#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int my_pow(int a, int b) {
int r = 1;
while (b) {
if (b % 2) {
r = (long long) r * a % MOD;
}
a = (long long) a * a % MOD;
b /= 2;
}
return r;
}
int my_inv(int a) {
return my_pow(a, MOD - 2);
}
int main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
int n;
cin >> n;
// from the bottom
vector<pair<int,int>> a(n);
for (pair<int,int>& p : a) {
cin >> p.first >> p.second;
}
// vector<int> perm(2 * n);
// for (int i = 0; i < 2 * n; i++) {
// perm[i] = i + 1;
// }
// random_shuffle(perm.begin(), perm.end());
// for (int i = 0; i < n; i++) {
// int x = min(perm[2*i], perm[2*i+1]);
// int y = max(perm[2*i], perm[2*i+1]);
// a[i] = {x, y};
// }
// from the top
reverse(a.begin(), a.end());
vector<vector<int>> edges(n);
set<pair<int,int>> s;
for (int i = 0; i < n; i++) {
auto it = s.lower_bound({a[i].first,0});
while (it != s.end() && it->first < a[i].second) {
auto it2 = it;
it2++;
edges[it->second].push_back(i);
s.erase(it);
it = it2;
}
s.insert({a[i].first, i});
s.insert({a[i].second, i});
/*
for (int x : {a[i].first, a[i].second}) {
// if (i + 1 < n) {
// int k = i + 1 + rand() % (n - (i + 1));
// edges[i].push_back(k);
// }
for (int k = i + 1; k < n; k++) {
if (a[k].first < x && x < a[k].second) {
edges[i].push_back(k);
break;
}
}
}
edges[i].resize(2);*/
}
for (int i = 0; i < n; i++) {
edges[i].resize(2);
// if (i + 1 < n) {
// for (int& x : edges[i]) {
// x = i + 1 + rand() % (n - (i + 1));
// }
// }
}
vector<int> answer(n);
const int MAGIC = 128;
vector<bitset<MAGIC>> mask(n);
for (int start = 0; start < n; start += MAGIC) {
for (int i = start; i < min(n, start + MAGIC); i++) {
mask[i][i-start] = 1;
mask[edges[i][0]] |= mask[i];
mask[edges[i][1]] |= mask[i];
answer[i] += mask[i].count();
mask[i] = 0;
}
for (int i = start + MAGIC; i < n; i++) {
mask[edges[i][0]] |= mask[i];
mask[edges[i][1]] |= mask[i];
answer[i] += mask[i].count();
mask[i] = 0;
}
}
int total = 0;
for (int i = 0; i < n; i++) {
total = (total + my_inv(answer[i])) % MOD;
}
cout << total << 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 | #include <bits/stdc++.h> using namespace std; const int MOD = 1e9 + 7; int my_pow(int a, int b) { int r = 1; while (b) { if (b % 2) { r = (long long) r * a % MOD; } a = (long long) a * a % MOD; b /= 2; } return r; } int my_inv(int a) { return my_pow(a, MOD - 2); } int main() { cin.tie(0); ios_base::sync_with_stdio(0); int n; cin >> n; // from the bottom vector<pair<int,int>> a(n); for (pair<int,int>& p : a) { cin >> p.first >> p.second; } // vector<int> perm(2 * n); // for (int i = 0; i < 2 * n; i++) { // perm[i] = i + 1; // } // random_shuffle(perm.begin(), perm.end()); // for (int i = 0; i < n; i++) { // int x = min(perm[2*i], perm[2*i+1]); // int y = max(perm[2*i], perm[2*i+1]); // a[i] = {x, y}; // } // from the top reverse(a.begin(), a.end()); vector<vector<int>> edges(n); set<pair<int,int>> s; for (int i = 0; i < n; i++) { auto it = s.lower_bound({a[i].first,0}); while (it != s.end() && it->first < a[i].second) { auto it2 = it; it2++; edges[it->second].push_back(i); s.erase(it); it = it2; } s.insert({a[i].first, i}); s.insert({a[i].second, i}); /* for (int x : {a[i].first, a[i].second}) { // if (i + 1 < n) { // int k = i + 1 + rand() % (n - (i + 1)); // edges[i].push_back(k); // } for (int k = i + 1; k < n; k++) { if (a[k].first < x && x < a[k].second) { edges[i].push_back(k); break; } } } edges[i].resize(2);*/ } for (int i = 0; i < n; i++) { edges[i].resize(2); // if (i + 1 < n) { // for (int& x : edges[i]) { // x = i + 1 + rand() % (n - (i + 1)); // } // } } vector<int> answer(n); const int MAGIC = 128; vector<bitset<MAGIC>> mask(n); for (int start = 0; start < n; start += MAGIC) { for (int i = start; i < min(n, start + MAGIC); i++) { mask[i][i-start] = 1; mask[edges[i][0]] |= mask[i]; mask[edges[i][1]] |= mask[i]; answer[i] += mask[i].count(); mask[i] = 0; } for (int i = start + MAGIC; i < n; i++) { mask[edges[i][0]] |= mask[i]; mask[edges[i][1]] |= mask[i]; answer[i] += mask[i].count(); mask[i] = 0; } } int total = 0; for (int i = 0; i < n; i++) { total = (total + my_inv(answer[i])) % MOD; } cout << total << endl; } |
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