結果
| 問題 |
No.5020 Averaging
|
| コンテスト | |
| ユーザー |
 tabae326
|
| 提出日時 | 2024-02-25 14:58:10 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 603 ms / 1,000 ms |
| コード長 | 11,331 bytes |
| コンパイル時間 | 5,058 ms |
| コンパイル使用メモリ | 275,508 KB |
| 実行使用メモリ | 6,548 KB |
| スコア | 32,774,152 |
| 最終ジャッジ日時 | 2024-02-25 14:58:48 |
| 合計ジャッジ時間 | 37,636 ms |
|
ジャッジサーバーID （参考情報） |
judge12 / judge11 |
| 純コード判定しない問題か言語 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 50 |
ソースコード
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
using ll = long long;
using pl = std::pair<long long, long long>;
//using mint = atcoder::modint1000000007;
using mint = atcoder::modint998244353;
#define rep(i, srt, end) for (long long i = (srt); i < (long long)(end); i++)
#define all(v) (v).begin(), (v).end()
#define dump(var) do{ if(debug::enable) { std::cerr << #var << " : "; debug::print(var); } } while(0);
constexpr int di[4] = {1, -1, 0, 0};
constexpr int dj[4] = {0, 0, 1, -1};
constexpr long long inf = 1LL<<60;
template<typename T> inline void chmax(T &a, T b) { a = std::max(a, b); };
template<typename T> inline void chmin(T &a, T b) { a = std::min(a, b); };
template<typename T> void vprint(const std::vector<T>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i] << (i == v.size()-1 ? "\n" : " "); } }
template<typename T> void vprintln(const std::vector<T>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i] << "\n"; } }
template<int M> void vprint(const std::vector<atcoder::static_modint<M>>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i].val() << (i == v.size()-1 ? "\n" : " "); } }
template<int M> void vprintln(const std::vector<atcoder::static_modint<M>>& v) { for(int i = 0; i < v.size(); i++) { std::cout << v[i].val() << "\n"; } }
namespace debug {
#if defined(ONLINE_JUDGE)
const bool enable = false;
#else
const bool enable = true;
#endif
template<typename T> void push(const T& e) { std::cerr << e; }
template<int M> void push(const atcoder::static_modint<M>& e) { std::cerr << e.val(); }
template<typename T1, typename T2> void push(const std::pair<T1, T2>& e) { std::cerr << "("; push(e.first); std::cerr << ","; push(e.second); std::cerr << ")"; }
template<typename T1, typename T2, typename T3> void push(const std::tuple<T1, T2, T3>& e) { std::cerr << "("; push(get<0>(e)); std::cerr << ","; push(get<1>(e)); std::cerr << ","; push(get<2>(e)); std::cerr << ")"; }
template<typename T> void print(const T& e) { push(e); std::cerr << "\n"; }
template<typename T> void print(const std::vector<T>& v) { for(int i = 0; i < v.size(); i++) { push(v[i]); std::cerr << " "; } std::cerr << "\n"; }
template<typename T> void print(const std::vector<std::vector<T>>& v) { std::cerr << "\n"; for(int i = 0; i < v.size(); i++) { std::cerr << i << ": "; print(v[i]); } }
};
struct RandGenerator {
random_device seed_gen;
mt19937 engine;
mt19937_64 engine64;
static const int pshift = 1000000000;
RandGenerator() : engine(seed_gen()), engine64(seed_gen()) {}
/*mod以下の乱数を返す（32bit）*/
int rand(int mod) {
return engine() % mod;
}
/*mod以下の乱数を返す（64bit）*/
long long randll(long long mod) {
return engine64() % mod;
}
/*確率pでTrueを返す*/
bool pjudge(double p) {
int p_int;
if(p > 1) p_int = pshift;
else p_int = p * pshift;
return rand(pshift) < p_int;
}
} ryuka;
#include <sys/time.h>
struct timer {
