#include <bits/stdc++.h> #define all(x) (x).begin(),(x).end() using namespace std; using ll = long long; //using ld = long double; //#define int ll #define sz(x) ((int)(x).size()) using pii = pair<int,int>; using tii = tuple<int,int,int>; using tiii = tuple<int,int,int,int>; const int mod = 1e9 + 7, nmax = 1e6 + 5; struct Mint { int val; Mint(ll x = 0): val((x % mod + mod) % mod) {;} Mint operator +(const Mint& x) { return Mint(val + x.val); } Mint operator -(const Mint& x) { return Mint(val - x.val); } Mint operator *(const Mint& x) { return Mint((ll)val * x.val); } Mint operator +=(const Mint& x) { return *this = Mint(val + x.val); } Mint operator -=(const Mint& x) { return *this = Mint(val - x.val); } Mint operator *=(const Mint& x) { return *this = Mint((ll)val * x.val); } Mint operator ^(const int& _b) const { Mint accum = 1, a = *this; int b = _b; while(b) { accum = (b & 1? accum * a : accum); a *= a; b >>= 1; } return accum; } Mint operator /(const Mint& x) { return Mint((ll)val * (x ^ (mod - 2)).val); } Mint operator /=(const Mint& x) { return *this = Mint((ll)val * (x ^ (mod - 2)).val); } }; vector<vector<pii>> divisions; namespace Recolor { set<int> starts; int atr_ends[nmax]; int atr_color[nmax]; int CC[nmax]; int query(int p) { //return CC[p]; return atr_color[*prev(starts.upper_bound(p))]; } vector<int> color(int l, int r, int C) { if(prev(starts.upper_bound(l)) == prev(starts.upper_bound(r + 1))) { auto it = prev(starts.upper_bound(l)); auto elements = vector<int>{atr_color[*it]}; atr_ends[r + 1] = atr_ends[*it]; atr_ends[*it] = l - 1; atr_color[r + 1] = atr_color[*it]; atr_color[l] = C; atr_ends[l] = r; starts.emplace(l); starts.emplace(r + 1); return elements; } vector<int> elements; auto it = prev(starts.upper_bound(l)); elements.emplace_back(atr_color[*it]); if(*it <= l - 1) { atr_ends[*it] = l - 1; } else starts.erase(it); while((it = starts.upper_bound(l)) != starts.end() && *it <= r) { //if(C == 81) cerr << " ! " << *it << ' ' << atr_ends[*it] << ' ' << atr_color[l] << '\n'; elements.emplace_back(atr_color[*it]); if(atr_ends[*it] <= r) { starts.erase(it); } else { starts.emplace(r + 1); atr_color[r + 1] = atr_color[*it]; atr_ends[r + 1] = atr_ends[*it]; starts.erase(it); } } sort(all(elements)); elements.erase(unique(all(elements)), end(elements)); atr_ends[l] = r; atr_color[l] = C; starts.emplace(l); return elements; } void init(int n) { starts.emplace(0); atr_ends[0] = 2 * n + 1; atr_color[0] = 0; starts.emplace(2 * n + 2); return; } } namespace RectSum { vector<int> rez; vector<tiii> qs; void init() { rez.assign(1, 0); } int add_query(int h1, int h2, int l, int r) { int id = sz(rez); qs.emplace_back(h1, l, r, -id); qs.emplace_back(h2, l, r, id); rez.emplace_back(0); return id; } #define lsb(x) (x & -x) struct AIB { vector<int> tree; void init(int n) { tree.assign(n + 10, 0); } int query(int p) { int sum = 0; while(p > 0) sum += tree[p], p -= lsb(p); return sum; } void upd(int p, int x) { while(p < sz(tree)) tree[p] += x, p += lsb(p); return; } int query(int l, int r) { return query(r) - query(l - 1); } }; void initialise_sums(vector<pii> pcts) { sort(all(pcts)); sort(all(qs)); int ptr = 0; AIB aib; aib.init(sz(pcts) * 2); for(auto [h, p] : pcts) { while(ptr < sz(qs) && get<0>(qs[ptr]) < h) { rez[abs(get<3>(qs[ptr]))] += ((abs(get<3>(qs[ptr]))) / (get<3>(qs[ptr]))) * aib.query(get<1>(qs[ptr]), get<2>(qs[ptr])), ptr++; } aib.upd(p, 1); } while(ptr < sz(qs)) { rez[abs(get<3>(qs[ptr]))] += ((abs(get<3>(qs[ptr]))) / (get<3>(qs[ptr]))) * aib.query(get<1>(qs[ptr]), get<2>(qs[ptr])), ptr++; } return; } int