#include <algorithm> #include <cassert> #include <cstdio> #include <vector> #define REP(a, n) for (int a = 0; a < (n); ++a) #define FOR(a, b, c) for (int a = (b); a <= (c); ++a) #define FORD(a, b, c) for (int a = (b); a >= (c); --a) typedef long long LL; using namespace std; template<class T> inline int vsize(const T &t) { return t.size(); } ///////////////// #define MOD 1'000'000'007 void gcdExtended(LL a, LL b, LL &x, LL &y) { if (a == 0) { x = 0, y = 1; } else { LL y1; gcdExtended(b % a, a, y, y1); x = y1 - (b / a) * y; } } LL inv(int A) { LL x, y; gcdExtended(A, MOD, x, y); return (x % MOD + MOD) % MOD; } LL licz = 0, mian = 1; inline void dodaj(LL l2, LL m2) { licz = (licz * m2 + l2 * mian) % MOD; mian = (mian * m2) % MOD; } ///// #define MAXN 500'005 #define SIZE (1<<20) void dp_wstaw(int *dp, int p, int v) { p += SIZE; while (p) { dp[p] += v; p /= 2; } } int dp_ile(int *dp, int x, int y, int p = 1, int s = SIZE) { // koniec wliczamy if (x==0 && y==s-1) return dp[p]; s /= 2; return (x<s ? dp_ile(dp, x, min(y, s-1), 2*p, s) : 0) + (y>=s ? dp_ile(dp, max(0, x-s), y-s, 2*p+1, s) : 0); } int dp_ilezeruj(int *dp, int x, int y, int p = 1, int s = SIZE) { // koniec wliczamy int ret = 0; if (s==1) { ret = dp[p]; dp[p] = 0; } else { s /= 2; if (x<s && dp[2*p]) ret += dp_ilezeruj(dp, x, min(y, s-1), 2*p, s); if (y>=s && dp[2*p+1]) ret += dp_ilezeruj(dp, max(0, x-s), y-s, 2*p+1, s); dp[p] = dp[2*p]+dp[2*p+1]; } return ret; } int lewe[2*SIZE], prawe[2*SIZE]; ///// #define SIZE2 (SIZE*4) int N; int kra[MAXN][2]; //, dach[MAXN]; int d_status[2*SIZE2]; // 0 = na calosci to samo, 1 = schodz w dol int d_kto[2*SIZE2]; int d_koniec[MAXN][2], d_par[MAXN][2]; int d_find(int a, int b) { return d_par[a][b]==a ? a : (d_par[a][b] = d_find(d_par[a][b], b)); } void szukaj(int x, int y, vector<int> &wyn, int p = 1, int s = SIZE2) { if (d_status[p]==0) { if (d_kto[p]) wyn.push_back(d_kto[p]); return; } s /= 2; if (x<s) szukaj(x, min(y, s-1), wyn, 2*p, s); if (y>=s) szukaj(max(0, x-s), y-s, wyn, 2*p+1, s); } void ustaw(int x, int y, int ja, int p = 1, int s = SIZE2) { if (x==0 && y==s-1) { d_status[p] = 0; d_kto[p] = ja; return; } if (d_status[p]==0) { d_status[p] = 1; d_status[2*p] = d_status[2*p+1] = 0; d_kto[2*p] = d_kto[2*p+1] = d_kto[p]; } s /= 2; if (x<s) ustaw(x, min(y, s-1), ja, 2*p, s); if (y>=s) ustaw(max(0, x-s), y-s, ja, 2*p+1, s); } void ustaw_p(int x, int ja, int p = 1, int s = SIZE2) { if (s==1) { d_status[p] = 0; d_kto[p] = ja; return; } if (d_status[p]==0) { d_status[p] = 1; d_status[2*p] = d_status[2*p+1] = 0; d_kto[2*p] = d_kto[2*p+1] = d_kto[p]; } s /= 2; if (x<s) ustaw_p(x, ja, 2*p, s); else ustaw_p(x-s, ja, 2*p+1, s); } int znajdz_dach(int