double global_start;
double gettime() {
struct timeval tv;
gettimeofday(&tv, NULL);
return tv.tv_sec + tv.tv_usec * 1e-6;
}
void init() {
global_start = gettime();
}
double elapsed() {
return gettime() - global_start;
}
} toki;
constexpr ll TARGET = 500000000000000000;
ll N;
vector<pl> V;
struct State {
vector<long long> idx;
long long end_pos;
long long score;
State() : score(-inf) {};
long long calc_score();
static State initState();
static State generateState(const State& input_state);
};
template<class STATE>
struct IterationControl {
int iteration_counter;
int swap_counter;
double average_time;
double start_time;
IterationControl() : iteration_counter(0), swap_counter(0) {}
STATE climb(double time_limit, STATE initial_state);
STATE anneal(double time_limit, double temp_start, double temp_end, STATE initial_state);
};
// 2べき判定
bool is_2beki(ll val) {
ll cnt = 0;
while(val) {
cnt += val % 2;
val /= 2;
}
return cnt == 1;
}
// 与えられた集合に対して、全パターンを試し、
// 最もTARGETに近くなるパターンと、その誤差を返す。
pair<ll, vector<ll>> search_lowest_diff_pattern(const vector<ll>& idx) {
const ll size = idx.size();
ll best_diff = inf;
ll best_mask = -1;
rep(mask, 0, 1<<size) {
// 0が含まれていなければスキップ
if(!(mask & 1)) continue;
unsigned long long sum_front = 0;
unsigned long long sum_back = 0;
rep(i, 1, size) {
if(mask & (1<<i)) {
sum_front = (sum_front + V[idx[i]].first) / 2;
sum_back = (sum_back + V[idx[i]].second) / 2;
}
}
ll max_ave = max(sum_front / size, sum_back / size);
if(abs(TARGET - max_ave) < best_diff) {
best_diff = abs(TARGET - max_ave);
best_mask = mask;
}
}
assert(best_mask != -1);
vector<ll> res;
rep(i, 0, size) if(best_mask & (1<<i)) res.push_back(i);
return {best_diff, res};
}
// 前から順に足していって、もっとも誤差が小さくなるタイミングを返す
pl calc_max_diff(const vector<ll>& idx) {
const ll size = idx.size();
ll sum_front = V[idx[0]].first;
ll sum_back = V[idx[0]].second;
ll min_diff = inf, min_i = 0;
rep(i, 1, size) {
sum_front = (sum_front + V[idx[i]].first) / 2;
sum_back = (sum_back + V[idx[i]].second) / 2;
ll diff = max(abs(TARGET - sum_front), abs(TARGET - sum_back));
if(diff < min_diff) {
min_diff = diff;
min_i = i;
}
}
return {min_diff, min_i};
}
// ビット全探索ができるサイズ N=10くらいまで、ピックアップして、
// 平均値をなるべく5*10^17に近づけようとしてみる
// N=10の場合、unsiged long longならばオーバーフローしない。
vector<ll> decide_indicies_to_use(const double time_limit = 0.6) {
const double start_time = toki.gettime();
ll best_diff = inf;
vector<ll> best_idx_to_use;
vector<ll> idx(N);
iota(all(idx), 0);
ll counter = 0;
while(toki.gettime() - start_time < time_limit) {
counter++;
shuffle(all(idx), ryuka.engine);
rep(i, 0, idx.size()) {
if(idx[i] == 0 && i != 0) {
swap(idx[i], idx[0]);
break;
}
}
auto [diff, pos] = calc_max_diff(idx);
if(diff < best_diff) {
best_diff = diff;
best_idx_to_use = vector<ll>(idx.begin(), idx.begin()+pos+1);
}
}
dump(counter);
dump(toki.gettime() - start_time);
assert(!best_idx_to_use.empty());
assert(best_idx_to_use[0] == 0);
return best_idx_to_use;
}
// 順々に足す
vector<pl> add_ordinally(const vector<ll>& idx) {
vector<pl> ans;
rep(i, 1, idx.size()) ans.push_back({0, idx[i]});
return ans;
}
// トーナメント方式でたす
vector<pl> add_uniformly(const vector<ll>& idx) {
assert(idx[0] == 0);
assert(is_2beki(idx.size()));
vector<pl> debug_v = V;
vector<pl> ans;
for(ll b = 0; (1<<b) < idx.size(); b++) {