query(int id) { return rez[abs(id)] * (id / abs(id)); } } int highest_link[nmax], right_sum[nmax], left_sum[nmax]; int rd[nmax], rjump[nmax], rp[nmax]; int ld[nmax], ljump[nmax], lp[nmax]; int dom_d[nmax], dom_jump[nmax], dom_p[nmax]; struct dirLink { int level, crease, last; } left_link[nmax], right_link[nmax]; vector<int> mergepoint_id[nmax]; int dom_lca(int a, int b) { if(dom_d[a] < dom_d[b]) swap(a, b); while(dom_d[a] > dom_d[b]) { if(dom_d[dom_jump[a]] > dom_d[b]) a = dom_jump[a]; a = dom_p[a]; } while(a != b) { if(dom_jump[a] != dom_jump[b]) a = dom_jump[a], b = dom_jump[b]; a = dom_p[a], b = dom_p[b]; } //cerr << a << '\n'; return a; } signed main() { cin.tie(0) -> sync_with_stdio(0); int n; cin >> n; RectSum::init(); vector<pii> segm(n + 1); for(auto &[l, r] : segm | views::drop(1)) cin >> l >> r; segm[0] = pii{0, 2 * n + 1}; reverse(1 + all(segm)); { // highest link and creases initialisation Recolor::init(2 * n); int ptr = 1; // probabil ca ar fi mers mai bine daca spargeam artificial fiecare segment in left/right pointer (????), defapt nu, sa imi bag pula daca mai stiu ceva // stiu ca imi iau o mare muie, that is for sure for(auto [l, r] : segm | views::drop(1)) { int LC = Recolor::query(l), RC = Recolor::query(r); int idom = LC; //for(int i = l; i <= r; i++) //idom = dom_lca(idom, Recolor::query(i)); auto C = Recolor::color(l, r, ptr); for(auto i : C) idom = dom_lca(idom, i); highest_link[ptr] = idom; dom_d[ptr] = dom_d[idom] + 1; dom_jump[ptr] = dom_p[ptr] = idom; if(dom_d[idom] + dom_d[dom_jump[dom_jump[idom]]] == 2 * dom_d[dom_jump[idom]]) dom_jump[ptr] = dom_jump[dom_jump[idom]]; lp[ptr] = ljump[ptr] = LC; rp[ptr] = rjump[ptr] = RC; ld[ptr] = ld[LC] + 1; rd[ptr] = rd[RC] + 1; if(ld[LC] + ld[ljump[ljump[LC]]] == 2 * ld[ljump[LC]]) ljump[ptr] = ljump[ljump[LC]]; if(rd[RC] + rd[rjump[rjump[RC]]] == 2 * rd[rjump[RC]]) rjump[ptr] = rjump[rjump[RC]]; int node_l = ptr, node_r = ptr; pii before_disaster(ptr, ptr); { while(ld[node_l] > ld[highest_link[ptr]]) { if(ld[ljump[node_l]] > ld[highest_link[ptr]]) node_l = ljump[node_l]; before_disaster.first = node_l; node_l = lp[node_l]; } while(rd[node_r] > rd[highest_link[ptr]]) { if(rd[rjump[node_r]] > rd[highest_link[ptr]]) node_r = rjump[node_r]; before_disaster.second = node_r; node_r = rp[node_r]; } } highest_link[ptr] = node_l; left_link[ptr].level = LC; right_link[ptr].level = RC; left_link[ptr].crease = RectSum::add_query(0, LC, segm[LC].first, l - 1); right_link[ptr].crease = RectSum::add_query(0, RC, r + 1, segm[RC].second); left_link[ptr].last = before_disaster.first; right_link[ptr].last = before_disaster.second; mergepoint_id[ptr].emplace_back(RectSum::add_query(0, ptr, l, r)); mergepoint_id[ptr].emplace_back(RectSum::add_query(0, highest_link[ptr], segm[before_disaster.first].first, segm[before_disaster.second].second)); ptr++; } } { // facem id-urile vector<pii> pcts; for(int i = 1; i <= n; i++) pcts.emplace_back(i, (segm[i].first + segm[i].second) / 2); RectSum::initialise_sums(pcts); } { // acum calculam sumele Mint sum = 0; for(int i = 1; i <= n; i++) { right_sum[i] = right_sum[right_link[i].level] + RectSum::query(right_link[i].crease); left_sum[i] = left_sum[left_link[i].level] + RectSum::query(left_link[i].crease); int here = right_sum[i] + left_sum[i] - left_sum[left_link[i].last] - right_sum[right_link[i].last] + RectSum::query(mergepoint_id[i][0]) + RectSum::query(-mergepoint_id[i][1]); sum += Mint(1) / Mint(here); } cout << sum.val << '\n'; } } /** Anul asta nu se da centroid -- Rugaciunile mele */
