test/aoj/3506.test.cpp

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• Last update: 2024-09-20 12:04:43+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/challenges/sources/UOA/UAPC/3506

Depends on

• Union-Find (src/DataStructure/UnionFind.hpp)
• グラフ (src/Graph/Graph.hpp)
• 区間に辺を張るテク (src/Graph/RangeToRangeGraph.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• 座標圧縮 (src/Misc/compress.hpp)

Code

// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/challenges/sources/UOA/UAPC/3506
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 128
#include <iostream>
#include <deque>
#include <vector>
#include <algorithm>
#include "src/Misc/compress.hpp"
#include "src/DataStructure/UnionFind.hpp"
#include "src/Graph/RangeToRangeGraph.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 int x[N], y[N];
 for (int i= 0; i < N; ++i) cin >> x[i] >> y[i];
 vector vx(x, x + N), vy(y, y + N);
 auto idx= compress(vx);
 auto idy= compress(vy);
 for (int i= 0; i < N; ++i) x[i]= idx(x[i]), y[i]= idy(y[i]);
 int X= vx.size(), Y= vy.size();
 vector<int> x2i[X], y2i[Y];
 for (int i= 0; i < N; ++i) x2i[x[i]].push_back(i), y2i[y[i]].push_back(i);
 UnionFind uf(N);
 for (int z= X; z--;)
  for (int i= x2i[z].size(); --i;) uf.unite(x2i[z][i], x2i[z][i - 1]);
 for (int z= Y; z--;)
  for (int i= y2i[z].size(); --i;) uf.unite(y2i[z][i], y2i[z][i - 1]);
 int lx[N], rx[N], ly[N], ry[N];
 fill_n(lx, N, N + 1), fill_n(ly, N, N + 1);
 fill_n(rx, N, -1), fill_n(ry, N, -1);
 for (int i= 0; i < N; ++i) {
  int r= uf.leader(i);
  lx[r]= min(lx[r], x[i]);
  rx[r]= max(rx[r], x[i]);
  ly[r]= min(ly[r], y[i]);
  ry[r]= max(ry[r], y[i]);
 }
 RangeToRangeGraph<int> r2r(N + X + Y);
 for (int i= 0; i < N; ++i) {
  if (rx[i] == -1) continue;
  r2r.add_from_range(N + lx[i], N + rx[i] + 1, i, 0);
  r2r.add_to_range(i, N + lx[i], N + rx[i] + 1, 1);
  r2r.add_from_range(N + X + ly[i], N + X + ry[i] + 1, i, 0);
  r2r.add_to_range(i, N + X + ly[i], N + X + ry[i] + 1, 1);
 }
 int n= r2r.graph.vertex_size();
 auto adj= r2r.graph.adjacency_edge(1);
 deque<int> dq;
 int s= uf.leader(0), g= uf.leader(N - 1);
 int dist[n], used[n];
 static constexpr int INF= 1 << 30;
 fill_n(dist, n, INF);
 fill_n(used, n, 0);
 dist[s]= 0;
 dq.push_back(s);
 while (!dq.empty()) {
  int v= dq.front();
  dq.pop_front();
  if (v == g) break;
  if (used[v]) continue;
  used[v]= true;
  for (int e: adj[v]) {
   int u= r2r.graph[e].to(v);
   int w= r2r.weight[e];
   if (dist[u] > dist[v] + w) {
    dist[u]= dist[v] + w;
    if (w) dq.push_back(u);
    else dq.push_front(u);
   }
  }
 }
 cout << (dist[g] == INF ? -1 : dist[g]) << '\n';
 return 0;
}

#line 1 "test/aoj/3506.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/challenges/sources/UOA/UAPC/3506
