ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#158758 | #31. MST | jijidawang | 100 | 366ms | 41456kb | C++11 | 3.3kb | 2022-08-18 19:41:57 | 2022-08-18 19:41:59 |
answer
#include <bits/stdc++.h>
typedef long long ll;typedef unsigned long long ull; typedef double db;typedef long double ldb;
#define fre(x) freopen(#x ".in","r",stdin),freopen(#x ".out","w",stdout)
#define Rep(i,a,b) for(int i=a;i<=b;++i)
#define Dwn(i,a,b) for(int i=a;i>=b;--i)
#define pii pair<int,int>
#define mair make_pair
#define fir first
#define sec second
#define int ll
using namespace std;
const int maxn=40+10,M=2e3+10,Mod=1e9+7,inv2=500000004;
const ull base=131;
int pw(int x,int p){int res=1,base=x;while(p){if(p&1)res=1LL*res*base%Mod;base=1LL*base*base%Mod;p>>=1;}return res;}
int Inv(int x){return pw(x,Mod-2);}
struct Sits{
bitset<44>bit;
int cnt[maxn];
void Del(int x,int d){cnt[x]-=d;if(!cnt[x])bit[x]=0;}
void Add(int x,int d){if(!cnt[x] && d)bit[x]=1;cnt[x]+=d;}
ull Hash(){ ull hs=0; for(int i=1;i<=40;++i)hs=hs*base+cnt[i];return hs; }
}P[50000];
int tot=1;
int a[maxn],n;
struct eg{int from,to,next;int x,y;}e[M*M];
int head[40010],len;
void lqx(int from,int to,int x,int y)
{ e[++len].from=from,e[len].to=to,e[len].next=head[from],head[from]=len;e[len].x=x,e[len].y=y; }
unordered_map<ull,int>Vis;
void BDFS(){
queue<int>q;
P[1].bit.set(1);P[1].cnt[1]=n;
q.push(1);Vis[P[1].Hash()]=1;
while(!q.empty()){
int u=q.front();q.pop();
int x=P[u].bit._Find_first();
Sits A=P[u];
while(x<42 && P[u].bit[x]){
if(P[u].cnt[x]>=2){
A.Del(x,2);A.Add(x+x,1);
if(Vis.find(A.Hash())==Vis.end()){ P[++tot]=A; q.push(tot);Vis[A.Hash()]=tot; }
lqx(u,Vis[A.Hash()],x,x);
A.Add(x,2),A.Del(x+x,1);
}
int y=P[u].bit._Find_next(x);
while(y<42 && P[u].bit[y]){
A.Del(x,1),A.Del(y,1),A.Add(x+y,1);
if(Vis.find(A.Hash())==Vis.end()){ P[++tot]=A; q.push(tot);Vis[A.Hash()]=tot; }
lqx(u,Vis[A.Hash()],x,y);
A.Add(x,1),A.Add(y,1),A.Del(x+y,1);
y=P[u].bit._Find_next(y);
}
x=P[u].bit._Find_next(x);
}
}
cerr<<tot<<"\n";
cerr<<len<<"\n";
}
int dp[41][40010];
int fac[M],inv[M];
void Init(const int N=1600){
fac[0]=inv[0]=1;
Rep(i,1,N)fac[i]=1LL*fac[i-1]*i%Mod;
inv[N]=Inv(fac[N]);
Dwn(i,N-1,1)inv[i]=1LL*(inv[i+1])*(i+1)%Mod;
}
int Down(int n,int m){if(n<m)return 0;return 1LL*fac[n]*inv[n-m]%Mod;}
void solve(){
cin>>n;Rep(i,1,n-1)cin>>a[i];
sort(a+1,a+n);BDFS();Init();
dp[0][1]=1;
Rep(x,1,n-1){
if(x>1){
for(int u=1;u<=tot;++u)if(dp[x-1][u]){
int sum=0;
int y=P[u].bit._Find_first();
while(y<42 && P[u].bit[y]){
sum+=(1LL*y*(y-1)/2*P[u].cnt[y])%Mod;
y=P[u].bit._Find_next(y);
}
sum-=a[x-1];
dp[x-1][u]=1LL*dp[x-1][u]*Down(sum,a[x]-a[x-1]-1)%Mod;
}
}
for(int u=1;u<=tot;++u)if(dp[x-1][u]){
for(int i=head[u];i;i=e[i].next){
int v=e[i].to;int a=e[i].x,b=e[i].y;
if(a!=b)dp[x][v]=(dp[x][v]+1LL*dp[x-1][u]*P[u].cnt[a]%Mod*a%Mod*P[u].cnt[b]%Mod*b%Mod)%Mod;
else dp[x][v]=(dp[x][v]+1LL*dp[x-1][u]*P[u].cnt[a]%Mod*(P[u].cnt[a]-1)%Mod*inv2%Mod*a%Mod*a%Mod)%Mod;
}
}
}
int u;
Rep(i,1,tot)if(P[i].bit[n]){u=i;break;}
cerr<<dp[n-1][u]<<"\n";
//dp[n-1][u]=1LL*dp[n-1][u]*pw(1LL*n*(n-1)/2,1LL*n*(n-1)/2-a[n-1])%Mod;
int lim=n*(n-1)/2-a[n-1];
Rep(i,1,lim)dp[n-1][u]=1LL*dp[n-1][u]*i%Mod;
cout<<dp[n-1][u]<<"\n";
}
#undef int
int main (){ ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);return solve(),0; }
Details
小提示:点击横条可展开更详细的信息
Test #1:
score: 5
Accepted
time: 0ms
memory: 22252kb
input:
4 1 2 3
output:
576
result:
ok single line: '576'
Test #2:
score: 5
Accepted
time: 10ms
memory: 22248kb
input:
4 1 2 4
output:
144
result:
ok single line: '144'
Test #3:
score: 5
Accepted
time: 3ms
memory: 22252kb
input:
5 1 2 3 4
output:
2160000
result:
ok single line: '2160000'
Test #4:
score: 5
Accepted
time: 0ms
memory: 22252kb
input:
5 1 2 3 6
output:
276480
result:
ok single line: '276480'
Test #5:
score: 5
Accepted
time: 0ms
memory: 22260kb
input:
6 1 2 3 4 5
output:
350972052
result:
ok single line: '350972052'
Test #6:
score: 5
Accepted
time: 0ms
memory: 22256kb
input:
6 1 2 4 7 11
output:
12441600
result:
ok single line: '12441600'
Test #7:
score: 5
Accepted
time: 0ms
memory: 22264kb
input:
7 1 2 3 4 5 6
output:
373181939
result:
ok single line: '373181939'
Test #8:
score: 5
Accepted
time: 7ms
memory: 22264kb
input:
7 1 2 3 6 7 10
output:
655119719
result:
ok single line: '655119719'
Test #9:
score: 5
Accepted
time: 0ms
memory: 22332kb
input:
15 1 2 3 4 5 6 7 8 9 10 11 12 13 14
output:
778980097
result:
ok single line: '778980097'
Test #10:
score: 5
Accepted
time: 4ms
memory: 22328kb
input:
15 1 2 3 7 8 10 11 13 15 18 21 25 27 30
output:
72110308
result:
ok single line: '72110308'
Test #11:
score: 5
Accepted
time: 7ms
memory: 22500kb
input:
20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
output:
521592645
result:
ok single line: '521592645'
Test #12:
score: 5
Accepted
time: 3ms
memory: 22496kb
input:
20 1 2 3 5 7 9 11 16 21 26 28 32 37 41 42 47 48 50 55
output:
185224996
result:
ok single line: '185224996'
Test #13:
score: 5
Accepted
time: 11ms
memory: 23024kb
input:
25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
output:
83240183
result:
ok single line: '83240183'
Test #14:
score: 5
Accepted
time: 0ms
memory: 23020kb
input:
25 1 2 4 7 10 13 15 16 17 18 21 25 27 31 36 40 42 43 47 52 56 60 63 64
output:
649967979
result:
ok single line: '649967979'
Test #15:
score: 5
Accepted
time: 15ms
memory: 24576kb
input:
30 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
output:
587585839
result:
ok single line: '587585839'
Test #16:
score: 5
Accepted
time: 24ms
memory: 24572kb
input:
30 1 2 3 5 10 12 16 20 24 27 28 29 31 32 36 41 44 45 49 51 54 58 62 66 68 70 74 79 84
output:
219192987
result:
ok single line: '219192987'
Test #17:
score: 5
Accepted
time: 47ms
memory: 28996kb
input:
35 1 2 3 5 8 9 12 13 14 15 18 21 25 30 33 36 38 41 43 45 49 54 57 59 64 69 70 74 78 80 81 83 87 89
output:
758370424
result:
ok single line: '758370424'
Test #18:
score: 5
Accepted
time: 36ms
memory: 28996kb
input:
35 1 2 4 7 9 13 15 19 23 28 32 36 40 41 43 47 49 50 55 56 61 64 67 69 72 75 76 78 80 85 90 93 95 98
output:
509074597
result:
ok single line: '509074597'
Test #19:
score: 5
Accepted
time: 97ms
memory: 41452kb
input:
40 1 2 4 6 8 12 15 16 19 21 26 28 31 35 36 38 41 43 47 50 55 57 58 63 65 69 74 76 78 83 85 90 91 92 ...
output:
124674859
result:
ok single line: '124674859'
Test #20:
score: 5
Accepted
time: 102ms
memory: 41456kb
input:
40 1 2 4 5 7 12 13 16 18 23 27 28 32 35 39 42 43 45 47 50 53 54 57 59 61 66 70 72 77 82 87 91 96 98 ...
output:
186165705
result:
ok single line: '186165705'