#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004004004004004LL; double EPS = 1e-16; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } // 手元環境(Visual Studio) #ifdef _MSC_VER #include "local.hpp" // 提出用(gcc) #else inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif #endif // 折りたたみ用 //--------------AtCoder 専用-------------- #include using namespace atcoder; //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } using vm = vector; using vvm = vector; using vvvm = vector; //---------------------------------------- //【最小 swap 回数】O(n) /* * ビット列 s[0..n) に対し,隣接要素の swap を繰り返すことで t[0..n) に変化させるときの * swap の最小回数を返す(不可能なら INFL) */ ll swap_distance(const string& s, const string& t, char one = '1') { // verify : https://atcoder.jp/contests/tkppc6-2/tasks/tkppc6_2_b int n = sz(s); if (sz(t) != n) return INFL; // a[i] : s[0..n) における i 番目の 1 の位置 // b[i] : t[0..n) における i 番目の 1 の位置 vi a, b; rep(i, n) { if (s[i] == one) a.push_back(i); if (t[i] == one) b.push_back(i); } int m = sz(a); if (sz(b) != m) return INFL; ll res = 0; // 1 同士の swap をしても無駄なので,追い越しはせず 1 を順に対応させていくのが最善 rep(j, m) res += abs(a[j] - b[j]); return res; } pil naive(int n, vi a) { int x = n / 2; string s; rep(i, n) s += '0' + (a[i] > x); ll y = INFL; if (n & 1) { string t; rep(i, n) t += '1' - i % 2; y = swap_distance(s, t); } else { for (int m = 0; m <= n; m += 2) { string t; rep(i, n) t += '1' - ((i % 2) ^ (i >= m)); dump(t); chmin(y, swap_distance(s, t)); } } return make_pair(x, y); } pil WA(int n, vi a) { int x = n / 2; string s; rep(i, n) s += '0' + (a[i] > x); string t; if (n & 1) { rep(i, n) t += '1' - i % 2; } else { if (s[0] == '0' && s[n - 1] == '1') { rep(i, n) t += '0' + i % 2; } else if (s[0] == '1' && s[n - 1] == '0') { rep(i, n) t += '1' - i % 2; } else { bool fast = false; int ib = -1; int m = x / 2 * 2; // even rep(i, n) { if (i & 1) { if (s[i] == '1' && (fast || s[n - 1 - i] == '0')) { if (fast) { if (ib & 1) m = n - 1 - ib; else m = n - ib; } else m = n - 1 - i; break; } if (s[n - 1 - i] == '1' && (fast || s[i] == '0')) { if (fast) { if (ib & 1) m = ib - 1; else m = ib; } else m = i - 1; break; } if (s[i] == '1' && s[n - 1 - i] == '1') { fast = true; ib = i; } } else { if (s[i] == '0' && (fast || s[n - 1 - i] == '1')) { if (fast) { if (ib & 1) m = n - 1 - ib; else m = n - ib; } else m = n - i; break; } if (s[n - 1 - i] == '0' && (fast || s[i] == '1')) { if (fast) { if (ib & 1) m = ib - 1; else m = ib; } else m = i; break; } if (s[i] == '0' && s[n - 1 - i] == '0') { fast = true; ib = i; } } } rep(i, n) t += '0' + (i % 2) ^ (i < m); } } dump(s); dump(t); ll y = swap_distance(s, t); return make_pair(x, y); } //【ランダム三分探索(下に凸)】O(log(r - l)) /* * 階差の符号変化が - → 0 → + である関数 f(x) の開区間 (l, r) における最小値を与える x を返す. * そうでなくても運が良ければ正しい x を返す. */ template ll random_ternary_search_lc(ll l, ll r, function& f) { static bool first_call = true; mt19937 mt; uniform_int_distribution rnd; if (first_call) { first_call = false; mt.seed((int)time(NULL)); rnd = uniform_int_distribution(0, INFL); } while (r - l > 2) { ll m1 = l + 1 + rnd(mt) % (r - l - 1); ll m2 = l + 1 + rnd(mt) % (r - l - 1); if (m1 > m2) swap(m1, m2); if (f(m1) > f(m2)) l = m1; else r = m2; } return l + 1; /* f の定義の雛形 function f = [&](ll x) { return x; }; */ } pil solve(int n, vi a) { auto start = chrono::system_clock::now(); int x = n / 2; string s; rep(i, n) s += '0' + (a[i] > x); ll y = INFL; if (n & 1) { string t; rep(i, n) t += '1' - i % 2; y = swap_distance(s, t); } else { while (1) { function f = [&](ll hm) { string t; rep(i, n) t += '1' - ((i % 2) ^ (i >= hm * 2)); return swap_distance(s, t); }; ll hm = random_ternary_search_lc(-1LL, n / 2 + 1LL, f); string t; rep(i, n) t += '1' - ((i % 2) ^ (i >= hm * 2)); if(chmin(y, swap_distance(s, t))) dump(y); auto now = chrono::system_clock::now(); auto msec = chrono::duration_cast(now - start).count(); if (msec >= 1900) break; } } return make_pair(x, y); } void find_bug() { #ifdef _MSC_VER // 合わない入力例を見つける. mt19937_64 mt; mt.seed((int)time(NULL)); uniform_int_distribution rnd(0LL, 1LL << 62); mute_dump = true; int n = 6; vi a(n); iota(all(a), 1); repp(a) { auto res_naive = naive(n, a); auto res_solve = solve(n, a); if (res_naive != res_solve) { cout << "----------error!----------" << endl; cout << "input:" << endl; cout << a << endl; cout << "results:" << endl; cout << res_naive << endl; cout << res_solve << endl; cout << "--------------------------" << endl; } } mute_dump = false; #endif } /* ----------error!---------- input: 1 4 2 5 6 3 results: (3,1) (3,3) -------------------------- */ int main() { input_from_file("input.txt"); // output_to_file("output.txt"); // find_bug(); return 0; int n; cin >> n; vi a(n); cin >> a; dump(naive(n, a)); int x; ll y; tie(x, y) = solve(n, a); cout << x << " " << y << endl; }