for(ll i = 0; i < idx.size(); i += (1<<b) * 2) {
ll u = idx[i];
ll v = idx[i + (1<<b)];
ans.push_back({u, v});
ll ave_front = (debug_v[u].first + debug_v[v].first) / 2;
ll ave_back = (debug_v[u].second + debug_v[v].second) / 2;
debug_v[u] = debug_v[v] = {ave_front, ave_back};
}
}
dump(debug_v);
return ans;
}
void print_ans(const vector<pl>& ans) {
cout << ans.size() << endl;
for(auto [u, v]: ans) {
cout << u+1 << " " << v+1 << endl;
}
}
long long State::calc_score() {
ll a = 0, b = 0;
rep(i, 0, end_pos) {
a = (a + V[idx[i]].first) / 2;
b = (b + V[idx[i]].second) / 2;
}
ll diff = max(abs(a - TARGET), abs(b - TARGET));
this->score = 2000000 - 100000 * log10(diff+1);
return this->score;
}
State State::initState() {
State res;
res.idx.resize(N);
iota(all(res.idx), 0);
shuffle(res.idx.begin()+1, res.idx.end(), ryuka.engine);
auto [_, pos] = calc_max_diff(res.idx);
res.end_pos = pos + 1;
res.calc_score();
return res;
}
State State::generateState(const State& input_state) {
State res = input_state;
ll i = ryuka.rand(N-1) + 1;
ll j = ryuka.rand(N) + 1;
if(i == j) j++;
shuffle(res.idx.begin() + i, res.idx.begin() + j, ryuka.engine);
assert(res.idx[0] == 0);
res.calc_score();
return res;
}
template<class STATE>
STATE IterationControl<STATE>::climb(double time_limit, STATE initial_state) {
start_time = toki.gettime();
average_time = 0;
STATE best_state = initial_state;
double time_stamp = start_time;
cerr << "[INFO] - IterationControl::climb - Starts climbing...\n";
while(time_stamp - start_time + average_time < time_limit) {
STATE current_state = STATE::generateState(best_state);
if(current_state.score > best_state.score) {
swap(best_state, current_state);
swap_counter++;
}
iteration_counter++;
time_stamp = toki.gettime();
average_time = (time_stamp - start_time) / iteration_counter;
}
cerr << "[INFO] - IterationControl::climb - Iterated " << iteration_counter << " times and swapped " << swap_counter << " times.\n";
return best_state;
}
template<class STATE>
STATE IterationControl<STATE>::anneal(double time_limit, double temp_start, double temp_end, STATE initial_state) {
start_time = toki.gettime();
average_time = 0;
STATE best_state = initial_state;
double elapsed_time = 0;
cerr << "[INFO] - IterationControl::anneal - Starts annealing...\n";
while(elapsed_time + average_time < time_limit) {
double normalized_time = elapsed_time / time_limit;
double temp_current = pow(temp_start, 1.0 - normalized_time) * pow(temp_end, normalized_time);
STATE current_state = STATE::generateState(best_state);
long long delta = current_state.score - best_state.score;
if(delta > 0 || ryuka.pjudge(exp(1.0 * delta / temp_current)) ) {
swap(best_state, current_state);
swap_counter++;
}
iteration_counter++;
elapsed_time = toki.gettime() - start_time;
average_time = elapsed_time / iteration_counter;
}
cerr << "[INFO] - IterationControl::anneal - Iterated " << iteration_counter << " times and swapped " << swap_counter << " times.\n";
return best_state;
}
void solve() {
// 入力を受け取る。
cin >> N;
V.resize(N);
for(auto& [a, b]: V) cin >> a >> b;
// 実際に使うインデックスを決定する。
vector<ll> idx_to_use = decide_indicies_to_use();
dump(idx_to_use);
// 平均をとるように加算していく
vector<pl> ans = add_ordinally(idx_to_use);
// 出力
print_ans(ans);
}
int main() {
toki.init();
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}