#814352 (C++17) No.2119 一般化百五減算

提出ソース
結果

問題	No.2119 一般化百五減算
ユーザー	iiljj
提出日時	2022-11-04 22:45:41
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	RE
実行時間	-
コード長	14,658 bytes
コンパイル時間	1,693 ms
コンパイル使用メモリ	152,596 KB
実行使用メモリ	6,884 KB
最終ジャッジ日時	2024-07-18 20:42:44
合計ジャッジ時間	4,231 ms
ジャッジサーバーID （参考情報）	judge2 / judge5
このコードへのチャレンジ
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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	RE	-
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	RE	-
testcase_07	AC	2 ms 5,376 KB
testcase_08	RE	-
testcase_09	AC	1 ms 5,376 KB
testcase_10	RE	-
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	2 ms 5,376 KB
testcase_15	AC	2 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	2 ms 5,376 KB
testcase_18	AC	2 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	RE	-
testcase_21	AC	19 ms 6,032 KB
testcase_22	RE	-
testcase_23	AC	218 ms 6,624 KB
testcase_24	RE	-
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ソースコード

raw source code
/* #region Head */

// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath>   // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define ISIZE(x) ((int)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))

#define endl '\n'

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
    REP(i, 0, SIZE(arr)) is >> arr[i];
    return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
    if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
        os << get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
            os << ' ';
        } else if constexpr (end_line) {
            os << '\n';
        }
        return operator<< <N + 1, end_line>(os, a);
    }
    return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(cout, a); }

void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << ' ';
    pprint(move(tail)...);
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#ifndef MYLOCAL
#undef DEBUG_
#endif

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    assert((cin >> __VA_ARGS__));

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {
    for (int i = 0; i < ISIZE(v); ++i) v[i]--;
}
template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {
    for (int i = 0; i < ISIZE(v); ++i) v[i]++;
}

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

inline pll divmod(ll dividend, ll modulus) noexcept {
    assert(modulus > 0);
    ll q = dividend / modulus;
    ll r = dividend - q * modulus;
    if (r < 0) {
        r += modulus;
        q -= 1;
    }
    return {q, r};
}

tuple<ll, ll, ll> extgcd(ll a, ll b) {
    if (b == 0) return {a, 1, 0};
    auto [g, x, y] = extgcd(b, a % b);
    // dump(a, b, g, x, y);
    return {g, y, x - a / b * y};
}

ll mod_linear_equation(ll a, ll b, ll n) {
    assert(a > 0 && n > 0);
    auto [d, x, y] = extgcd(a, n);
    n /= d;
    return b % d == 0 ? ((b / d * x) % n + n) % n : -1;
}

template <typename T> pair<T, vc<T>> extextgcd(vc<T> &coef) {
    // search min abs
    T mi = 0;
    ll argmi = -1;
    int nonzero_cnt = 0;
    REP(i, 0, SIZE(coef)) if (coef[i] != 0) {
        ++nonzero_cnt;
        if (argmi == -1 || abs(coef[i]) < abs(mi)) mi = coef[i], argmi = i;
    }
    if (nonzero_cnt == 0) {
        // 任意の整数が解になる
        return {0, coef};
    }
    if (nonzero_cnt == 1) {
        vc<T> ans = coef;
        ans[argmi] = 1;
        return {mi, ans};
    }
    vc<T> coef_nxt = coef;
    REP(i, 0, SIZE(coef_nxt)) if (i != argmi) coef_nxt[i] %= mi;
    auto [g, ans] = extextgcd(coef_nxt);
    REP(i, 0, SIZE(ans)) if (i != argmi) ans[argmi] -= coef[i] / mi * ans[i];
    // dump(coef, g, ans);
    return {g, ans};
}

// ベクトル同士の足し算
template <typename T> vc<T> operator+(const vc<T> &v0, const vc<T> &v1) {
    assert(SIZE(v0) == SIZE(v1));
    vc<T> ret = v0;
    REP(i, 0, SIZE(v0)) ret[i] += v1[i];
    return ret;
}
template <typename T> vc<T> &operator+=(vc<T> &v0, const vc<T> &v1) {
    assert(SIZE(v0) == SIZE(v1));
    REP(i, 0, SIZE(v0)) v0[i] += v1[i];
    return v0;
}
// ベクトル同士の引き算
template <typename T> vc<T> operator-(const vc<T> &v0, const vc<T> &v1) {
    assert(SIZE(v0) == SIZE(v1));
    vc<T> ret = v0;
    REP(i, 0, SIZE(v0)) ret[i] -= v1[i];
    return ret;
}
template <typename T> vc<T> &operator-=(vc<T> &v0, const vc<T> &v1) {
    assert(SIZE(v0) == SIZE(v1));
    REP(i, 0, SIZE(v0)) v0[i] -= v1[i];
    return v0;
}
template <typename T> vc<T> operator*(const vc<T> &v, const T c) {
    vc<T> ret = v;
    REP(i, 0, SIZE(v)) ret[i] *= c;
    return ret;
}
template <typename T> vc<T> &operator*=(vc<T> &v, const T c) {
    REP(i, 0, SIZE(v)) v[i] *= c;
    return v;
}

