#include <bits/stdc++.h> #pragma GCC optimize("O3", "unroll-loops") #define pb emplace_back #define ins insert #define mp make_pair #define ssize(x) (int)x.size() #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define pii pair <int, int> #define pll pair <ll, ll> #define pld pair <ld, ld> #define st first #define nd second using namespace std; using ll = int_fast64_t; // using lll = __int128_t; using ld = long double; const int oo = 1e9 + 7; const ll ool = 1e18; const int mod = 1e9 + 7; void solve(){ int n; cin >> n; vector <pii> tab(n); for(auto &[x, y]: tab) cin >> x >> y; vector <ll> cnt(n); vector <vector<int>> g(n); for(int i = 1; i < n; i ++){ int l = tab[i].st, r = tab[i].nd; for(int j = i - 1; j >= 0; j --){ if(l != -1){ if(tab[j].st <= l && tab[j].nd >= l){ g[j].pb(i); l = -1; } } if(r != -1){ if(tab[j].st <= r && tab[j].nd >= r){ g[j].pb(i); r = -1; } } } } vector <bool> vis(n); function <void(int)> dfs = [&](int v){ vis[v] = 1; for(auto u: g[v]){ if(!vis[u]) dfs(u); } }; for(int i = 0; i < n; i ++){ dfs(i); for(int j = 0; j < n; j ++){ if(vis[j]) ++ cnt[i]; } -- cnt[i]; fill(all(vis), 0); } vector <ll> fact(n + 3, 1); for(ll i = 1; i <= n; i ++) fact[i] = (fact[i - 1] * i) % mod; auto fp = [&](ll a, ll b){ ll r = 1; while(b){ if(b & 1) r = (r * a) % mod; a = (a * a) % mod; b >>= 1; } return r; }; ll ans = 0; for(int i = 0; i < n; i ++){ ll rn = 0; for(ll j = 0; j < n; j ++){ if(cnt[i] > n - j - 1){ rn += fact[n - 1]; rn %= mod; continue; } ll x = (fact[n - j - 1] * fp(fact[n - j - 1 - cnt[i]], mod - 2)) % mod; x = (x * fact[n - 1 - cnt[i]]) % mod; rn += (fact[n - 1] - x + mod) % mod; rn %= mod; } ans += (fact[n] - rn + mod) % mod; ans %= mod; } cout << (ans * fp(fact[n], mod - 2)) % mod << '\n'; } signed main(){ ios_base::sync_with_stdio(0); cin.tie(0); int t; t = 1; // cin >> t; while(t --) 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 96 97 98 99 | #include <bits/stdc++.h> #pragma GCC optimize("O3", "unroll-loops") #define pb emplace_back #define ins insert #define mp make_pair #define ssize(x) (int)x.size() #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define pii pair <int, int> #define pll pair <ll, ll> #define pld pair <ld, ld> #define st first #define nd second using namespace std; using ll = int_fast64_t; // using lll = __int128_t; using ld = long double; const int oo = 1e9 + 7; const ll ool = 1e18; const int mod = 1e9 + 7; void solve(){ int n; cin >> n; vector <pii> tab(n); for(auto &[x, y]: tab) cin >> x >> y; vector <ll> cnt(n); vector <vector<int>> g(n); for(int i = 1; i < n; i ++){ int l = tab[i].st, r = tab[i].nd; for(int j = i - 1; j >= 0; j --){ if(l != -1){ if(tab[j].st <= l && tab[j].nd >= l){ g[j].pb(i); l = -1; } } if(r != -1){ if(tab[j].st <= r && tab[j].nd >= r){ g[j].pb(i); r = -1; } } } } vector <bool> vis(n); function <void(int)> dfs = [&](int v){ vis[v] = 1; for(auto u: g[v]){ if(!vis[u]) dfs(u); } }; for(int i = 0; i < n; i ++){ dfs(i); for(int j = 0; j < n; j ++){ if(vis[j]) ++ cnt[i]; } -- cnt[i]; fill(all(vis), 0); } vector <ll> fact(n + 3, 1); for(ll i = 1; i <= n; i ++) fact[i] = (fact[i - 1] * i) % mod; auto fp = [&](ll a, ll b){ ll r = 1; while(b){ if(b & 1) r = (r * a) % mod; a = (a * a) % mod; b >>= 1; } return r; }; ll ans = 0; for(int i = 0; i < n; i ++){ ll rn = 0; for(ll j = 0; j < n; j ++){ if(cnt[i] > n - j - 1){ rn += fact[n - 1]; rn %= mod; continue; } ll x = (fact[n - j - 1] * fp(fact[n - j - 1 - cnt[i]], mod - 2)) % mod; x = (x * fact[n - 1 - cnt[i]]) % mod; rn += (fact[n - 1] - x + mod) % mod; rn %= mod; } ans += (fact[n] - rn + mod) % mod; ans %= mod; } cout << (ans * fp(fact[n], mod - 2)) % mod << '\n'; } signed main(){ ios_base::sync_with_stdio(0); cin.tie(0); int t; t = 1; // cin >> t; while(t --) solve(); return 0; } |