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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#507114 | #5746. DAG Generation | chimera | RE | 0ms | 4572kb | C++14 | 1.9kb | 2024-08-06 11:05:11 | 2024-08-06 11:05:12 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const ll MOD = 1000000009;
// idea: isolate one vertex at a time.
// what is the probability that vertex has the exact same set of connections?
// operation: add it to a random point in sequence and add edges in and out randomly.
// P(same) = 1/2^(n-1) * P(same set of previous vertices are possible next time.)
// idea: each individual vertex is only bad if (A) it is chosen and (B) it is on different side
// imagine we have L vertices before, R vertices after.
// fix positions for each of them: (N choose 1 + L + R)/(N!) = 1/(X!)(N-X)!
// each then remains on the right side: (L!)(R!)/(L + R + 1)!
ll modexp(ll a, ll x) {
ll r = 1;
while(x) {
if(x&1) (r *= a) %= MOD;
(a *= a) %= MOD;
x >>= 1;
}
return r;
}
ll modinv(ll x) {return modexp(x, MOD-2);}
vector<ll> facts(100001);
vector<ll> ifacts(100001);
ll nck(ll n, ll k) {
ll r = facts[n];
r *= ifacts[k]; r %= MOD;
r *=ifacts[n-k]; r %= MOD;
return r;
}
const ll MAXN = 101;
int main() {
facts[0] = 1;
for(ll i = 1; i < facts.size(); i++) facts[i] = facts[i-1]*i % MOD;
ifacts.back() = modinv(facts.back());
for(ll i = facts.size()-2; i >= 0; i--) {
ifacts[i] = (i+1)*ifacts[i+1] % MOD;
}
vector<ll> anses(MAXN);
vector<ll> bylr(MAXN);
bylr[0]=1;
ll one_half = modinv(2);
anses[1]=1;
for(ll i = 2; i < anses.size(); i++) {
anses[i] = anses[i-1];
ll goods = 0;
goods = ((modexp(2,i)-1+MOD)%MOD)*modinv(i) %MOD;
goods %= MOD;
anses[i] *= goods;
anses[i] %= MOD;
(anses[i] *= modexp(one_half, 2*(i-1))) %= MOD;
}
ll T; cin >> T; while(T--) {
ll N; cin >> N;
ll ans = 1-anses[N] + MOD;
ans %= MOD;
cout << ans << "\n";
}
}
詳細信息
Test #1:
score: 100
Accepted
time: 0ms
memory: 4436kb
input:
4 1 2 3 100
output:
0 375000004 117187502 778748905
result:
ok 4 number(s): "0 375000004 117187502 778748905"
Test #2:
score: 0
Accepted
time: 0ms
memory: 4572kb
input:
5 1 2 3 4 5
output:
0 375000004 117187502 213897708 995024095
result:
ok 5 number(s): "0 375000004 117187502 213897708 995024095"
Test #3:
score: -100
Runtime Error
input:
100000 64268 66535 9758 42907 84212 83488 27748 86198 80658 11614 93419 2528 96160 79473 83517 43109 37111 46603 93665 54540 84236 62717 24719 57225 8333 15728 40821 31719 13096 75018 76890 46244 75863 59618 67460 10326 84775 11276 83363 72071 9353 94316 9469 3969 78568 53071 96835 50125 2728 46756 ...