ja) { d_par[ja][0] = d_par[ja][1] = ja; int L = d_koniec[ja][0] = kra[ja][0]; int R = d_koniec[ja][1] = kra[ja][1]; vector<int> nad; szukaj(3*L, 3*R, nad); ustaw(3*L+2, 3*R, ja); // sort(nad.begin(), nad.end()); // nad.resize(unique(nad.begin(), nad.end()) - nad.begin()); int ret = 0; int lewy = 0, prawy = 0; for (int n : nad) { int ll, rr; int Ln = d_koniec[ll = d_find(n, 0)][0]; int Rn = d_koniec[rr = d_find(n, 1)][1]; if (Ln<L && Rn>R) ret = n; if (Rn<=R) { if (!lewy) d_koniec[lewy = rr][1] = L; else d_par[rr][1] = lewy; } if (Ln>=L) { if (!prawy) d_koniec[prawy = ll][0] = R; else d_par[ll][0] = prawy; } } ustaw_p(3*L+1, ret); ustaw_p(3*R+1, ret); return ret; } ///// int wynik[MAXN], naddachowe[MAXN]; int main() { scanf("%d", &N); FORD(a, N, 1) scanf("%d%d", &kra[a][0], &kra[a][1]); FOR(a, 1, N) { int poza = dp_ile(lewe, 0, kra[a][0]-1)+dp_ile(prawe, kra[a][1]+1, 2*N+100); int na_mnie = dp_ilezeruj(lewe, kra[a][0], kra[a][1]); dp_wstaw(lewe, kra[a][1], na_mnie+1); na_mnie = dp_ilezeruj(prawe, kra[a][0], kra[a][1]); dp_wstaw(prawe, kra[a][0], na_mnie+1); int d = znajdz_dach(a); naddachowe[a] = a-poza; if (d) poza += naddachowe[d]; wynik[a] = a-poza; dodaj(1, wynik[a]); //fprintf(stderr, "%d -> %d\n", a, wynik[a]); // fprintf(stderr, "%d -> %d / %d\n", a, wynik[a], d); } int res = licz*inv(mian)%MOD; printf("%d\n", res); }
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 | #include <algorithm> #include <cassert> #include <cstdio> #include <vector> #define REP(a, n) for (int a = 0; a < (n); ++a) #define FOR(a, b, c) for (int a = (b); a <= (c); ++a) #define FORD(a, b, c) for (int a = (b); a >= (c); --a) typedef long long LL; using namespace std; template<class T> inline int vsize(const T &t) { return t.size(); } ///////////////// #define MOD 1'000'000'007 void gcdExtended(LL a, LL b, LL &x, LL &y) { if (a == 0) { x = 0, y = 1; } else { LL y1; gcdExtended(b % a, a, y, y1); x = y1 - (b / a) * y; } } LL inv(int A) { LL x, y; gcdExtended(A, MOD, x, y); return (x % MOD + MOD) % MOD; } LL licz = 0, mian = 1; inline void dodaj(LL l2, LL m2) { licz = (licz * m2 + l2 * mian) % MOD; mian = (mian * m2) % MOD; } ///// #define MAXN 500'005 #define SIZE (1<<20) void dp_wstaw(int *dp, int p, int v) { p += SIZE; while (p) { dp[p] += v; p /= 2; } } int dp_ile(int *dp, int x, int y, int p = 1, int s = SIZE) { // koniec wliczamy if (x==0 && y==s-1) return dp[p]; s /= 2; return (x<s ? dp_ile(dp, x, min(y, s-1), 2*p, s) : 0) + (y>=s ? dp_ile(dp, max(0, x-s), y-s, 2*p+1, s) : 0); } int dp_ilezeruj(int *dp, int x, int y, int p = 1, int s = SIZE) { // koniec wliczamy int ret = 0; if (s==1) { ret = dp[p]; dp[p] = 0; } else { s /= 2; if (x<s && dp[2*p]) ret += dp_ilezeruj(dp, x, min(y, s-1), 2*p, s); if (y>=s && dp[2*p+1]) ret += dp_ilezeruj(dp, max(0, x-s), y-s, 2*p+1, s); dp[p] = dp[2*p]+dp[2*p+1]; } return ret; } int lewe[2*SIZE], prawe[2*SIZE]; ///// #define SIZE2 (SIZE*4) int N; int kra[MAXN][2]; //, dach[MAXN]; int d_status[2*SIZE2]; // 0 = na calosci to samo, 1 = schodz w dol int d_kto[2*SIZE2]; int d_koniec[MAXN][2], d_par[MAXN][2]; int d_find(int a, int b) { return d_par[a][b]==a ? a : (d_par[a][b] = d_find(d_par[a][b], b)); } void szukaj(int x, int y, vector<int> &wyn, int p = 1, int s = SIZE2) { if (d_status[p]==0) { if (d_kto[p]) wyn.push_back(d_kto[p]); return; } s /= 2; if (x<s) szukaj(x, min(y, s-1), wyn, 2*p, s); if (y>=s) szukaj(max(0, x-s), y-s, wyn, 2*p+1, s); } void ustaw(int x, int y, int ja, int p = 1, int s = SIZE2) { if (x==0 && y==s-1) { d_status[p] = 0; d_kto[p] = ja; return; } if (d_status[p]==0) { d_status[p] = 1; d_status[2*p] = d_status[2*p+1] = 0; d_kto[2*p] = d_kto[2*p+1] = d_kto[p]; } s /= 2; if (x<s) ustaw(x, min(y, s-1), ja, 2*p, s); if (y>=s) ustaw(max(0, x-s), y-s, ja, 2*p+1, s); } void ustaw_p(int x, int ja, int p = 1, int s = SIZE2) { if (s==1) { d_status[p] = 0; d_kto[p] = ja; return; } if (d_status[p]==0) { d_status[p] = 1; d_status[2*p] = d_status[2*p+1] = 0; d_kto[2*p] = d_kto[2*p+1] = d_kto[p]; } s /= 2; if (x<s) ustaw_p(x, ja, 2*p, s); else ustaw_p(x-s, ja, 2*p+1, s); } int znajdz_dach(int ja) { d_par[ja][0] = d_par[ja][1] = ja; int L = d_koniec[ja][0] = kra[ja][0]; int R = d_koniec[ja][1] = kra[ja][1]; vector<int> nad; szukaj(3*L, 3*R, nad); ustaw(3*L+2, 3*R, ja); // sort(nad.begin(), nad.end()); // nad.resize(unique(nad.begin(), nad.end()) - nad.begin()); int ret = 0; int lewy = 0, prawy = 0; for (int n : nad) { int ll, rr; int Ln = d_koniec[ll = d_find(n, 0)][0]; int Rn = d_koniec[rr = d_find(n, 1)][1]; if (Ln<L && Rn>R) ret = n; if (Rn<=R) { if (!lewy) d_koniec[lewy = rr][1] = L; else d_par[rr][1] = lewy; } if (Ln>=L) { if (!prawy) d_koniec[prawy = ll][0] = R; else d_par[ll][0] = prawy; } } ustaw_p(3*L+1, ret); ustaw_p(3*R+1, ret); return ret; } ///// int wynik[MAXN], naddachowe[MAXN]; int main() { scanf("%d", &N); FORD(a, N, 1) scanf("%d%d", &kra[a][0], &kra[a][1]); FOR(a, 1, N) { int poza = dp_ile(lewe, 0, kra[a][0]-1)+dp_ile(prawe, kra[a][1]+1, 2*N+100); int na_mnie = dp_ilezeruj(lewe, kra[a][0], kra[a][1]); dp_wstaw(lewe, kra[a][1], na_mnie+1); na_mnie = dp_ilezeruj(prawe, kra[a][0], kra[a][1]); dp_wstaw(prawe, kra[a][0], na_mnie+1); int d = znajdz_dach(a); naddachowe[a] = a-poza; if (d) poza += naddachowe[d]; wynik[a] = a-poza; dodaj(1, wynik[a]); //fprintf(stderr, "%d -> %d\n", a, wynik[a]); // fprintf(stderr, "%d -> %d / %d\n", a, wynik[a], d); } int res = licz*inv(mian)%MOD; printf("%d\n", res); } |