#include<bits/stdc++.h> using namespace std; vector<int>graf[500010]; const long long mod = 1000000007; long long silnie[500010]; long long osilnie[500010]; long long qp(long long a, long long b){ if(!b)return 1; if(b%2)return a*qp(a, b-1)%mod; auto c = qp(a, b/2); return c*c%mod; } long long o[500010]; void preprocess(int n) { o[1] = 1; for(long long i=2;i<=n;i++) o[i] = mod - (mod / i) * o[mod % i] % mod; } int policz[500010]; int lewy[500010], prawy[500010]; int mini[500010], maxi[500010]; const int base = 1<<20; int tree2[2*base], lazy2[2*base]; void push2(int x){ if(lazy2[x] == 0)return; tree2[x*2] = lazy2[x*2] = tree2[x*2+1] = lazy2[x*2+1] = lazy2[x]; lazy2[x] = 0; } int miotla(int w, int l, int p, int a, int b){ // printf("%d %d %d %d %d\n", w, l, p, a, b, tree2[w], lazy2[w]); if(l>b || p<a)return 0; if(a<=l && p<=b){ return tree2[w]; } push2(w); int pom = max(miotla(w*2, l, (l+p)/2, a, b), miotla(w*2+1, (l+p)/2+1, p, a, b)); tree2[w] = max(tree2[w*2], tree2[w*2+1]); return pom; } void zamiec(int w, int l, int p, int a, int b, int val){ if(l>b || p<a)return; if(a<=l && p<=b){ tree2[w] = val; lazy2[w] = val; return; } push2(w); zamiec(w*2, l, (l+p)/2, a, b, val); zamiec(w*2+1, (l+p)/2+1, p, a, b, val); tree2[w] = max(tree2[w*2], tree2[w*2+1]); } pair<int,int> jumpL[500010][21], jumpR[500010][21]; int main() { int n, i, j, a, b; scanf("%d", &n); silnie[0] = 1; for(int i=1;i<=n;i++) silnie[i] = (silnie[i-1]*i)%mod; osilnie[n] = qp(silnie[n], mod-2); for(int i=n-1;i>=0;i--)osilnie[i] = (osilnie[i+1]*(i+1))%mod; preprocess(n+5); mini[0] = 1000010; long long on = qp(n ,mod-2); vector<pair<int,int>>stosik; for(i=1;i<=n;i++){ scanf("%d%d", &a, &b); mini[i] = lewy[i] = a; maxi[i] = prawy[i] = b; int pom = miotla(1, 0, base-1, a, a); // printf("%d ", pom); if(pom!=0) graf[i].push_back(pom); pom = miotla(1, 0, base-1, b, b); // printf("%d\n", pom); if(pom!=0 && (graf[i].size()==0||graf[i][0]!=pom)) graf[i].push_back(pom); for(auto j: graf[i])mini[i] = min(mini[i], mini[j]); for(auto j: graf[i])maxi[i] = max(maxi[i], maxi[j]); if(graf[i].size()==2){ if(maxi[graf[i][0]]>mini[graf[i][1]]){ // printf("MAJA CZESC WSPOLNA\n"); if(prawy[graf[i][0]]>lewy[graf[i][1]]){ graf[i].push_back(min(graf[i][0], graf[i][1])); } else{ int j1=20, j2=20; int pom1 = graf[i][0], pom2 = graf[i][1]; while(j1>=0 && jumpR[pom1][j1].first==0)j1--; while(j2>=0 && jumpL[pom2][j2].first==0)j2--; while(j1>=0 || j2>=0){ // printf("%d %d %d %d\n", pom1, pom2, j1, j2); pair<int,int>pom3, pom4; if(j1==-1) pom3 = {pom1, prawy[pom1]}; else pom3 = jumpR[pom1][j1]; if(j2==-1) pom4 = {pom2, lewy[pom2]}; else pom4 = jumpL[pom2][j2]; if(pom3.second < pom4.second){ if(j2==-1)pom1 = jumpR[pom1][j1--].first; else if(j1==-1)pom2 = jumpL[pom2][j2--].first; else{ if(pom3.first>pom4.first) pom1 = jumpR[pom1][j1--].first; else pom2 = jumpL[pom2][j2--].first; } } else{ if(j1==-1)j2--; else if(j2==-1)j1--; else{ if(pom3.first<pom4.first)j1--; else j2--; } } } // printf("%d %d %d %d\n", pom1, pom2, j1, j2); // printf("%d %d %d\n", kon, skoczL(graf[i][1], kon), skoczR(graf[i][0], kon)); if(prawy[pom1]>lewy[pom2]) pom = min(pom1, pom2); else{ if(jumpR[pom1][0].second>lewy[pom2] && jumpR[pom1][0].first>pom2)pom = pom2; else if(jumpL[pom2][0].first>pom1 && jumpL[pom2][0].second<prawy[pom1])pom = pom1; else pom = min(jumpR[pom1][0].first, jumpL[pom2][0].first); } graf[i].push_back(pom); } } } if(graf[i].size()){ if(graf[i].size()<3){ jumpR[i][0] = {graf[i].back(), max(prawy[i], prawy[graf[i].back()])}; jumpL[i][0] = {graf[i][0], min(lewy[i], lewy[graf[i][0]])}; } else{ jumpR[i][0] = {graf[i][1], max(prawy[i], prawy[graf[i][1]])}; jumpL[i][0] = {graf[i][0], min(lewy[i], lewy[graf[i][0]])}; } } for(int j=1;j<21;j++){ jumpL[i][j] = {jumpL[jumpL[i][j-1].first][j-1].first, min(jumpL[i][j-1].second, jumpL[jumpL[i][j-1].first][j-1].second)}; jumpR[i][j] = {jumpR[jumpR[i][j-1].first][j-1].first, max(jumpR[i][j-1].second, jumpR[jumpR[i][j-1].first][j-1].second)}; } zamiec(1, 0, base-1, a, b, i); } for(i=n;i>=1;i--){ policz[i]++; // printf("%d: %d ", i, policz[i]);for(auto j: graf[i])printf("%d ", j);printf("\n"); if(graf[i].size()==3){ policz[graf[i][0]]+=policz[i]; policz[graf[i][1]]+=policz[i]; policz[graf[i][2]]-=policz[i]; } else{ for(auto j: graf[i])policz[j]+=policz[i]; } } long long wynik = 0; for(i=1;i<=n;i++){ // printf("i:%d: POLICZ:%d GRAF: ", i, policz[i]);for(auto j: graf[i])printf("%d ", j);printf("\n"); policz[i]--; long long pom = on*silnie[n-1-policz[i]]%mod*osilnie[n-1]%mod*(silnie[n]*(n-policz[i])%mod*o[policz[i]+1]%mod*osilnie[n-policz[i]]%mod)%mod; wynik = (wynik + pom)%mod; } printf("%lld\n", wynik); }
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 | #include<bits/stdc++.h> using namespace std; vector<int>graf[500010]; const long long mod = 1000000007; long long silnie[500010]; long long osilnie[500010]; long long qp(long long a, long long b){ if(!b)return 1; if(b%2)return a*qp(a, b-1)%mod; auto c = qp(a, b/2); return c*c%mod; } long long o[500010]; void preprocess(int n) { o[1] = 1; for(long long i=2;i<=n;i++) o[i] = mod - (mod / i) * o[mod % i] % mod; } int policz[500010]; int lewy[500010], prawy[500010]; int mini[500010], maxi[500010]; const int base = 1<<20; int tree2[2*base], lazy2[2*base]; void push2(int x){ if(lazy2[x] == 0)return; tree2[x*2] = lazy2[x*2] = tree2[x*2+1] = lazy2[x*2+1] = lazy2[x]; lazy2[x] = 0; } int miotla(int w, int l, int p, int a, int b){ // printf("%d %d %d %d %d\n", w, l, p, a, b, tree2[w], lazy2[w]); if(l>b || p<a)return 0; if(a<=l && p<=b){ return tree2[w]; } push2(w); int pom = max(miotla(w*2, l, (l+p)/2, a, b), miotla(w*2+1, (l+p)/2+1, p, a, b)); tree2[w] = max(tree2[w*2], tree2[w*2+1]); return pom; } void zamiec(int w, int l, int p, int a, int b, int val){ if(l>b || p<a)return; if(a<=l && p<=b){ tree2[w] = val; lazy2[w] = val; return; } push2(w); zamiec(w*2, l, (l+p)/2, a, b, val); zamiec(w*2+1, (l+p)/2+1, p, a, b, val); tree2[w] = max(tree2[w*2], tree2[w*2+1]); } pair<int,int> jumpL[500010][21], jumpR[500010][21]; int main() { int n, i, j, a, b; scanf("%d", &n); silnie[0] = 1; for(int i=1;i<=n;i++) silnie[i] = (silnie[i-1]*i)%mod; osilnie[n] = qp(silnie[n], mod-2); for(int i=n-1;i>=0;i--)osilnie[i] = (osilnie[i+1]*(i+1))%mod; preprocess(n+5); mini[0] = 1000010; long long on = qp(n ,mod-2); vector<pair<int,int>>stosik; for(i=1;i<=n;i++){ scanf("%d%d", &a, &b); mini[i] = lewy[i] = a; maxi[i] = prawy[i] = b; int pom = miotla(1, 0, base-1, a, a); // printf("%d ", pom); if(pom!=0) graf[i].push_back(pom); pom = miotla(1, 0, base-1, b, b); // printf("%d\n", pom); if(pom!=0 && (graf[i].size()==0||graf[i][0]!=pom)) graf[i].push_back(pom); for(auto j: graf[i])mini[i] = min(mini[i], mini[j]); for(auto j: graf[i])maxi[i] = max(maxi[i], maxi[j]); if(graf[i].size()==2){ if(maxi[graf[i][0]]>mini[graf[i][1]]){ // printf("MAJA CZESC WSPOLNA\n"); if(prawy[graf[i][0]]>lewy[graf[i][1]]){ graf[i].push_back(min(graf[i][0], graf[i][1])); } else{ int j1=20, j2=20; int pom1 = graf[i][0], pom2 = graf[i][1]; while(j1>=0 && jumpR[pom1][j1].first==0)j1--; while(j2>=0 && jumpL[pom2][j2].first==0)j2--; while(j1>=0 || j2>=0){ // printf("%d %d %d %d\n", pom1, pom2, j1, j2); pair<int,int>pom3, pom4; if(j1==-1) pom3 = {pom1, prawy[pom1]}; else pom3 = jumpR[pom1][j1]; if(j2==-1) pom4 = {pom2, lewy[pom2]}; else pom4 = jumpL[pom2][j2]; if(pom3.second < pom4.second){ if(j2==-1)pom1 = jumpR[pom1][j1--].first; else if(j1==-1)pom2 = jumpL[pom2][j2--].first; else{ if(pom3.first>pom4.first) pom1 = jumpR[pom1][j1--].first; else pom2 = jumpL[pom2][j2--].first; } } else{ if(j1==-1)j2--; else if(j2==-1)j1--; else{ if(pom3.first<pom4.first)j1--; else j2--; } } } // printf("%d %d %d %d\n", pom1, pom2, j1, j2); // printf("%d %d %d\n", kon, skoczL(graf[i][1], kon), skoczR(graf[i][0], kon)); if(prawy[pom1]>lewy[pom2]) pom = min(pom1, pom2); else{ if(jumpR[pom1][0].second>lewy[pom2] && jumpR[pom1][0].first>pom2)pom = pom2; else if(jumpL[pom2][0].first>pom1 && jumpL[pom2][0].second<prawy[pom1])pom = pom1; else pom = min(jumpR[pom1][0].first, jumpL[pom2][0].first); } graf[i].push_back(pom); } } } if(graf[i].size()){ if(graf[i].size()<3){ jumpR[i][0] = {graf[i].back(), max(prawy[i], prawy[graf[i].back()])}; jumpL[i][0] = {graf[i][0], min(lewy[i], lewy[graf[i][0]])}; } else{ jumpR[i][0] = {graf[i][1], max(prawy[i], prawy[graf[i][1]])}; jumpL[i][0] = {graf[i][0], min(lewy[i], lewy[graf[i][0]])}; } } for(int j=1;j<21;j++){ jumpL[i][j] = {jumpL[jumpL[i][j-1].first][j-1].first, min(jumpL[i][j-1].second, jumpL[jumpL[i][j-1].first][j-1].second)}; jumpR[i][j] = {jumpR[jumpR[i][j-1].first][j-1].first, max(jumpR[i][j-1].second, jumpR[jumpR[i][j-1].first][j-1].second)}; } zamiec(1, 0, base-1, a, b, i); } for(i=n;i>=1;i--){ policz[i]++; // printf("%d: %d ", i, policz[i]);for(auto j: graf[i])printf("%d ", j);printf("\n"); if(graf[i].size()==3){ policz[graf[i][0]]+=policz[i]; policz[graf[i][1]]+=policz[i]; policz[graf[i][2]]-=policz[i]; } else{ for(auto j: graf[i])policz[j]+=policz[i]; } } long long wynik = 0; for(i=1;i<=n;i++){ // printf("i:%d: POLICZ:%d GRAF: ", i, policz[i]);for(auto j: graf[i])printf("%d ", j);printf("\n"); policz[i]--; long long pom = on*silnie[n-1-policz[i]]%mod*osilnie[n-1]%mod*(silnie[n]*(n-policz[i])%mod*o[policz[i]+1]%mod*osilnie[n-policz[i]]%mod)%mod; wynik = (wynik + pom)%mod; } printf("%lld\n", wynik); } |