#include <bits/stdc++.h>
using namespace std;
//{
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define VAR(v, i) __typeof(i) v=(i)
#define all(v) (v).begin(),(v).end()
#define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define PII pair<int,int>
#define st first
#define nd second
#define pb push_back
#define lint long long int
#define VI vector<int>
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; ++it)
*this << ", " + 2 * (it == d.b) << *it;
ris << "]";
}
};
//{
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define make( x) int (x); scanf("%d",&(x));
#define make2( x, y) int (x), (y); scanf("%d%d",&(x),&(y));
#define make3(x, y, z) int (x), (y), (z); scanf("%d%d%d",&(x),&(y),&(z));
#define make4(x, y, z, t) int (x), (y), (z), (t); scanf("%d%d%d%d",&(x),&(y),&(z),&(t));
#define makev(v,n) VI (v); FOR(i,0,(n)) { make(a); (v).pb(a);}
#define IOS ios_base::sync_with_stdio(0)
#define HEAP priority_queue
#define read( x) scanf("%d",&(x));
#define read2( x, y) scanf("%d%d",&(x),&(y));
#define read3(x, y, z) scanf("%d%d%d",&(x),&(y),&(z));
#define read4(x, y, z, t) scanf("%d%d%d%d",&(x),&(y),&(z),&(t));
#define readv(v,n) FOR(i,0,(n)) { make(a); (v).pb(a);}
#define jeb() fflush(stdout);
//}
int mod = 1e9 + 7;
vector<PII> v;
int inv[500005];
int nad[1000005];
int anc[500005];
VI dol[500005];
int main() {
make(n);
inv[1] = 1;
FOR(i,2,n+1) {
int q = mod / i ;
int r = mod - q * i;
inv[i] = ((mod - q) * 1LL * inv[r])%mod;
}
FOR(i,0,n) {
make2(a, b); a--; b--;
v.pb({a,b});
}
// mamy DAG odpowiedz to suma 1/(#poprzednicy(v) + 1)
// dla ogolnego daga nie ma algosa :(
// trzeba jakos wykorzystac strukture
FOR(i,0,2*n) {
nad[i] = -1;
if (i < n) anc[i] = 0;
}
FOR(i,0,n) {
int a = v[i].st, b = v[i].nd;
if (nad[a] == -1 && nad[b] != -1) {
dol[i] = dol[nad[b]];
} else if (nad[a] != -1 && nad[b] == -1) {
dol[i] = dol[nad[a]];
} else if (nad[a] != -1 && nad[b] != -1) {
int i1 = 0, i2 = 0;
int p1 = nad[a], p2 = nad[b];
while (i1 < dol[p1].size() && i2 < dol[p2].size()) {
if (dol[p1][i1] < dol[p2][i2]) {
dol[i].pb(dol[p1][i1]); i1++;
} else if (dol[p1][i1] > dol[p2][i2]) {
dol[i].pb(dol[p2][i2]); i2++;
} else if (dol[p1][i1] == dol[p2][i2]) {
dol[i].pb(dol[p1][i1]); i1++; i2++;
}
}
FOR(ii,i1,dol[p1].size()) dol[i].pb(dol[p1][ii]);
FOR(ii,i2,dol[p2].size()) dol[i].pb(dol[p2][ii]);
}
dol[i].pb(i);
FOR(j,0,dol[i].size()) {
anc[dol[i][j]]++;
}
FOR(j,a,b+1) nad[j] = i;
}
int ans = 0;
FOR(i,0,n) {
ans = ans + inv[anc[i]];
if (ans >= mod) ans -= mod;
}
printf("%d\n", ans);
}
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 | #include <bits/stdc++.h> using namespace std; //{ #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define FORD(i, a, b) for(int i = (a); i >= (b); --i) #define VAR(v, i) __typeof(i) v=(i) #define all(v) (v).begin(),(v).end() #define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i) #define PII pair<int,int> #define st first #define nd second #define pb push_back #define lint long long int #define VI vector<int> #define sim template < class c #define ris return * this #define dor > debug & operator << #define eni(x) sim > typename \ enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) { sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; } sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...); struct debug { ~debug() { cerr << endl; } eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i)); } sim, class b dor(pair < b, c > d) { ris << "(" << d.first << ", " << d.second << ")"; } sim dor(rge<c> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; } }; //{ #define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] " #define make( x) int (x); scanf("%d",&(x)); #define make2( x, y) int (x), (y); scanf("%d%d",&(x),&(y)); #define make3(x, y, z) int (x), (y), (z); scanf("%d%d%d",&(x),&(y),&(z)); #define make4(x, y, z, t) int (x), (y), (z), (t); scanf("%d%d%d%d",&(x),&(y),&(z),&(t)); #define makev(v,n) VI (v); FOR(i,0,(n)) { make(a); (v).pb(a);} #define IOS ios_base::sync_with_stdio(0) #define HEAP priority_queue #define read( x) scanf("%d",&(x)); #define read2( x, y) scanf("%d%d",&(x),&(y)); #define read3(x, y, z) scanf("%d%d%d",&(x),&(y),&(z)); #define read4(x, y, z, t) scanf("%d%d%d%d",&(x),&(y),&(z),&(t)); #define readv(v,n) FOR(i,0,(n)) { make(a); (v).pb(a);} #define jeb() fflush(stdout); //} int mod = 1e9 + 7; vector<PII> v; int inv[500005]; int nad[1000005]; int anc[500005]; VI dol[500005]; int main() { make(n); inv[1] = 1; FOR(i,2,n+1) { int q = mod / i ; int r = mod - q * i; inv[i] = ((mod - q) * 1LL * inv[r])%mod; } FOR(i,0,n) { make2(a, b); a--; b--; v.pb({a,b}); } // mamy DAG odpowiedz to suma 1/(#poprzednicy(v) + 1) // dla ogolnego daga nie ma algosa :( // trzeba jakos wykorzystac strukture FOR(i,0,2*n) { nad[i] = -1; if (i < n) anc[i] = 0; } FOR(i,0,n) { int a = v[i].st, b = v[i].nd; if (nad[a] == -1 && nad[b] != -1) { dol[i] = dol[nad[b]]; } else if (nad[a] != -1 && nad[b] == -1) { dol[i] = dol[nad[a]]; } else if (nad[a] != -1 && nad[b] != -1) { int i1 = 0, i2 = 0; int p1 = nad[a], p2 = nad[b]; while (i1 < dol[p1].size() && i2 < dol[p2].size()) { if (dol[p1][i1] < dol[p2][i2]) { dol[i].pb(dol[p1][i1]); i1++; } else if (dol[p1][i1] > dol[p2][i2]) { dol[i].pb(dol[p2][i2]); i2++; } else if (dol[p1][i1] == dol[p2][i2]) { dol[i].pb(dol[p1][i1]); i1++; i2++; } } FOR(ii,i1,dol[p1].size()) dol[i].pb(dol[p1][ii]); FOR(ii,i2,dol[p2].size()) dol[i].pb(dol[p2][ii]); } dol[i].pb(i); FOR(j,0,dol[i].size()) { anc[dol[i][j]]++; } FOR(j,a,b+1) nad[j] = i; } int ans = 0; FOR(i,0,n) { ans = ans + inv[anc[i]]; if (ans >= mod) ans -= mod; } printf("%d\n", ans); } |
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