#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = a; i < (b); ++i) #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() typedef long long ll; typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef vector<int> vi; typedef vector<ll> vl; #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.first << ", " << p.second << ")"; } 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(...) 42 #endif const ll MOD = 1000000007; ll rev(ll a, ll b = MOD - 2) { if (!b) return 1; if (b & 1) return (a * rev(a, b - 1)) % MOD; ll temp = rev(a, b / 2); return (temp * temp) % MOD; } main() { cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit); int Z = 1; // cin >> Z; while (Z--) { int n; cin >> n; vector<pii> V(n); for (auto &[x, y] : V) cin >> x >> y; reverse(all(V)); vector<pii> G(n, {-1, -1}); set<pii> S; for (int i = 0; i < n; i++) { auto t = S.upper_bound({V[i].first, -1}); auto en = t; while (en != S.end() && (*en).first < V[i].second) { if (G[(*en).second].first < 0) G[(*en).second].first = i; else G[(*en).second].second = i; en = next(en); } if (t != S.end()) S.erase(t, en); S.insert({V[i].first, i}); S.insert({V[i].second, i}); } for (auto &[x, y] : G) if (x == y) y = -1; vector<set<int>> T(n); vi H(n, 0), val(n, 1), ans(n, 1); vector<vi> P(n); for (int i = 0; i < n; i++) { H[i] = i; T[i].insert(i); } for (int i = 0; i < n; i++) if (G[i].first >= 0) { P[G[i].first].push_back(i); if (G[i].second >= 0) P[G[i].second].push_back(i); } for (int i = 0; i < n; i++) { for (auto &p : P[i]) if (G[p].second == i || G[p].second < 0) if (T[i].size() < T[p].size()) swap(T[i], T[p]); for (auto &p : P[i]) for (auto &x : T[p]) T[i].insert(x); queue<int> Q; for (auto &x : T[i]) { if (x != i) { ans[i] += val[x]; if (H[x] == i) { val[i] += val[x]; Q.push(x); continue; } } if (G[i].first >= 0) { if (G[i].second >= 0) H[x] = max(H[x], G[i].second); else H[x] = max(H[x], G[i].first); } } while (Q.size()) { T[i].erase(Q.front()); Q.pop(); } // debug(i, val[i], ans[i], T[i]); } ll sum = 0; for (auto &a : ans) sum = (sum + rev(a)) % MOD; cout << sum << 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 | #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = a; i < (b); ++i) #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() typedef long long ll; typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef vector<int> vi; typedef vector<ll> vl; #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.first << ", " << p.second << ")"; } 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(...) 42 #endif const ll MOD = 1000000007; ll rev(ll a, ll b = MOD - 2) { if (!b) return 1; if (b & 1) return (a * rev(a, b - 1)) % MOD; ll temp = rev(a, b / 2); return (temp * temp) % MOD; } main() { cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit); int Z = 1; // cin >> Z; while (Z--) { int n; cin >> n; vector<pii> V(n); for (auto &[x, y] : V) cin >> x >> y; reverse(all(V)); vector<pii> G(n, {-1, -1}); set<pii> S; for (int i = 0; i < n; i++) { auto t = S.upper_bound({V[i].first, -1}); auto en = t; while (en != S.end() && (*en).first < V[i].second) { if (G[(*en).second].first < 0) G[(*en).second].first = i; else G[(*en).second].second = i; en = next(en); } if (t != S.end()) S.erase(t, en); S.insert({V[i].first, i}); S.insert({V[i].second, i}); } for (auto &[x, y] : G) if (x == y) y = -1; vector<set<int>> T(n); vi H(n, 0), val(n, 1), ans(n, 1); vector<vi> P(n); for (int i = 0; i < n; i++) { H[i] = i; T[i].insert(i); } for (int i = 0; i < n; i++) if (G[i].first >= 0) { P[G[i].first].push_back(i); if (G[i].second >= 0) P[G[i].second].push_back(i); } for (int i = 0; i < n; i++) { for (auto &p : P[i]) if (G[p].second == i || G[p].second < 0) if (T[i].size() < T[p].size()) swap(T[i], T[p]); for (auto &p : P[i]) for (auto &x : T[p]) T[i].insert(x); queue<int> Q; for (auto &x : T[i]) { if (x != i) { ans[i] += val[x]; if (H[x] == i) { val[i] += val[x]; Q.push(x); continue; } } if (G[i].first >= 0) { if (G[i].second >= 0) H[x] = max(H[x], G[i].second); else H[x] = max(H[x], G[i].first); } } while (Q.size()) { T[i].erase(Q.front()); Q.pop(); } // debug(i, val[i], ans[i], T[i]); } ll sum = 0; for (auto &a : ans) sum = (sum + rev(a)) % MOD; cout << sum << endl; } } |