/** * date : 2022-12-17 23:20:25 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N,F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } template using minpq = priority_queue, greater>; } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // struct log_table { double l[65536]; constexpr log_table() : l() { unsigned long long x = 88172645463325252ULL; double log_u64max = log(2) * 64; for (int i = 0; i < 65536; i++) { x = x ^ (x << 7); x = x ^ (x >> 9); l[i] = log(double(x)) - log_u64max; } } }; using namespace std; namespace fastio { static constexpr int SZ = 1 << 17; char inbuf[SZ], outbuf[SZ]; int in_left = 0, in_right = 0, out_right = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; inline void load() { int len = in_right - in_left; memmove(inbuf, inbuf + in_left, len); in_right = len + fread(inbuf + len, 1, SZ - len, stdin); in_left = 0; } inline void flush() { fwrite(outbuf, 1, out_right, stdout); out_right = 0; } inline void skip_space() { if (in_left + 32 > in_right) load(); while (inbuf[in_left] <= ' ') in_left++; } inline void rd(char& c) { if (in_left + 32 > in_right) load(); c = inbuf[in_left++]; } template inline void rd(T& x) { if (in_left + 32 > in_right) load(); char c; do c = inbuf[in_left++]; while (c < '-'); [[maybe_unused]] bool minus = false; if constexpr (is_signed::value == true) { if (c == '-') minus = true, c = inbuf[in_left++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = inbuf[in_left++]; } if constexpr (is_signed::value == true) { if (minus) x = -x; } } inline void rd() {} template inline void rd(Head& head, Tail&... tail) { rd(head); rd(tail...); } inline void wt(char c) { if (out_right > SZ - 32) flush(); outbuf[out_right++] = c; } inline void wt(bool b) { if (out_right > SZ - 32) flush(); outbuf[out_right++] = b ? '1' : '0'; } inline void wt(const string &s) { if (out_right + s.size() > SZ - 32) flush(); memcpy(outbuf + out_right, s.data(), sizeof(char) * s.size()); out_right += s.size(); } template inline void wt(T x) { if (out_right > SZ - 32) flush(); if (!x) { outbuf[out_right++] = '0'; return; } if constexpr (is_signed::value == true) { if (x < 0) outbuf[out_right++] = '-', x = -x; } int i = 12; char buf[16]; while (x >= 10000) { memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; i -= 4; } if (x < 100) { if (x < 10) { outbuf[out_right] = '0' + x; ++out_right; } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; outbuf[out_right] = '0' + q; outbuf[out_right + 1] = '0' + r; out_right += 2; } } else { if (x < 1000) { memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3); out_right += 3; } else { memcpy(outbuf + out_right, pre.num + (x << 2), 4); out_right += 4; } } memcpy(outbuf + out_right, buf + i + 4, 12 - i); out_right += 12 - i; } inline void wt() {} template inline void wt(Head&& head, Tail&&... tail) { wt(head); wt(forward(tail)...); } template inline void wtn(Args&&... x) { wt(forward(x)...); wt('\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::skip_space; using fastio::wt; using fastio::wtn; namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = u64(chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count()) * 10150724397891781847ULL; _x ^= _x << 7; return _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % (r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % (r - l); } // choose n numbers from [l, r) without overlapping vector randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector ret; for (auto& x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } template void randshf(vector& v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; struct Timer { chrono::high_resolution_clock::time_point st; Timer() { reset(); } void reset() { st = chrono::high_resolution_clock::now(); } chrono::milliseconds::rep elapsed() { auto ed = chrono::high_resolution_clock::now(); return chrono::duration_cast(ed - st).count(); } }; using namespace Nyaan; // ref : https://codeforces.com/blog/entry/61203 const int segDelta[2][2] = {{2, 1}, {3, 0}}; const int rotateDelta[4] = {3, 0, 0, 1}; int64_t hilbertOrder(int x, int y, int pow, int rotate) { if (pow == 0) return 0; int hpow = 1 << (pow - 1); bool xflag = x < hpow, yflag = y < hpow; int nx = xflag ? x : x - hpow; int ny = yflag ? y : y - hpow; int seg = (rotate + segDelta[xflag][yflag]) & 3; int nrot = (rotate + rotateDelta[seg]) & 3; int64_t subSquareSize = int64_t(1) << (2 * pow - 2); int64_t ans = int64_t(seg) << (2 * pow - 