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 128
#include <iostream>
#include <deque>
#include <vector>
#include <algorithm>
#line 4 "src/Misc/compress.hpp"
template <class T> auto compress(std::vector<T> &v) {
 return std::sort(v.begin(), v.end()), v.erase(std::unique(v.begin(), v.end()), v.end()), [&v](T x) { return std::lower_bound(v.begin(), v.end(), x) - v.begin(); };
}
#line 4 "src/DataStructure/UnionFind.hpp"
class UnionFind {
 std::vector<int> par;
public:
 UnionFind(int n): par(n, -1) {}
 int leader(int u) { return par[u] < 0 ? u : par[u]= leader(par[u]); }
 bool unite(int u, int v) {
  if ((u= leader(u)) == (v= leader(v))) return false;
  if (par[u] > par[v]) std::swap(u, v);
  return par[u]+= par[v], par[v]= u, true;
 }
 bool connected(int u, int v) { return leader(u) == leader(v); }
 int size(int u) { return -par[leader(u)]; }
};
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 3 "src/Graph/RangeToRangeGraph.hpp"
template <typename cost_t= int> class RangeToRangeGraph {
 int n;
 inline int to_upper_idx(int i) const { return i >= n ? i - n : n + i; }
 inline int to_lower_idx(int i) const { return i >= n ? i - n : n + n + i; }
public:
 Graph graph;
 std::vector<cost_t> weight;
 RangeToRangeGraph(int n): n(n), graph(n * 3) {
  for (int i= 2; i < n + n; ++i) add(to_upper_idx(i / 2), to_upper_idx(i));
  for (int i= 2; i < n + n; ++i) add(to_lower_idx(i), to_lower_idx(i / 2));
 }
 void add(int s, int t, cost_t w= 0) { graph.add_edge(s, t), weight.emplace_back(w); }
 // [s_l, s_r) -> t
 void add_from_range(int s_l, int s_r, int t, cost_t w= 0) {
  for (int l= s_l + n, r= s_r + n; l < r; l>>= 1, r>>= 1) {
   if (l & 1) add(to_lower_idx(l++), t, w);
   if (r & 1) add(to_lower_idx(--r), t, w);
  }
 }
 // s -> [t_l, t_r)
 void add_to_range(int s, int t_l, int t_r, cost_t w= 0) {
  for (int l= t_l + n, r= t_r + n; l < r; l>>= 1, r>>= 1) {
   if (l & 1) add(s, to_upper_idx(l++), w);
   if (r & 1) add(s, to_upper_idx(--r), w);
  }
 }
 // [s_l, s_r) -> [t_l, t_r)
 void add_from_range_to_range(int s_l, int s_r, int t_l, int t_r, cost_t w= 0) { add_from_range(s_l, s_r, graph.n, w), add_to_range(graph.n, t_l, t_r, 0), ++graph.n; }
};
#line 11 "test/aoj/3506.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 int x[N], y[N];
 for (int i= 0; i < N; ++i) cin >> x[i] >> y[i];
 vector vx(x, x + N), vy(y, y + N);
 auto idx= compress(vx);
 auto idy= compress(vy);
 for (int i= 0; i < N; ++i) x[i]= idx(x[i]), y[i]= idy(y[i]);
 int X= vx.size(), Y= vy.size();
 vector<int> x2i[X], y2i[Y];
 for (int i= 0; i < N; ++i) x2i[x[i]].push_back(i), y2i[y[i]].push_back(i);
 UnionFind uf(N);
 for (int z= X; z--;)
  for (int i= x2i[z].size(); --i;) uf.unite(x2i[z][i], x2i[z][i - 1]);
 for (int z= Y; z--;)
  for (int i= y2i[z].size(); --i;) uf.unite(y2i[z][i], y2i[z][i - 1]);
 int lx[N], rx[N], ly[N], ry[N];
 fill_n(lx, N, N + 1), fill_n(ly, N, N + 1);
 fill_n(rx, N, -1), fill_n(ry, N, -1);
 for (int i= 0; i < N; ++i) {
  int r= uf.leader(i);
  lx[r]= min(lx[r], x[i]);
  rx[r]= max(rx[r], x[i]);
  ly[r]= min(ly[r], y[i]);
  ry[r]= max(ry[r], y[i]);
 }
 RangeToRangeGraph<int> r2r(N + X + Y);
 for (int i= 0; i < N; ++i) {
  if (rx[i] == -1) continue;
  r2r.add_from_range(N + lx[i], N + rx[i] + 1, i, 0);
  r2r.add_to_range(i, N + lx[i], N + rx[i] + 1, 1);
  r2r.add_from_range(N + X + ly[i], N + X + ry[i] + 1, i, 0);
  r2r.add_to_range(i, N + X + ly[i], N + X + ry[i] + 1, 1);
 }
 int n= r2r.graph.vertex_size();
 auto adj= r2r.graph.adjacency_edge(1);
 deque<int> dq;
 int s= uf.leader(0), g= uf.leader(N - 1);
 int dist[n], used[n];
 static constexpr int INF= 1 << 30;
 fill_n(dist, n, INF);
 fill_n(used, n, 0);
 dist[s]= 0;
 dq.push_back(s);
 while (!dq.empty()) {
  int v= dq.front();
  dq.pop_front();
  if (v == g) break;
  if (used[v]) continue;
  used[v]= true;
  for (int e: adj[v]) {
   int u= r2r.graph[e].to(v);
   int w= r2r.weight[e];
   if (dist[u] > dist[v] + w) {
    dist[u]= dist[v] + w;
    if (w) dq.push_back(u);
    else dq.push_front(u);
   }
  }
 }
 cout << (dist[g] == INF ? -1 : dist[g]) << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	00_example_00.in	AC	6 ms	4 MB
g++-13	00_example_01.in	AC	6 ms	4 MB
g++-13	00_example_02.in	AC	6 ms	4 MB
g++-13	handmade_00.in	AC	6 ms	4 MB
g++-13	handmade_01.in	AC	6 ms	4 MB
g++-13	handmade_02.in	AC	5 ms	4 MB
g++-13	handmade_03.in	AC	106 ms	80 MB
g++-13	large_00.in	AC	116 ms	70 MB
g++-13	large_01.in	AC	135 ms	69 MB
g++-13	large_02.in	AC	135 ms	69 MB
g++-13	large_03.in	AC	126 ms	70 MB
g++-13	large_04.in	AC	124 ms	69 MB
g++-13	mini_00.in	AC	7 ms	4 MB
g++-13	mini_01.in	AC	6 ms	4 MB
g++-13	mini_02.in	AC	6 ms	4 MB
g++-13	random_00.in	AC	25 ms	15 MB
g++-13	random_01.in	AC	108 ms	48 MB
g++-13	random_02.in	AC	59 ms	36 MB
g++-13	random_03.in	AC	43 ms	28 MB
g++-13	random_04.in	AC	22 ms	13 MB
g++-13	special_long_mountain_00.in	AC	139 ms	57 MB
g++-13	special_long_mountain_01.in	AC	105 ms	59 MB
g++-13	special_long_mountain_02.in	AC	108 ms	59 MB
g++-13	special_long_mountain_03.in	AC	106 ms	57 MB
g++-13	special_long_mountain_04.in	AC	146 ms	58 MB
g++-13	special_long_mountain_05.in	AC	114 ms	55 MB
g++-13	special_long_mountain_06.in	AC	146 ms	59 MB
g++-13	special_long_mountain_07.in	AC	152 ms	58 MB
g++-13	special_long_mountain_08.in	AC	135 ms	59 MB
g++-13	special_long_mountain_09.in	AC	144 ms	55 MB
g++-13	special_long_mountain_mega_00.in	AC	181 ms	73 MB
g++-13	special_long_mountain_mega_01.in	AC	120 ms	63 MB
g++-13	special_long_tate_00.in	AC	107 ms	58 MB
g++-13	special_long_yoko_00.in	AC	116 ms	60 MB
g++-13	special_mountain_tate_00.in	AC	96 ms	80 MB
g++-13	special_mountain_tate_rev_00.in	AC	118 ms	81 MB
g++-13	special_mountain_yoko_00.in	AC	95 ms	80 MB
g++-13	special_pole_random_00.in	AC	126 ms	62 MB
g++-13	special_pole_random_01.in	AC	136 ms	60 MB
g++-13	special_pole_random_02.in	AC	134 ms	62 MB
g++-13	special_pole_random_03.in	AC	119 ms	63 MB
g++-13	special_pole_random_04.in	AC	156 ms	61 MB
g++-13	special_pole_random_05.in	AC	125 ms	61 MB
g++-13	special_pole_random_06.in	AC	117 ms	61 MB
g++-13	special_pole_random_07.in	AC	114 ms	62 MB
g++-13	special_pole_random_08.in	AC	110 ms	62 MB
g++-13	special_pole_random_09.in	AC	148 ms	61 MB
g++-13	special_pole_random_10.in	AC	151 ms	61 MB
g++-13	special_pole_random_11.in	AC	137 ms	62 MB
g++-13	special_pole_random_12.in	AC	131 ms	61 MB
g++-13	special_pole_random_13.in	AC	113 ms	61 MB
g++-13	special_pole_random_14.in	AC	140 ms	61 MB
g++-13	special_pole_sort_00.in	AC	104 ms	60 MB
g++-13	special_pole_sort_01.in	AC	102 ms	62 MB
g++-13	special_pole_sort_02.in	AC	103 ms	62 MB
g++-13	special_pole_sort_03.in	AC	101 ms	63 MB
g++-13	special_pole_sort_04.in	AC	104 ms	60 MB
g++-13	special_pole_sort_05.in	AC	104 ms	61 MB
g++-13	special_pole_sort_06.in	AC	102 ms	60 MB
g++-13	special_pole_sort_07.in	AC	101 ms	61 MB
g++-13	special_pole_sort_08.in	AC	82 ms	63 MB
g++-13	special_pole_sort_09.in	AC	97 ms	61 MB
g++-13	special_spiral_00.in	AC	92 ms	57 MB
g++-13	special_spiral_01.in	AC	94 ms	55 MB
g++-13	special_spiral_rev_00.in	AC	88 ms	56 MB
g++-13	special_spiral_rev_01.in	AC	90 ms	56 MB
g++-13	special_spiral_zero_00.in	AC	61 ms	41 MB
g++-13	special_spiral_zero_01.in	AC	60 ms	40 MB
g++-13	special_square_random_00.in	AC	62 ms	32 MB
g++-13	special_square_random_01.in	AC	65 ms	32 MB
g++-13	special_square_random_02.in	AC	64 ms	32 MB
clang++-18	00_example_00.in	AC	6 ms	4 MB
clang++-18	00_example_01.in	AC	5 ms	4 MB
clang++-18	00_example_02.in	AC	5 ms	4 MB
clang++-18	handmade_00.in	AC	5 ms	4 MB
clang++-18	handmade_01.in	AC	5 ms	4 MB
clang++-18	handmade_02.in	AC	6 ms	4 MB
clang++-18	handmade_03.in	AC	111 ms	81 MB
clang++-18	large_00.in	AC	119 ms	69 MB
clang++-18	large_01.in	AC	141 ms	69 MB
clang++-18	large_02.in	AC	129 ms	70 MB
clang++-18	large_03.in	AC	122 ms	70 MB
clang++-18	large_04.in	AC	120 ms	69 MB
clang++-18	mini_00.in	AC	7 ms	4 MB
clang++-18	mini_01.in	AC	6 ms	4 MB
clang++-18	mini_02.in	AC	5 ms	4 MB
clang++-18	random_00.in	AC	24 ms	15 MB
clang++-18	random_01.in	AC	93 ms	47 MB
clang++-18	random_02.in	AC	57 ms	36 MB
clang++-18	random_03.in	AC	41 ms	29 MB
clang++-18	random_04.in	AC	21 ms	13 MB
clang++-18	special_long_mountain_00.in	AC	124 ms	58 MB
clang++-18	special_long_mountain_01.in	AC	99 ms	58 MB
clang++-18	special_long_mountain_02.in	AC	102 ms	58 MB
clang++-18	special_long_mountain_03.in	AC	103 ms	58 MB
clang++-18	special_long_mountain_04.in	AC	130 ms	57 MB
clang++-18	special_long_mountain_05.in	AC	105 ms	55 MB
clang++-18	special_long_mountain_06.in	AC	125 ms	58 MB
clang++-18	special_long_mountain_07.in	AC	126 ms	58 MB
clang++-18	special_long_mountain_08.in	AC	133 ms	60 MB
clang++-18	special_long_mountain_09.in	AC	126 ms	54 MB
clang++-18	special_long_mountain_mega_00.in	AC	147 ms	77 MB
clang++-18	special_long_mountain_mega_01.in	AC	115 ms	62 MB
clang++-18	special_long_tate_00.in	AC	100 ms	58 MB
clang++-18	special_long_yoko_00.in	AC	102 ms	58 MB
clang++-18	special_mountain_tate_00.in	AC	92 ms	82 MB
clang++-18	special_mountain_tate_rev_00.in	AC	118 ms	80 MB
clang++-18	special_mountain_yoko_00.in	AC	97 ms	80 MB
clang++-18	special_pole_random_00.in	AC	120 ms	61 MB
clang++-18	special_pole_random_01.in	AC	131 ms	63 MB
clang++-18	special_pole_random_02.in	AC	131 ms	60 MB
clang++-18	special_pole_random_03.in	AC	114 ms	62 MB
clang++-18	special_pole_random_04.in	AC	147 ms	61 MB
clang++-18	special_pole_random_05.in	AC	140 ms	62 MB
clang++-18	special_pole_random_06.in	AC	114 ms	62 MB
clang++-18	special_pole_random_07.in	AC	110 ms	61 MB
clang++-18	special_pole_random_08.in	AC	110 ms	62 MB
clang++-18	special_pole_random_09.in	AC	136 ms	62 MB
clang++-18	special_pole_random_10.in	AC	139 ms	63 MB
clang++-18	special_pole_random_11.in	AC	127 ms	63 MB
clang++-18	special_pole_random_12.in	AC	120 ms	60 MB
clang++-18	special_pole_random_13.in	AC	108 ms	61 MB
clang++-18	special_pole_random_14.in	AC	132 ms	61 MB
clang++-18	special_pole_sort_00.in	AC	104 ms	61 MB
clang++-18	special_pole_sort_01.in	AC	102 ms	62 MB
clang++-18	special_pole_sort_02.in	AC	103 ms	59 MB
clang++-18	special_pole_sort_03.in	AC	104 ms	63 MB
clang++-18	special_pole_sort_04.in	AC	102 ms	60 MB
clang++-18	special_pole_sort_05.in	AC	103 ms	62 MB
clang++-18	special_pole_sort_06.in	AC	103 ms	62 MB
clang++-18	special_pole_sort_07.in	AC	103 ms	61 MB
clang++-18	special_pole_sort_08.in	AC	85 ms	60 MB
clang++-18	special_pole_sort_09.in	AC	101 ms	61 MB
clang++-18	special_spiral_00.in	AC	93 ms	57 MB
clang++-18	special_spiral_01.in	AC	93 ms	54 MB
clang++-18	special_spiral_rev_00.in	AC	83 ms	57 MB
clang++-18	special_spiral_rev_01.in	AC	87 ms	54 MB
clang++-18	special_spiral_zero_00.in	AC	59 ms	40 MB
clang++-18	special_spiral_zero_01.in	AC	59 ms	41 MB
clang++-18	special_square_random_00.in	AC	60 ms	34 MB
clang++-18	special_square_random_01.in	AC	64 ms	33 MB
clang++-18	special_square_random_02.in	AC	64 ms	32 MB

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