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 22:44:38 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
RE
|
実行時間 | - |
コード長 | 14,658 bytes |
コンパイル時間 | 1,859 ms |
コンパイル使用メモリ | 152,184 KB |
実行使用メモリ | 6,948 KB |
最終ジャッジ日時 | 2024-07-18 20:41:40 |
合計ジャッジ時間 | 3,183 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
other | AC * 16 RE * 6 WA * 3 |
ソースコード
/* #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 cerrvoid 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 absT 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 absT 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};}// Problemvoid 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) {assert(false);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) {pprint("NaN");return;}}pprint(cc);}// entry pointint main() {solve();return 0;}