結果
| 問題 |
No.2382 Amidakuji M
|
| コンテスト | |
| ユーザー |
 iiljj
|
| 提出日時 | 2023-07-14 22:43:09 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 17,571 bytes |
| コンパイル時間 | 1,881 ms |
| コンパイル使用メモリ | 145,380 KB |
| 最終ジャッジ日時 | 2025-02-15 14:24:18 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 12 WA * 7 |
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>(std::cout, a); }
void pprint() { std::cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
std::cout << head;
if (sizeof...(Tail) > 0) std::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((std::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), std::cin.tie(nullptr), std::cout.tie(nullptr);
std::cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) std::cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { std::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;
/* #region SegTree */
template <typename T> // T: 要素
struct SegmentTree {
using F = function<T(T, T)>; // 要素と要素をマージする関数．max とか．
ll n; // 木のノード数
F f; // 区間クエリで使う演算，結合法則を満たす演算．区間最大値のクエリを投げたいなら max 演算．
T ti; // 値配列の初期値．演算 f に関する単位元．区間最大値なら単位元は 0. (a>0 なら max(a,0)=max(0,a)=a)
vc<T> dat; // 1-indexed 値配列 (index は木の根から順に 1 | 2 3 | 4 5 6 7 | 8 9 10 11 12 13 14 15 | ...)
// コンストラクタ．
SegmentTree() {}
// コンストラクタ．
SegmentTree(F f, T ti) : f(f), ti(ti) {}
// 指定要素数のセグメント木を初期化する
void init(ll n_) {
n = 1;
while (n < n_) n <<= 1;
dat.assign(n << 1, ti);
}
// ベクトルからセグメント木を構築する
void build(const vc<T> &v) {
ll n_ = v.size();
init(n_);
REP(i, 0, n_) dat[n + i] = v[i];
REPR(i, n - 1, 1) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
}
// インデックス k の要素の値を x にする．
void set_val(ll k, T x) {
dat[k += n] = x;
while (k >>= 1) dat[k] = f(dat[(k << 1) | 0], dat[(k << 1) | 1]); // 上へ登って更新していく
}
// インデックス k の要素の値を取得する．
T get_val(ll k) { return dat[k + n]; }
// 半開区間 [a, b) に対するクエリを実行する
T query(ll a, ll b) {
if (a >= b) return ti;
// assert(a<b)
T vl = ti, vr = ti;
for (ll l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) {
if (l & 1) vl = f(vl, dat[l++]);
if (r & 1) vr = f(dat[--r], vr);
}
return f(vl, vr);
}
// セグメント木上の二分探索
template <typename C> int find(ll st, C &check, T &acc, ll k, ll l, ll r) {
if (l + 1 == r) {
acc = f(acc, dat[k]);
return check(acc) ? k - n : -1;
}
ll m = (l + r) >> 1;
if (m <= st) return find(st, check, acc, (k << 1) | 1, m, r);
if (st <= l && !check(f(acc, dat[k]))) {
acc = f(acc, dat[k]);
return -1;
}
ll vl = find(st, check, acc, (k << 1) | 0, l, m);
if (~vl) return vl;
return find(st, check, acc, (k << 1) | 1, m, r);
}
// セグメント木上の二分探索．check(query(st, idx)) が真となる idx を返す．
template <typename C> int find(ll st, C &check) {
T acc = ti;
return find(st, check, acc, 1, 0, n);
}
};
/* #endregion */
template <class T> ll inversion(vc<T> &a) {
ll n = SIZE(a);
// 座圧
// CoordCompress1D cc(a);
auto f = [](ll a, ll b) { return a + b; };
SegmentTree<ll> seg(f, 0);
seg.init(a.size());
ll ret = 0;
REP(i, 0, n) {
ll zi = a[i]; // cc.zip(a[i]);
ll leq_cnt = seg.query(0, zi + 1);
// 今まで i 個使用，そのうち leq_cnt 個が a[i] 以下
// -> i-leq_cnt 個が a[i] より大きい（=転倒する必要がある）
ret += i - leq_cnt;
seg.set_val(zi, seg.get_val(zi) + 1);
}
return ret;
}
// 1次不定方程式の解の1つを求める．
// gcd(a_0, a_1, ..., a_n) と，
// a_0 x_0 + a_1 x_1 + ... + a_n x_n = gcd(a_0, a_1, ..., a_n)
// を満たす整数 (x_0, x_1, ..., x_n) を返す
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;
}
// 1次不定方程式の一般解をパラメタ表示する．
// gcd(a_0, a_1, ..., a_n) と，
// a_0 x_0 + a_1 x_1 + ... + a_n x_n = gcd(a_0, a_1, ..., a_n)
// の整数解 (x_0, x_1, ..., x_n) のパラメタ表示の係数行列を返す
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};
}
// 1次不定方程式の一般解をパラメタ表示する．
// a_0 x_0 + a_1 x_1 + ... + a_n x_n = c
// の整数解 (x_0, x_1, ..., x_n) のパラメタ表示の係数行列を返す．
// 行列の一番右の列は定数項．
// 解があるかどうか，status として返す．
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, m); //
vll p(n);
cin >> p;
p--;
ll inv = inversion(p);
dump(inv);
// inv + a*2 = b*m となる a>=0, b>=0 のうち，最小の b を求めたい．
// m*b + (-2)*a = inv
vll coef = {m, -2};
dump(coef);
auto [status, param] = parameterize_equation(coef, inv);
if (status == -1) {
pprint(-1);
return;
}
assert(status == 0);
dump(param);
ll num = inv - m * param[0][1];
ll den = m * param[0][0];
if (den < 0) {
den *= -1;
num *= -1;
}
dump(num, den);
ll k = (num < 0) ? (num / den) : CEIL(num, den);
ll ans = m * (param[0][0] * k + param[0][1]);
pprint(ans);
}
// entry point
int main() {
solve();
return 0;
}