template <typename T> pair<T, vc<vc<T>>> parameterize(vc<T> &coef) {
    // search min abs
    T mi = 0;
    ll argmi = -1;
    int nonzero_cnt = 0;
    REP(i, 0, SIZE(coef)) if (coef[i] != 0) {
        ++nonzero_cnt;
        if (argmi == -1 || abs(coef[i]) < abs(mi)) mi = coef[i], argmi = i;
    }
    if (nonzero_cnt == 0) {
        // 任意の整数が解になる
        vc<vc<T>> param(SIZE(coef), vc<T>(SIZE(coef) + 1, 0));
        REP(i, 0, SIZE(coef)) param[i][i] = 1;
        return {0, param};
    }
    if (nonzero_cnt == 1) {
        vc<vc<T>> param(SIZE(coef), vc<T>(SIZE(coef) + 1, 0));
        REP(i, 0, SIZE(coef)) param[i][i] = 1;
        // vll ans = coef;
        // ans[argmi] = 1;
        param[argmi][argmi] = 0;
        param[argmi][SIZE(coef)] = 1;
        return {mi, param};
    }
    vc<T> coef_nxt = coef;
    REP(i, 0, SIZE(coef_nxt)) if (i != argmi) coef_nxt[i] %= mi;
    auto [g, param] = parameterize(coef_nxt);
    REP(i, 0, SIZE(param)) if (i != argmi) param[argmi] -= param[i] * (coef[i] / mi);
    // dump(coef, g, ans);
    return {g, param};
}

template <typename T> pair<int, vc<vc<T>>> parameterize_equation(vc<T> &coef, const T c) {
    auto [g, param] = parameterize(coef); //
    if (g == 0) {
        // 任意の整数が解になる
        return {-2, param};
    }
    if (c % g != 0) {
        // 解なし
        return {-1, param};
    }

    // いらない変数が1つあるはずなので削る
    {
        ll idx = -1;
        REP(i, 0, SIZE(coef)) {
            bool zero = true;
            REP(j, 0, SIZE(coef)) if (param[j][i] != 0) {
                zero = false;
                break;
            }
            if (zero) {
                idx = i;
                break;
            }
        }
        if (idx != -1) {
            REP(i, 0, SIZE(coef)) param[i].erase(param[i].begin() + idx);
        }
    }
    // 倍率を掛ける
    {
        T a = c / g;
        // REP(i, 0, SIZE(coef)) param[i] *= a;
        REP(i, 0, SIZE(coef)) param[i].back() *= a;
    }
    return {0, param};
}

// Problem
void solve() {
    VAR(ll, n, mt);
    vll bt(mt), ct(mt);
    REP(i, 0, mt) cin >> bt[i], ct[i];

    vll b, c;
    REP(i, 0, mt) {
        if (bt[i] != 1) {
            b.push_back(bt[i]);
            c.push_back(ct[i]);
        }
    }
    ll m = SIZE(b);
    if (m == 0) {
        pprint(0);
        return;
    }

    REP(i, 0, m) {
        if (c[i] < 0) {
            auto [q, r] = divmod(c[i], b[i]);
            c[i] = r;
        } else {
            c[i] %= b[i];
        }
    }
    dump(b, c);

    ll cc = c[0];
    vll coef = {b[0], 0};
    if (cc > n) {
        pprint("NaN");
        return;
    }
    REP(i, 1, m) {
        coef[1] = -b[i];
        auto [status, param] = parameterize_equation(coef, c[i] - cc);
        dump(status, param);
        if (status == -1) {
            pprint("NaN");
            return;
        }
        // y = param[1][0] * k + param[1][1]
        //   = b[i] * (param[1][0] * k + param[1][1]) + c[i]
        ll b2 = b[i] * param[1][0];
        ll c2 = b[i] * param[1][1] + c[i];
        if (c2 < 0) {
            auto [q, r] = divmod(c2, b2);
            c2 = r;
        } else {
            c2 %= b2;
        }
        cc = c2;
        coef[0] = b2;
        if (c2 > n) {
            assert(false);
            pprint("NaN");
            return;
        }
    }
    pprint(cc);
}

// entry point
int main() {
    solve();
    return 0;
}
yukicoder

結果

テストケース

ソースコード
