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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
#588555#8211. Enumerating SubstringsfzxAC ✓537ms82128kbC++144.8kb2024-09-25 13:10:592024-09-25 13:10:59

Judging History

你现在查看的是最新测评结果

  • [2024-09-25 13:10:59]
  • 评测
  • 测评结果:AC
  • 用时:537ms
  • 内存:82128kb
  • [2024-09-25 13:10:59]
  • 提交

answer

#include <bits/stdc++.h>
#define int long long 
using namespace std;
const int INFM=2e3+5;
const int INFN=1e6+5;
const int Mod=1e9+7;
bool vis[INFM];
int n,m,k,fav[INFN],L[INFM],R[INFM],ifav[INFN],f[INFM][INFM],B[INFM][INFM];
int ksm(int x,int y) {
    int ba=x%Mod,ans=1;
    while (y) {
        if (y&1) ans=(ans*ba)%Mod;
        ba=(ba*ba)%Mod;y>>=1;
    }
    return ans;
}
void init() {
    int N=1e6;fav[0]=1;
    for (int i=1;i<=N;i++) fav[i]=fav[i-1]*i%Mod;
    ifav[N]=ksm(fav[N],Mod-2);
    for (int i=N-1;~i;i--) ifav[i]=ifav[i+1]*(i+1)%Mod;
}
int C(int x,int y) {
    if (x<y) return 0;
    return fav[x]*ifav[y]%Mod*ifav[x-y]%Mod;
}
int calc(int x,int y) {
    return (ksm(x,y+1)-1)*ksm(x-1,Mod-2)%Mod;
}
signed main()
{
    ios::sync_with_stdio(false);
    cin>>n>>m>>k;init();int res=0;
    for (int i=0;i<=m+3;i++)
        for (int j=0;j<=m+3;j++)
            f[i][j]=0;
    f[0][0]=1;
    for (int i=0;i<m;i++)
        for (int j=0;j<=i;j++) {
            f[i+1][j+1]+=f[i][j]*(k-j-(i-j)/2);
            if (j) f[i+1][j-1]+=f[i][j]*j;
            f[i+1][j+1]%=Mod;
            if (j) f[i+1][j-1]%=Mod;
        }
    int sum=0;
    for (int j=0;j<=m;j++) sum+=f[m][j],sum%=Mod;
    for (int i=1;i<=n;i++) {
        if (i+m-1>n) continue;
        res+=sum*ksm(k,n-m)%Mod;res%=Mod;
    }
    for (int j=0;j<=m;j++) {
        B[j][0]=1;
        int ba=k-j-(m-j)/2+1;
        for (int u=1;u<=m;u++)
            B[j][u]=B[j][u-1]*ba%Mod,ba++;
    }
    int res2=0,invk=ksm(k,Mod-2);
    for (int b=1;b<=m/2;b++) {
        // b  ... b
        int sum=0;
        for (int j=0;j<=m-b*2;j++) {
            // if (k-j-(m-b*2-j)/2<b) continue;
            // int cnt3=1;
            // for (int q=k-j-(m-b*2-j)/2;q>=k-j-(m-b*2-j)/2-b+1;q--) cnt3*=q,cnt3%=Mod;
            // for (int q=1;q<=b;q++) cnt3*=ifav[q]*fav[q-1]%Mod,cnt3%=Mod;
            sum+=f[m-b*2][j]*B[j][b]%Mod;
            sum%=Mod;
        }
        int A=ksm(invk*invk%Mod,m-b),L7=ksm(invk,m-b),invA=ksm(A-1,Mod-2),S3=0,L6=ksm(invk,b);
        L6*=sum;L6%=Mod;
        for (int i=1;i<=m;i++) {
            int cnt=1;
            // m-b
            if (i-1<m-b) cnt*=1,cnt%=Mod;
            else cnt*=1-L7,cnt%=Mod;
            // (m-b)*j<=n-b-i+1
            int li=(n-b-i+1)/(m-b),S2=0;
            if (A==1) S2-=li/2,S2%=Mod;
            else S2=-(ksm(A,li/2+1)-A)*invA%Mod;
            S2*=cnt;S2%=Mod;
            S2*=L6;S2%=Mod;
            res2+=S2;res2%=Mod;
        }
        if (m+1<=n-b+1) {
            for (int k=0;k<m;k++) vis[k]=0;
            for (int i=m+1;i<=n-b+1;i++) {
                if (vis[(n-b-i+1)%(m-b)]) break;
                vis[(n-b-i+1)%(m-b)]=1;L[(n-b-i+1)%(m-b)]=(n-b-i+1);
            }
            for (int k=0;k<m;k++) vis[k]=0;
            for (int i=n-b+1;i>=m+1;i--) {
                if (vis[(n-b-i+1)%(m-b)]) break;
                vis[(n-b-i+1)%(m-b)]=1;R[(n-b-i+1)%(m-b)]=(n-b-i+1);
            }
            for (int i=0;i<m-b;i++) {
                if (!vis[i]) continue;
                int S2=0;
                int ll=R[i]/(m-b),rr=L[i]/(m-b);
                if (ll>rr) continue;
                if (ll==rr) {
                    if (A==1) {
                        for (int li=ll;li<=rr;li++) 
                            S2-=li/2,S2%=Mod;
                    } else {
                        for (int li=ll;li<=rr;li++) 
                            S2+=-ksm(A,li/2+1),S2%=Mod;
                        S2*=invA%Mod;S2%=Mod;
                        S2+=A*invA%Mod*(rr-ll+1)%Mod;S2%=Mod;
                    }
                    S3+=S2;S3%=Mod;
                    continue;
                }
                if (A==1) {

