結果
| 問題 | No.1571 All Your Cycles Are Same Lengths |
| ユーザー |
 iiljj
|
| 提出日時 | 2021-06-27 14:35:23 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 13,408 bytes |
| コンパイル時間 | 1,835 ms |
| コンパイル使用メモリ | 142,960 KB |
| 最終ジャッジ日時 | 2025-01-22 14:22:46 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 10 |
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 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 << "}";
}
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
#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__; \
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; }
/* #endregion */
// #include <atcoder/all>
// using namespace atcoder;
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, q); //
vll n(q), t(q);
REP(i, 0, q) cin >> n[i], t[i];
REP(i, 0, q) {
ll ni = n[i], ti = t[i];
if (ni == 2) {
if (ti % 2 == 0) {
Yn(true);
pprint(1, 2, ti / 2);
} else {
Yn(false);
}
} else {
vll coef = {2, (ni - 2)};
auto [status, param] = parameterize_equation(coef, ti);
if (status == 0) {
// dump(param);
if (param[0][1] < 0) {
if (param[0][0] > 0) {
while (param[0][1] < 0) {
param[0][1] += param[0][0];
param[1][1] += param[1][0];
}
} else {
while (param[0][1] < 0) {
param[0][1] -= param[0][0];
param[1][1] -= param[1][0];
}
}
}
ll a = param[0][1], b = param[1][1];
if (a >= 0 && b >= 0) {
Yn(true);
REPM(j, 1, ni - 1) REPM(k, j + 1, ni) {
if (j == 1)
pprint(j, k, a);
else
pprint(j, k, b);
}
} else {
Yn(false);
}
} else {
Yn(false);
}
}
}
}
// entry point
int main() {
solve();
return 0;
}