#include<bits/stdc++.h> using namespace std; const long long mod = 1e9 + 7; long long fast_pow(long long a, long long b) { if(b == 0) return 1; long long res = 1; a %= mod; while(b > 0) { if(b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; } vector<vector<int>> G; vector<int> anc; vector<int> vis; void dfs(int v, int num) { vis[v] = num; anc[v]++; for(auto x : G[v]) { if(vis[x] != num) { dfs(x, num); } } } void solve() { int n; cin >> n; vector<pair<int, int>> pol(n); for(int i = 0; i < n; i++) cin >> pol[i].first >> pol[i].second; reverse(pol.begin(), pol.end()); set<pair<int, int>> s; G.assign(n + 1, vector<int>()); vector<int> st(n + 1, 0); for(int i = 0; i < n; i++) { while(s.lower_bound({pol[i].first, 0}) != s.end() && (*s.lower_bound({pol[i].first, 0})).first < pol[i].second) { G[(*s.lower_bound({pol[i].first, 0})).second].push_back(i + 1); s.erase(s.lower_bound({pol[i].first, 0})); st[i + 1]++; } s.emplace(pol[i].first, i + 1); s.emplace(pol[i].second, i + 1); } anc.assign(n + 1, 0); //toposort queue<int> q; vector<int> topo; for(int i = 1; i <= n; i++) { if(st[i] == 0) q.push(i); } while(!q.empty()) { int v = q.front(); q.pop(); topo.push_back(v); for(auto x : G[v]) { st[x]--; if(st[x] == 0) q.push(x); } } //for(auto x : topo) cout << x << " "; //cout << "\n"; vis.assign(n + 1, 0); for(int i = 1; i <= n; i++) { dfs(i, i); } //for(int i = 1; i <= n; i++) anc[i]--; //for(int i = 1; i <= n; i++) cout << anc[i] << " "; //cout << "\n"; //calculating inverses vector<long long> inv(n + 1, 0); for(int i = 0; i <= n; i++) inv[i] = fast_pow(i, mod - 2); long long ans = 0LL; for(auto x : topo) { ans = (ans + inv[anc[x]]) % mod; } cout << ans << "\n"; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); solve(); return 0; }
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 | #include<bits/stdc++.h> using namespace std; const long long mod = 1e9 + 7; long long fast_pow(long long a, long long b) { if(b == 0) return 1; long long res = 1; a %= mod; while(b > 0) { if(b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; } vector<vector<int>> G; vector<int> anc; vector<int> vis; void dfs(int v, int num) { vis[v] = num; anc[v]++; for(auto x : G[v]) { if(vis[x] != num) { dfs(x, num); } } } void solve() { int n; cin >> n; vector<pair<int, int>> pol(n); for(int i = 0; i < n; i++) cin >> pol[i].first >> pol[i].second; reverse(pol.begin(), pol.end()); set<pair<int, int>> s; G.assign(n + 1, vector<int>()); vector<int> st(n + 1, 0); for(int i = 0; i < n; i++) { while(s.lower_bound({pol[i].first, 0}) != s.end() && (*s.lower_bound({pol[i].first, 0})).first < pol[i].second) { G[(*s.lower_bound({pol[i].first, 0})).second].push_back(i + 1); s.erase(s.lower_bound({pol[i].first, 0})); st[i + 1]++; } s.emplace(pol[i].first, i + 1); s.emplace(pol[i].second, i + 1); } anc.assign(n + 1, 0); //toposort queue<int> q; vector<int> topo; for(int i = 1; i <= n; i++) { if(st[i] == 0) q.push(i); } while(!q.empty()) { int v = q.front(); q.pop(); topo.push_back(v); for(auto x : G[v]) { st[x]--; if(st[x] == 0) q.push(x); } } //for(auto x : topo) cout << x << " "; //cout << "\n"; vis.assign(n + 1, 0); for(int i = 1; i <= n; i++) { dfs(i, i); } //for(int i = 1; i <= n; i++) anc[i]--; //for(int i = 1; i <= n; i++) cout << anc[i] << " "; //cout << "\n"; //calculating inverses vector<long long> inv(n + 1, 0); for(int i = 0; i <= n; i++) inv[i] = fast_pow(i, mod - 2); long long ans = 0LL; for(auto x : topo) { ans = (ans + inv[anc[x]]) % mod; } cout << ans << "\n"; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); solve(); return 0; } |