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 | #include <bits/stdc++.h> #define all(x) (x).begin(),(x).end() using namespace std; using ll = long long; //using ld = long double; //#define int ll #define sz(x) ((int)(x).size()) using pii = pair<int,int>; using tii = tuple<int,int,int>; using tiii = tuple<int,int,int,int>; const int mod = 1e9 + 7, nmax = 1e6 + 5; struct Mint { int val; Mint(ll x = 0): val((x % mod + mod) % mod) {;} Mint operator +(const Mint& x) { return Mint(val + x.val); } Mint operator -(const Mint& x) { return Mint(val - x.val); } Mint operator *(const Mint& x) { return Mint((ll)val * x.val); } Mint operator +=(const Mint& x) { return *this = Mint(val + x.val); } Mint operator -=(const Mint& x) { return *this = Mint(val - x.val); } Mint operator *=(const Mint& x) { return *this = Mint((ll)val * x.val); } Mint operator ^(const int& _b) const { Mint accum = 1, a = *this; int b = _b; while(b) { accum = (b & 1? accum * a : accum); a *= a; b >>= 1; } return accum; } Mint operator /(const Mint& x) { return Mint((ll)val * (x ^ (mod - 2)).val); } Mint operator /=(const Mint& x) { return *this = Mint((ll)val * (x ^ (mod - 2)).val); } }; vector<vector<pii>> divisions; namespace Recolor { set<int> starts; int atr_ends[nmax]; int atr_color[nmax]; int CC[nmax]; int query(int p) { //return CC[p]; return atr_color[*prev(starts.upper_bound(p))]; } vector<int> color(int l, int r, int C) { if(prev(starts.upper_bound(l)) == prev(starts.upper_bound(r + 1))) { auto it = prev(starts.upper_bound(l)); auto elements = vector<int>{atr_color[*it]}; atr_ends[r + 1] = atr_ends[*it]; atr_ends[*it] = l - 1; atr_color[r + 1] = atr_color[*it]; atr_color[l] = C; atr_ends[l] = r; starts.emplace(l); starts.emplace(r + 1); return elements; } vector<int> elements; auto it = prev(starts.upper_bound(l)); elements.emplace_back(atr_color[*it]); if(*it <= l - 1) { atr_ends[*it] = l - 1; } else starts.erase(it); while((it = starts.upper_bound(l)) != starts.end() && *it <= r) { //if(C == 81) cerr << " ! " << *it << ' ' << atr_ends[*it] << ' ' << atr_color[l] << '\n'; elements.emplace_back(atr_color[*it]); if(atr_ends[*it] <= r) { starts.erase(it); } else { starts.emplace(r + 1); atr_color[r + 1] = atr_color[*it]; atr_ends[r + 1] = atr_ends[*it]; starts.erase(it); } } sort(all(elements)); elements.erase(unique(all(elements)), end(elements)); atr_ends[l] = r; atr_color[l] = C; starts.emplace(l); return elements; } void init(int n) { starts.emplace(0); atr_ends[0] = 2 * n + 1; atr_color[0] = 0; starts.emplace(2 * n + 2); return; } } namespace RectSum { vector<int> rez; vector<tiii> qs; void init() { rez.assign(1, 0); } int add_query(int h1, int h2, int l, int r) { int id = sz(rez); qs.emplace_back(h1, l, r, -id); qs.emplace_back(h2, l, r, id); rez.emplace_back(0); return id; } #define lsb(x) (x & -x) struct AIB { vector<int> tree; void init(int n) { tree.assign(n + 10, 0); } int query(int p) { int sum = 0; while(p > 0) sum += tree[p], p -= lsb(p); return sum; } void upd(int p, int x) { while(p < sz(tree)) tree[p] += x, p += lsb(p); return; } int query(int l, int r) { return query(r) - query(l - 1); } }; void initialise_sums(vector<pii> pcts) { sort(all(pcts)); sort(all(qs)); int ptr = 0; AIB aib; aib.init(sz(pcts) * 2); for(auto [h, p] : pcts) { while(ptr < sz(qs) && get<0>(qs[ptr]) < h) { rez[abs(get<3>(qs[ptr]))] += ((abs(get<3>(qs[ptr]))) / (get<3>(qs[ptr]))) * aib.query(get<1>(qs[ptr]), get<2>(qs[ptr])), ptr++; } aib.upd(p, 1); } while(ptr < sz(qs)) { rez[abs(get<3>(qs[ptr]))] += ((abs(get<3>(qs[ptr]))) / (get<3>(qs[ptr]))) * aib.query(get<1>(qs[ptr]), get<2>(qs[ptr])), ptr++; } return; } int