2); int64_t add = hilbertOrder(nx, ny, pow - 1, nrot); ans += (seg == 1 || seg == 2) ? add : (subSquareSize - add - 1); return ans; } constexpr int N = 200000; constexpr int Q = 200000; int rui[200003], p[200003], d[200003]; pair xy[200003]; ll hil[200003]; void q() { Timer timer; /**/ { int d1, d2, d3, d4; rd(d1, d2, d3, d4); } rep(i, N) rd(rui[i + 1]), rui[i + 1] += rui[i]; rep1(i, Q) { rd(xy[i].fi, xy[i].se); xy[i].fi = rui[xy[i].fi - 1]; xy[i].se = rui[xy[i].se]; } //*/ /** rep(i, N) rui[i + 1] = rng(1, 100), rui[i + 1] += rui[i]; rep1(i, Q) { xy[i].fi = rng(1, N); xy[i].se = rng(1, N); if (xy[i].fi > xy[i].se) swap(xy[i].fi, xy[i].se); xy[i].fi = rui[xy[i].fi - 1]; xy[i].se = rui[xy[i].se]; } //*/ constexpr int start = 0; trc2(timer.elapsed()); ll pw = 1; while ((1LL << pw) <= rui[N]) pw++; rep(i, Q + 1) { p[i] = i; hil[i] = hilbertOrder(xy[i].fi, xy[i].se, pw, 0); } trc2(timer.elapsed()); sort(p, p + Q + 1, [&](int i, int j) { return hil[i] < hil[j]; }); /* [[maybe_unused]] int width = max(1, 1.0 * rui[N] / max(1.0, sqrt(Q * 2.0 / 3.0))); sort(p, p + Q + 1, [&](int a, int b) { auto [ax, ay] = xy[a]; auto [bx, by] = xy[b]; int ablock = ax / width, bblock = bx / width; if (ablock != bblock) return ablock < bblock; return ablock & 1 ? ay > by : ay < by; }); */ assert(p[0] == start); auto dist = [&](int i, int j) { auto& [x1, y1] = xy[i]; auto& [x2, y2] = xy[j]; return abs(x2 - x1) + abs(y2 - y1); }; [[maybe_unused]] auto dsum = [&]() { ll ans = 0; rep(i, Q) ans += dist(p[i], p[i + 1]); return ans; }; rep(i, Q) d[i] = dist(p[i], p[i + 1]); [[maybe_unused]] ll rev_count = 0; #ifdef NyaanLocal constexpr double TL = 4970; #else constexpr double TL = 4970; #endif constexpr int dmax_climb = 700; constexpr int dmax_sa = 40; auto climb = [&](int dmax) -> void { if (timer.elapsed() >= TL) return; trc2(dmax, dsum(), timer.elapsed(), rev_count); for (int i = 1; i <= Q; i++) { if (i % 5 == 0 and timer.elapsed() >= TL) break; int pre1 = d[i - 1]; int js = i + 1, je = min(i + dmax, Q); for (int j = je - 1; j >= js; j--) { // (i-1) - (i), (j) - (j+1) int pre2 = d[j]; int now1 = dist(p[i - 1], p[j]); int now2 = dist(p[i], p[j + 1]); if (now1 + now2 < pre1 + pre2) { reverse(p + i, p + j + 1); reverse(d + i, d + j); d[i - 1] = pre1 = now1; d[j] = now2; #ifdef NyaanLocal rev_count++; #endif } } } }; auto sa = [&](double end_time, double ratio = 0.2) -> void { constexpr int dmax = dmax_sa; double start_time = timer.elapsed(); if (start_time >= end_time) return; double inv_time = 1.0 / (end_time - start_time); double cur_time = start_time; double cur_score = dsum(); double start_temp = cur_score / 5e5; double end_temp = start_temp * ratio; double cur_temp = start_temp; double diff_temp = start_temp - end_temp; log_table rand_log; int iter = 0; for (;; iter++) { if ((iter & 0xFFFF) == 0) { #ifdef NyaanLocal if ((iter & 0x3FFFFF) == 0) trc2(dsum(), timer.elapsed(), iter, cur_temp, rev_count); #endif if ((cur_time = timer.elapsed()) > end_time) break; cur_temp = max( 0.0, start_temp - (cur_time - start_time) * diff_temp * inv_time); } // [1, Q - 1] int i = rng() % (Q - 1) + 1; // [1, dmax - 1] int dj = rng() % (dmax - 1) + 1; // if((iter & 0xFF) == 0) dj = rng() % (dmax_climb - 1) + 1; int j = i + dj; if (Q <= j) continue; int pre1 = d[i - 1]; int pre2 = d[j]; // int pre3 = d[j - 1]; int now1 = dist(p[i - 1], p[j]); int now2 = dist(p[i], p[j + 1]); // int now3 = dist(p[j], p[i]); // int now4 = dist(p[j - 1], p[j + 1]); int score = (pre1 + pre2) - (now1 + now2); if (score > cur_temp * rand_log.l[iter & 0xFFFF]) { reverse(p + i, p + j + 1); reverse(d + i, d + j); d[i - 1] = pre1 = now1; d[j] = now2; #ifdef NyaanLocal rev_count++; #endif } /* if(i + 1 == j) continue; int score2 = (pre1 + pre2 + pre3) - (now1 + now3 + now4); if (score2 > cur_temp * rand_log.l[(iter + 1) & 0xFFFF]) { int pj = p[j]; memmove(p + i + 1, p + i, sizeof(int) * (j - i)); memmove(d + i + 1, d + i, sizeof(int) * (j - i - 1)); p[i] = pj; d[i - 1] = now1; d[i] = now3; d[j] = now4; #ifdef NyaanLocal rev_count += TEN(9); #endif } */ } trc2(dsum(), timer.elapsed(), iter, cur_temp, rev_count); // cerr << "iter :" << iter << endl; }; rep(t, 2) climb(200); rep(t, 1) sa(TL * 0.3, 0.5); rep(t, 2) climb(200); rep(t, 1) sa(TL * 0.8, 0.2); rep(t, 10) climb(dmax_climb); trc2(dsum(), timer.elapsed(), rev_count); for (int i = 1; i <= Q; i++) { wt(p[i]); wt(" \n"[i == Q]); } } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }