#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3506" // #include "../../template/template.hpp" // #include "../../data-structure/divide-interval.hpp" #include "../../graph/graph-template.hpp" #include "../../shortest-path/bfs01.hpp" using namespace Nyaan; void q() { inl(N); vl X(N), Y(N); in2(X, Y); { auto xs = mkuni(X); rep(i, N) X[i] = lb(xs, X[i]); auto ys = mkuni(Y); rep(i, N) Y[i] = lb(ys, Y[i]); } DivideInterval dv(N); int B = dv.B; WeightedGraph<int> g(8 * B); auto add = [&](int i, int j, int c) { g[i].emplace_back(i, j, c); }; // [0B, 2B) : X 側の頂点, 親->子 // [2B, 4B) : X 側の頂点, 子->親 // [4B, 6B) : Y 側の頂点, 親->子 // [6B, 8B) : Y 側の頂点, 子->親 int offy = 4 * B; for (int off : vector{0, offy}) { rep(i, N) { add(i + 1 * B + off, i + 3 * B + off, 0); add(i + 3 * B + off, i + 1 * B + off, 0); } dv.push([&](int p, int c) { add(p + 0 * B + off, c + 0 * B + off, 0); add(c + 2 * B + off, p + 2 * B + off, 0); }); } // 元々貼られている辺は? rep(i, N) { int x = X[i] + B; int y = Y[i] + B + offy; add(x, y, 0), add(y, x, 0); } // 辺を追加 rep(t, 2) { int off1 = t ? offy : 0; int off2 = t ? 0 : offy; map<ll, vl> mp; rep(i, N) mp[X[i]].push_back(Y[i]); each2(k, v, mp) { int l = Min(v); int r = Max(v); if (l == r) continue; dv.apply(l, r + 1, [&](int i) { // X[k] -> Y[l, r] へ 重み 1 の有向辺 add(off1 + k + B, off2 + i, 1); // Y[l, r] -> X[k] へ 重み 1 の有向辺 add(off2 + 2 * B + i, off1 + k + B, 1); }); } swap(X, Y); } out(bfs01(g, X[0] + B)[X[N - 1] + B]); } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }
#line 1 "verify/verify-aoj-other/aoj-3506.test.cpp" #define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3506" // #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::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 <typename S> 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 <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &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 <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> 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 <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" 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 <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> 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 #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &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 <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #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) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 4 "verify/verify-aoj-other/aoj-3506.test.cpp" // #line 2 "data-structure/divide-interval.hpp" #line 5 "data-structure/divide-interval.hpp" using namespace std; // セグ木状に区間を分割したときの処理 // // 2*B 個の頂点を持つグラフを考える // B+i が元のグラフの頂点 i に対応する struct DivideInterval { int N, B; DivideInterval(int n) : N(n), B(1) { while (B < N) B *= 2; } // 初期化 // O(N) 根から葉方向へ push する // f(p, c) : p -> c へ伝播 template <typename F> void push(const F& f) { for (int p = 1; p < B; p++) { f(p, p * 2 + 0); f(p, p * 2 + 1); } } // O(N) 葉から根の方向に update する // f(p, c1, c2) : c1 と c2 の結果を p へマージ template <typename F> void update(const F& f) { for (int p = B - 1; p > 0; p--) { f(p, p * 2 + 0, p * 2 + 1); } } // [l, r) に対応する index の列を返す // 順番は左から右へ並んでいる // 例: [1, 11) : [1, 2), [2, 4), [4, 8), [8, 10), [10, 11) vector<int> range(int l, int r) { assert(0 <= l and l <= r and r <= N); vector<int> L, R; for (l += B, r += B; l < r; l >>= 1, r >>= 1) { if (l & 1) L.push_back(l), l++; if (r & 1) r--, R.push_back(r); } for (int i = (int)R.size() - 1; i >= 0; i--) L.push_back(R[i]); return L; } // [l, r) に対応する index に対してクエリを投げる(区間は昇順) // f(i) : 区間 i にクエリを投げる template <typename F> void apply(int l, int r, const F& f) { assert(0 <= l and l <= r and r <= N); for (int i : range(l, r)) f(i); } }; #line 2 "graph/graph-template.hpp" template <typename T> struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template <typename T> using Edges = vector<edge<T>>; template <typename T> using WeightedGraph = vector<Edges<T>>; using UnweightedGraph = vector<vector<int>>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template <typename T> WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph<T> g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template <typename T> Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) { Edges<T> es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template <typename T> vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector<vector<T>> d(N, vector<T>(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } /** * @brief グラフテンプレート * @docs docs/graph/graph-template.md */ #line 2 "shortest-path/bfs01.hpp" #line 4 "shortest-path/bfs01.hpp" // unreachable -> -1 template <typename T> vector<T> bfs01(WeightedGraph<T>& g, int start = 0) { int N = (int)g.size(); vector<T> d(N, -1); vector<int> vis(N, 0); deque<int> Q; d[start] = 0; Q.push_back(start); while (!Q.empty()) { int cur = Q.front(); Q.pop_front(); if (vis[cur]) continue; vis[cur] = 1; for (auto& dst : g[cur]) { if (d[dst] != -1 and d[dst] <= d[cur] + dst.cost) continue; d[dst] = d[cur] + dst.cost; if (dst.cost == 0) { Q.push_front(dst); } else { Q.push_back(dst); } } } return d; } #line 8 "verify/verify-aoj-other/aoj-3506.test.cpp" using namespace Nyaan; void q() { inl(N); vl X(N), Y(N); in2(X, Y); { auto xs = mkuni(X); rep(i, N) X[i] = lb(xs, X[i]); auto ys = mkuni(Y); rep(i, N) Y[i] = lb(ys, Y[i]); } DivideInterval dv(N); int B = dv.B; WeightedGraph<int> g(8 * B); auto add = [&](int i, int j, int c) { g[i].emplace_back(i, j, c); }; // [0B, 2B) : X 側の頂点, 親->子 // [2B, 4B) : X 側の頂点, 子->親 // [4B, 6B) : Y 側の頂点, 親->子 // [6B, 8B) : Y 側の頂点, 子->親 int offy = 4 * B; for (int off : vector{0, offy}) { rep(i, N) { add(i + 1 * B + off, i + 3 * B + off, 0); add(i + 3 * B + off, i + 1 * B + off, 0); } dv.push([&](int p, int c) { add(p + 0 * B + off, c + 0 * B + off, 0); add(c + 2 * B + off, p + 2 * B + off, 0); }); } // 元々貼られている辺は? rep(i, N) { int x = X[i] + B; int y = Y[i] + B + offy; add(x, y, 0), add(y, x, 0); } // 辺を追加 rep(t, 2) { int off1 = t ? offy : 0; int off2 = t ? 0 : offy; map<ll, vl> mp; rep(i, N) mp[X[i]].push_back(Y[i]); each2(k, v, mp) { int l = Min(v); int r = Max(v); if (l == r) continue; dv.apply(l, r + 1, [&](int i) { // X[k] -> Y[l, r] へ 重み 1 の有向辺 add(off1 + k + B, off2 + i, 1); // Y[l, r] -> X[k] へ 重み 1 の有向辺 add(off2 + 2 * B + i, off1 + k + B, 1); }); } swap(X, Y); } out(bfs01(g, X[0] + B)[X[N - 1] + B]); } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }