#include <iostream> #include <vector> #include <tuple> #include <queue> #include <numeric> const long long MOD = 1'000'000'000 + 7; struct segmentTree { int N = 1; std::vector<int> color; segmentTree(int n) { while(N < n) { N *= 2; } color.resize(2 * N, -1); } void insert(int l, int r, int v, int p, int q, int c) { if(q < l || r < p) { return; } if(p <= l && r <= q) { color[v] = c; return; } int m = (l + r) / 2; if(color[v] != -1) { color[2 * v] = color[v]; color[2 * v + 1] = color[v]; } insert(l, m, 2 * v, p, q, c); insert(m + 1, r, 2 * v + 1, p, q, c); if(color[2 * v] == color[2 * v + 1]) { color[v] = color[2 * v]; } else { color[v] = -1; } } void set(int p, int q, int c) { insert(0, N - 1, 1, p, q, c); } int get(int p) { p += N; int result = -1; while(p > 0) { if(color[p] != -1) { result = color[p]; } p /= 2; } return result; } }; long long mod_pow(long long a, long long b) { if(b == 0) { return 1; } if(b % 2 == 1) { return (a * mod_pow(a, b - 1)) % MOD; } long long x = mod_pow(a, b / 2); return (x * x) % MOD; } long long inverse(long long a) { return mod_pow(a, MOD - 2); } int main() { std::ios_base::sync_with_stdio(0); std::cin.tie(0); std::cin.tie(0); int N; std::cin >> N; std::vector<std::pair<int, int>> segments(N); for(auto& [p, q] : segments) { std::cin >> p >> q; q--; } std::vector<std::vector<int>> G(N); segmentTree tree(2*N); for(int i = 0; i < N; i++) { auto [p, q] = segments[i]; int left = tree.get(p); int right = tree.get(q); if(left != -1) { G[i].push_back(left); } if(right != -1 && right != left) { G[i].push_back(right); } tree.set(p, q, i); } auto simple_prob = [&]() { std::vector<long long> cnt(N); for(int i = 0; i < N; i++) { std::queue<int> Q; std::vector<bool> visited(N); Q.push(i); visited[i] = true; while(!Q.empty()) { int v = Q.front(); Q.pop(); for(int u : G[v]) { if(!visited[u]) { visited[u] = true; Q.push(u); cnt[u]++; } } } } return cnt; }; auto cnt = simple_prob(); long long A = 0, B = 1; for(int i = 0; i < N; i++) { long long C = 1, D = cnt[i] + 1; long long numerator = (A * D + B * C) % MOD; long long denominator = (B * D) % MOD; A = numerator; B = denominator; long long d = std::gcd(A, B); A /= d; B /= d; } std::cout << (A * inverse(B)) % MOD << '\n'; 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 | #include <iostream> #include <vector> #include <tuple> #include <queue> #include <numeric> const long long MOD = 1'000'000'000 + 7; struct segmentTree { int N = 1; std::vector<int> color; segmentTree(int n) { while(N < n) { N *= 2; } color.resize(2 * N, -1); } void insert(int l, int r, int v, int p, int q, int c) { if(q < l || r < p) { return; } if(p <= l && r <= q) { color[v] = c; return; } int m = (l + r) / 2; if(color[v] != -1) { color[2 * v] = color[v]; color[2 * v + 1] = color[v]; } insert(l, m, 2 * v, p, q, c); insert(m + 1, r, 2 * v + 1, p, q, c); if(color[2 * v] == color[2 * v + 1]) { color[v] = color[2 * v]; } else { color[v] = -1; } } void set(int p, int q, int c) { insert(0, N - 1, 1, p, q, c); } int get(int p) { p += N; int result = -1; while(p > 0) { if(color[p] != -1) { result = color[p]; } p /= 2; } return result; } }; long long mod_pow(long long a, long long b) { if(b == 0) { return 1; } if(b % 2 == 1) { return (a * mod_pow(a, b - 1)) % MOD; } long long x = mod_pow(a, b / 2); return (x * x) % MOD; } long long inverse(long long a) { return mod_pow(a, MOD - 2); } int main() { std::ios_base::sync_with_stdio(0); std::cin.tie(0); std::cin.tie(0); int N; std::cin >> N; std::vector<std::pair<int, int>> segments(N); for(auto& [p, q] : segments) { std::cin >> p >> q; q--; } std::vector<std::vector<int>> G(N); segmentTree tree(2*N); for(int i = 0; i < N; i++) { auto [p, q] = segments[i]; int left = tree.get(p); int right = tree.get(q); if(left != -1) { G[i].push_back(left); } if(right != -1 && right != left) { G[i].push_back(right); } tree.set(p, q, i); } auto simple_prob = [&]() { std::vector<long long> cnt(N); for(int i = 0; i < N; i++) { std::queue<int> Q; std::vector<bool> visited(N); Q.push(i); visited[i] = true; while(!Q.empty()) { int v = Q.front(); Q.pop(); for(int u : G[v]) { if(!visited[u]) { visited[u] = true; Q.push(u); cnt[u]++; } } } } return cnt; }; auto cnt = simple_prob(); long long A = 0, B = 1; for(int i = 0; i < N; i++) { long long C = 1, D = cnt[i] + 1; long long numerator = (A * D + B * C) % MOD; long long denominator = (B * D) % MOD; A = numerator; B = denominator; long long d = std::gcd(A, B); A /= d; B /= d; } std::cout << (A * inverse(B)) % MOD << '\n'; return 0; } |