#ifdef LOCAL class SS { int x[0]; }; extern "C" SS __sanitizer_print_stack_trace(); #define __last_state \ } \ ; \ SS x { \ __sanitizer_print_stack_trace() #endif #include <bits/stdc++.h> #include <chrono> #include <ext/pb_ds/assoc_container.hpp> #include <math.h> using namespace __gnu_pbds; using namespace std; #define endl "\n" #define mp make_pair #define st first #define nd second #define pii pair<int, int> #define vi vector<int> #define pb push_back #define _upgrade ios_base::sync_with_stdio(0), cout.setf(ios::fixed), cout.precision(10), cin.tie(0), cout.tie(0); #define rep(i, n) for (int i = 0; i < (n); ++i) #define fwd(i, a, b) for (int i = (a); i < (b); ++i) #define trav(a, x) for (auto &a : x) #define all(c) (c).begin(), (c).end() #define sz(X) (int)((X).size()) typedef long double ld; typedef unsigned long long ull; typedef long long ll; typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_set; // find_by_order(x) <-returns x-th element order_of_key(x) <- returns order of element x // mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());uniform_int_distribution<int> distr(0, 1e9);auto my_rand = bind(distr, gen); // my_rand() zwraca teraz liczbe z przedzialu [a, b] #ifdef LOCAL ostream &operator<<(ostream &out, string str) { for (char c : str) out << c; return out; } template <class L, class R> ostream &operator<<(ostream &out, pair<L, R> p) { return out << "(" << p.st << ", " << p.nd << ")"; } template <class L, class R, class S> ostream &operator<<(ostream &out, tuple<L, R, S> p) { auto &[a, b, c] = p; return out << "(" << a << ", " << b << ", " << c << ")"; } template <class T> auto operator<<(ostream &out, T a) -> decltype(a.begin(), out) { out << '{'; for (auto it = a.begin(); it != a.end(); it = next(it)) out << (it != a.begin() ? ", " : "") << *it; return out << '}'; } void dump() { cerr << "\n"; } template <class T, class... Ts> void dump(T a, Ts... x) { cerr << a << ", "; dump(x...); } #define debug(...) cerr << "[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__) #else #define debug(...) ; #endif const ll mod = 1e9 + 7; ull mod_mul(ull a, ull b) { return a * b % mod; } ull mod_pow(ull b, ull e) { ull ans = 1; for (; e; b = b * b % mod, e /= 2) if (e & 1) ans = ans * b % mod; return ans; } ull inv(ull a) { return mod_pow(a, mod - 2); } typedef vector<array<int, 2>> graph; graph build_graph(const vector<pii> &V) { int n = sz(V); graph G(n, {-1, -1}); set<pair<int, int>> S; for (int i = n - 1; i >= 0; i--) { auto [l, r] = V[i]; auto itr1 = S.upper_bound({l, 0}); auto itr2 = S.upper_bound({r, 0}); for (auto itr = itr1; itr != itr2; itr++) { auto [_, x] = *itr; G[x / 2][x & 1] = i; } S.erase(itr1, itr2); S.insert({l, 2 * i}); S.insert({r, 2 * i + 1}); } return G; } struct FT { vector<ll> s; FT(int n) : s(n) {} void update(int pos, ll dif) { // a[pos] += dif for (; pos < sz(s); pos |= pos + 1) s[pos] += dif; } ll query(int pos) { // sum of values in [0, pos) ll res = 0; for (; pos > 0; pos &= pos - 1) res += s[pos - 1]; return res; } }; vector<vi> build_parent(const graph &G) { int n = sz(G); vector<vi> res(n); vector<int> P(n); iota(all(P), 0); for (int i = n - 1; i >= 0; i--) { rep(j, 2) if (auto y = G[i][j]; y != -1) P[y] = max(P[y], P[i]); res[P[i]].push_back(i); } return res; } int brut(const graph &G) { int n = sz(G); vi cnt(n); vi vis(n); rep(i, n) { vis.assign(n, false); vector<int> Q(all(G[i])); while (sz(Q)) { auto x = Q.back(); Q.pop_back(); if (x == -1 or vis[x]) continue; cnt[x]++; vis[x] = true; Q.insert(Q.end(), all(G[x])); } } ll res = 0; debug(cnt); rep(i, n) res += inv(cnt[i] + 1); return res % mod; } typedef array<int, 3> tpl; int solve(const auto &V) { auto G = build_graph(V); auto P = build_parent(G); int n = sz(V); debug(G); debug(P); // L,R array<FT, 2> ft = {FT(2 * n + 3), FT(2 * n + 3)}; vi cnt(n); vector<vector<tpl>> T(n); auto get = [&](pii T) { auto [p, q] = T; return ft[0].query(q) - ft[1].query(p); }; for (int i = n - 1; i >= 0; i--) { for (auto y : P[i]) cnt[y] -= get(V[y]); cnt[i] += get(V[i]); array<int, 2> przedzil = {V[i].st, V[i].nd}; array<int, 2> A = {1, 1}; for (auto [typ, x, val] : T[i]) { A[typ] += val; ft[typ].update(x, -val); } rep(i, 2) ft[i].update(przedzil[i], A[i]); rep(j, 2) if (auto y = G[i][j]; y != -1) T[y].push_back({j, przedzil[j], A[j]}); } ll res = 0; debug(cnt); rep(i, n) res += inv(cnt[i] + 1); return res % mod; } vector<pii> gen_test(int n) { vector<int> X(2 * n); iota(all(X), 0ll); random_shuffle(all(X)); vector<pii> res; rep(i, n) res.push_back(minmax(X[i * 2] + 1, X[2 * i + 1] + 1)); return res; } int32_t main() { _upgrade; int n; cin >> n; vector<pii> V(n); for (auto &[a, b] : V) cin >> a >> b; { // while (true) { // auto V = gen_test(1000); // debug(V); // auto G = build_graph(V); // debug(G.back()); // auto res1 = brut(G); auto res = solve(V); // assert(res1 == res); cout << res << endl; } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 | #ifdef LOCAL class SS { int x[0]; }; extern "C" SS __sanitizer_print_stack_trace(); #define __last_state \ } \ ; \ SS x { \ __sanitizer_print_stack_trace() #endif #include <bits/stdc++.h> #include <chrono> #include <ext/pb_ds/assoc_container.hpp> #include <math.h> using namespace __gnu_pbds; using namespace std; #define endl "\n" #define mp make_pair #define st first #define nd second #define pii pair<int, int> #define vi vector<int> #define pb push_back #define _upgrade ios_base::sync_with_stdio(0), cout.setf(ios::fixed), cout.precision(10), cin.tie(0), cout.tie(0); #define rep(i, n) for (int i = 0; i < (n); ++i) #define fwd(i, a, b) for (int i = (a); i < (b); ++i) #define trav(a, x) for (auto &a : x) #define all(c) (c).begin(), (c).end() #define sz(X) (int)((X).size()) typedef long double ld; typedef unsigned long long ull; typedef long long ll; typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_set; // find_by_order(x) <-returns x-th element order_of_key(x) <- returns order of element x // mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());uniform_int_distribution<int> distr(0, 1e9);auto my_rand = bind(distr, gen); // my_rand() zwraca teraz liczbe z przedzialu [a, b] #ifdef LOCAL ostream &operator<<(ostream &out, string str) { for (char c : str) out << c; return out; } template <class L, class R> ostream &operator<<(ostream &out, pair<L, R> p) { return out << "(" << p.st << ", " << p.nd << ")"; } template <class L, class R, class S> ostream &operator<<(ostream &out, tuple<L, R, S> p) { auto &[a, b, c] = p; return out << "(" << a << ", " << b << ", " << c << ")"; } template <class T> auto operator<<(ostream &out, T a) -> decltype(a.begin(), out) { out << '{'; for (auto it = a.begin(); it != a.end(); it = next(it)) out << (it != a.begin() ? ", " : "") << *it; return out << '}'; } void dump() { cerr << "\n"; } template <class T, class... Ts> void dump(T a, Ts... x) { cerr << a << ", "; dump(x...); } #define debug(...) cerr << "[" #__VA_ARGS__ "]: ", dump(__VA_ARGS__) #else #define debug(...) ; #endif const ll mod = 1e9 + 7; ull mod_mul(ull a, ull b) { return a * b % mod; } ull mod_pow(ull b, ull e) { ull ans = 1; for (; e; b = b * b % mod, e /= 2) if (e & 1) ans = ans * b % mod; return ans; } ull inv(ull a) { return mod_pow(a, mod - 2); } typedef vector<array<int, 2>> graph; graph build_graph(const vector<pii> &V) { int n = sz(V); graph G(n, {-1, -1}); set<pair<int, int>> S; for (int i = n - 1; i >= 0; i--) { auto [l, r] = V[i]; auto itr1 = S.upper_bound({l, 0}); auto itr2 = S.upper_bound({r, 0}); for (auto itr = itr1; itr != itr2; itr++) { auto [_, x] = *itr; G[x / 2][x & 1] = i; } S.erase(itr1, itr2); S.insert({l, 2 * i}); S.insert({r, 2 * i + 1}); } return G; } struct FT { vector<ll> s; FT(int n) : s(n) {} void update(int pos, ll dif) { // a[pos] += dif for (; pos < sz(s); pos |= pos + 1) s[pos] += dif; } ll query(int pos) { // sum of values in [0, pos) ll res = 0; for (; pos > 0; pos &= pos - 1) res += s[pos - 1]; return res; } }; vector<vi> build_parent(const graph &G) { int n = sz(G); vector<vi> res(n); vector<int> P(n); iota(all(P), 0); for (int i = n - 1; i >= 0; i--) { rep(j, 2) if (auto y = G[i][j]; y != -1) P[y] = max(P[y], P[i]); res[P[i]].push_back(i); } return res; } int brut(const graph &G) { int n = sz(G); vi cnt(n); vi vis(n); rep(i, n) { vis.assign(n, false); vector<int> Q(all(G[i])); while (sz(Q)) { auto x = Q.back(); Q.pop_back(); if (x == -1 or vis[x]) continue; cnt[x]++; vis[x] = true; Q.insert(Q.end(), all(G[x])); } } ll res = 0; debug(cnt); rep(i, n) res += inv(cnt[i] + 1); return res % mod; } typedef array<int, 3> tpl; int solve(const auto &V) { auto G = build_graph(V); auto P = build_parent(G); int n = sz(V); debug(G); debug(P); // L,R array<FT, 2> ft = {FT(2 * n + 3), FT(2 * n + 3)}; vi cnt(n); vector<vector<tpl>> T(n); auto get = [&](pii T) { auto [p, q] = T; return ft[0].query(q) - ft[1].query(p); }; for (int i = n - 1; i >= 0; i--) { for (auto y : P[i]) cnt[y] -= get(V[y]); cnt[i] += get(V[i]); array<int, 2> przedzil = {V[i].st, V[i].nd}; array<int, 2> A = {1, 1}; for (auto [typ, x, val] : T[i]) { A[typ] += val; ft[typ].update(x, -val); } rep(i, 2) ft[i].update(przedzil[i], A[i]); rep(j, 2) if (auto y = G[i][j]; y != -1) T[y].push_back({j, przedzil[j], A[j]}); } ll res = 0; debug(cnt); rep(i, n) res += inv(cnt[i] + 1); return res % mod; } vector<pii> gen_test(int n) { vector<int> X(2 * n); iota(all(X), 0ll); random_shuffle(all(X)); vector<pii> res; rep(i, n) res.push_back(minmax(X[i * 2] + 1, X[2 * i + 1] + 1)); return res; } int32_t main() { _upgrade; int n; cin >> n; vector<pii> V(n); for (auto &[a, b] : V) cin >> a >> b; { // while (true) { // auto V = gen_test(1000); // debug(V); // auto G = build_graph(V); // debug(G.back()); // auto res1 = brut(G); auto res = solve(V); // assert(res1 == res); cout << res << endl; } } |