEP; i++) {
        mp[y] = i;
        y = mul(y, x);
        big = mul(big, x);
    }
    for (ll step = 0; step < 2 * TEN(10); step += STEP) {
        start = mul(start, big);
        // check [step + 1, step + STEP]
        if (mp.count(start)) {
            return (step + STEP) - mp[start];
        }
    }
    return -1;
}
ll discrete_logarithm(M start, M x, M y) {
    M _st = start;
    for (int i = 0; i < 100; i++) {
        if (i && start == y) return i;
        start = mul(start, x);
    }
    ll pred = 100 + discrete_logarithm_inside(start, x, y);
    if (mul(_st, pow_mod(x, pred)) != y) return -1;
    return pred;
}
ll pow_mod(ll x, ll n) {
    ll r = 1 % md;
    x %= md;
    while (n) {
        if (n & 1) r = (r * x) % md;
        x = (x * x) % md;
        n >>= 1;
    }
    return r;
}
ll discrete_logarithm(ll start, ll x, ll y) {
    if (start == y) return 0;
    auto mul = [&](ll a, ll b) {
        return (a * b) % md;
    };
    unordered_map<ll, ll> mp;
    ll big = 1; // x^m
    for (ll i = 0; i < STEP; i++) {
        mp[y] = i;
        y = mul(y, x);
        big = mul(big, x);
    }
    for (ll step = 0; step < md + 10; step += STEP) {
        start = mul(start, big);
        // check [step + 1, step + STEP]
        if (mp.count(start)) {
            return (step + STEP) - mp[start];
        }
    }
    return -1;
}
ll discrete_logarithm(ll x, ll y) {
    auto mul = [&](ll a, ll b) {
        return (a * b) % md;
    };
    ll start = 1;
    for (int i = 0; i < 100; i++) {
        if (i && start == y) return i;
        start = mul(start, x);
    }
    ll pred = 100 + discrete_logarithm(start, x, y);
    if (pow_mod(x, pred) != y) return -1;
    return pred;
}
int main() {
    M a, b;
    sc.read(md);
    sc.read(a[0][0], a[0][1], a[1][0], a[1][1]);
    sc.read(b[0][0], b[0][1], b[1][0], b[1][1]);
    ll da = det(a), db = det(b);
    if (da == 0) {
        if (db) pr.writeln(-1);
        else pr.writeln(discrete_logarithm(e(), a, b));
        return 0;
    }
    if (db == 0) {
        pr.writeln(-1);
        return 0;
    }
    // da ^ x = db
    ll x = discrete_logarithm(da, db);
    if (x == -1) {
        pr.writeln(-1);
        return 0;
    }
    ll y = discrete_logarithm(da, 1);
    assert(pow_mod(da, y) == 1);
    M a2 = pow_mod(a, x);
    ll u = (a2 == b) ? 0 : discrete_logarithm(a2, pow_mod(a, y), b);
    if (u != -1) u = (u * y) + x;
    pr.writeln(u);
    return 0;
}

yukicoder

結果

テストケース

ソースコード