query(int id) { return rez[abs(id)] * (id / abs(id)); } } int highest_link[nmax], right_sum[nmax], left_sum[nmax]; int rd[nmax], rjump[nmax], rp[nmax]; int ld[nmax], ljump[nmax], lp[nmax]; int dom_d[nmax], dom_jump[nmax], dom_p[nmax]; struct dirLink { int level, crease, last; } left_link[nmax], right_link[nmax]; vector<int> mergepoint_id[nmax]; int dom_lca(int a, int b) { if(dom_d[a] < dom_d[b]) swap(a, b); while(dom_d[a] > dom_d[b]) { if(dom_d[dom_jump[a]] > dom_d[b]) a = dom_jump[a]; a = dom_p[a]; } while(a != b) { if(dom_jump[a] != dom_jump[b]) a = dom_jump[a], b = dom_jump[b]; a = dom_p[a], b = dom_p[b]; } //cerr << a << '\n'; return a; } signed main() { cin.tie(0) -> sync_with_stdio(0); int n; cin >> n; RectSum::init(); vector<pii> segm(n + 1); for(auto &[l, r] : segm | views::drop(1)) cin >> l >> r; segm[0] = pii{0, 2 * n + 1}; reverse(1 + all(segm)); { // highest link and creases initialisation Recolor::init(2 * n); int ptr = 1; // probabil ca ar fi mers mai bine daca spargeam artificial fiecare segment in left/right pointer (????), defapt nu, sa imi bag pula daca mai stiu ceva // stiu ca imi iau o mare muie, that is for sure for(auto [l, r] : segm | views::drop(1)) { int LC = Recolor::query(l), RC = Recolor::query(r); int idom = LC; //for(int i = l; i <= r; i++) //idom = dom_lca(idom, Recolor::query(i)); auto C = Recolor::color(l, r, ptr); for(auto i : C) idom = dom_lca(idom, i); highest_link[ptr] = idom; dom_d[ptr] = dom_d[idom] + 1; dom_jump[ptr] = dom_p[ptr] = idom; if(dom_d[idom] + dom_d[dom_jump[dom_jump[idom]]] == 2 * dom_d[dom_jump[idom]]) dom_jump[ptr] = dom_jump[dom_jump[idom]]; lp[ptr] = ljump[ptr] = LC; rp[ptr] = rjump[ptr] = RC; ld[ptr] = ld[LC] + 1; rd[ptr] = rd[RC] + 1; if(ld[LC] + ld[ljump[ljump[LC]]] == 2 * ld[ljump[LC]]) ljump[ptr] = ljump[ljump[LC]]; if(rd[RC] + rd[rjump[rjump[RC]]] == 2 * rd[rjump[RC]]) rjump[ptr] = rjump[rjump[RC]]; int node_l = ptr, node_r = ptr; pii before_disaster(ptr, ptr); { while(ld[node_l] > ld[highest_link[ptr]]) { if(ld[ljump[node_l]] > ld[highest_link[ptr]]) node_l = ljump[node_l]; before_disaster.first = node_l; node_l = lp[node_l]; } while(rd[node_r] > rd[highest_link[ptr]]) { if(rd[rjump[node_r]] > rd[highest_link[ptr]]) node_r = rjump[node_r]; before_disaster.second = node_r; node_r = rp[node_r]; } } highest_link[ptr] = node_l; left_link[ptr].level = LC; right_link[ptr].level = RC; left_link[ptr].crease = RectSum::add_query(0, LC, segm[LC].first, l - 1); right_link[ptr].crease = RectSum::add_query(0, RC, r + 1, segm[RC].second); left_link[ptr].last = before_disaster.first; right_link[ptr].last = before_disaster.second; mergepoint_id[ptr].emplace_back(RectSum::add_query(0, ptr, l, r)); mergepoint_id[ptr].emplace_back(RectSum::add_query(0, highest_link[ptr], segm[before_disaster.first].first, segm[before_disaster.second].second)); ptr++; } } { // facem id-urile vector<pii> pcts; for(int i = 1; i <= n; i++) pcts.emplace_back(i, (segm[i].first + segm[i].second) / 2); RectSum::initialise_sums(pcts); } { // acum calculam sumele Mint sum = 0; for(int i = 1; i <= n; i++) { right_sum[i] = right_sum[right_link[i].level] + RectSum::query(right_link[i].crease); left_sum[i] = left_sum[left_link[i].level] + RectSum::query(left_link[i].crease); int here = right_sum[i] + left_sum[i] - left_sum[left_link[i].last] - right_sum[right_link[i].last] + RectSum::query(mergepoint_id[i][0]) + RectSum::query(-mergepoint_id[i][1]); sum += Mint(1) / Mint(here); } cout << sum.val << '\n'; } } /** Anul asta nu se da centroid -- Rugaciunile mele */ |