                    int L=ll,R=rr;
                    if (ll&1) S2+=-ll/2,S2%=Mod,ll++;
                    if (rr%2==0) S2+=-rr/2,S2%=Mod,rr--;
                    S2-=(ll/2+rr/2)*(rr/2-ll/2+1);S2%=Mod;
                    // for (int li=ll/2;li<=rr/2;li++) 
                    //     S2-=li*2,S2%=Mod;
                } else {
                    int L=ll,R=rr;
                    if (ll&1) S2+=-ksm(A,ll/2),S2%=Mod,ll++;
                    if (rr%2==0) S2+=-ksm(A,rr/2),S2%=Mod,rr--;
                    S2+=-(calc(A,rr/2)-calc(A,ll/2-1))*2;
                    // for (int li=ll/2;li<=rr/2;li++) 
                    //     S2+=-ksm(A,li)*2,S2%=Mod;
                    ll=L;rr=R;
                    S2*=invA*A%Mod;S2%=Mod;
                    S2+=A*invA%Mod*(rr-ll+1)%Mod;S2%=Mod;
                }
                S3+=S2;S3%=Mod;
            }
            S3*=(invk-ksm(invk,1+(m-b)));S3%=Mod;
            S3*=sum;S3%=Mod;S3*=ksm(invk,b-1);S3%=Mod;
            res2+=S3;res2%=Mod;
        }
    }
    res2*=ksm(k,n);res2%=Mod;res2+=Mod;res2%=Mod;
    res+=res2;res%=Mod;
    res+=Mod;res%=Mod;
    cout<<res<<"\n";
    return 0;
}

这程序好像有点Bug,我给组数据试试?

詳細信息

Test #1:

score: 100
Accepted
time: 3ms
memory: 22692kb

input:

4 2 3

output:

228

result:

ok 1 number(s): "228"

Test #2:

score: 0
Accepted
time: 537ms
memory: 82060kb

input:

999999 1999 12345678

output:

52352722

result:

ok 1 number(s): "52352722"

Test #3:

score: 0
Accepted
time: 9ms
memory: 23164kb

input:

7 4 2

output:

182

result:

ok 1 number(s): "182"

Test #4:

score: 0
Accepted
time: 7ms
memory: 22300kb

input:

4 3 4

output:

480

result:

ok 1 number(s): "480"

Test #5:

score: 0
Accepted
time: 11ms
memory: 22516kb

input:

3 1 1

output:

3

result:

ok 1 number(s): "3"

Test #6:

score: 0
Accepted
time: 7ms
memory: 22492kb

input:

5 5 1

output:

0

result:

ok 1 number(s): "0"

Test #7:

score: 0
Accepted
time: 12ms
memory: 23020kb

input:

7 4 3

output:

5784

result:

ok 1 number(s): "5784"

Test #8:

score: 0
Accepted
time: 3ms
memory: 22808kb

input:

5 2 4

output:

3932

result:

ok 1 number(s): "3932"

Test #9:

score: 0
Accepted
time: 3ms
memory: 21592kb

input:

8 2 2

output:

1522

result:

ok 1 number(s): "1522"

Test #10:

score: 0
Accepted
time: 8ms
memory: 21344kb

input:

8 1 2

output:

2048

result:

ok 1 number(s): "2048"

Test #11:

score: 0
Accepted
time: 8ms
memory: 21788kb

input:

7 5 3

output:

2430

result:

ok 1 number(s): "2430"

Test #12:

score: 0
Accepted
time: 8ms
memory: 22932kb

input:

10 4 3

output:

272004

result:

ok 1 number(s): "272004"

Test #13:

score: 0
Accepted
time: 90ms
memory: 42444kb

input:

675978 614 2

output:

0

result:

ok 1 number(s): "0"

Test #14:

score: 0
Accepted
time: 23ms
memory: 24604kb

input:

244613 38 1

output:

0

result:

ok 1 number(s): "0"

Test #15:

score: 0
Accepted
time: 61ms
memory: 69760kb

input:

186293 1462 1

output:

0

result:

ok 1 number(s): "0"

Test #16:

score: 0
Accepted
time: 25ms
memory: 50852kb

input:

24867 886 1

output:

0

result:

ok 1 number(s): "0"

Test #17:

score: 0
Accepted
time: 198ms
memory: 55256kb

input:

976164 1014 2

output:

0

result:

ok 1 number(s): "0"

Test #18:

score: 0
Accepted
time: 19ms
memory: 21560kb

input:

179356 2 716844809

output:

577866092

result:

ok 1 number(s): "577866092"

Test #19:

score: 0
Accepted
time: 50ms
memory: 27624kb

input:

621001 130 310625363

output:

892869197

result:

ok 1 number(s): "892869197"

Test #20:

score: 0
Accepted
time: 137ms
memory: 49116kb

input:

678862 850 754662812

output:

582264789

result:

ok 1 number(s): "582264789"

Test #21:

score: 0
Accepted
time: 165ms
memory: 55108kb

input:

650845 978 348443366

output:

825425732

result:

ok 1 number(s): "825425732"

Test #22:

score: 0
Accepted
time: 66ms
memory: 35972kb

input:

669914 402 87448112

output:

318098088

result:

ok 1 number(s): "318098088"

Test #23:

score: 0
Accepted
time: 112ms
memory: 40532kb

input:

998593 530 681228665

output:

408255654

result:

ok 1 number(s): "408255654"

Test #24:

score: 0
Accepted
time: 466ms
memory: 82060kb

input:

369361 1954 125266115

output:

509912384

result:

ok 1 number(s): "509912384"

Test #25:

score: 0
Accepted
time: 283ms
memory: 65772kb

input:

900226 1378 424079373

output:

406320917

result:

ok 1 number(s): "406320917"

Test #26:

score: 0
Accepted
time: 291ms
memory: 69828kb

input:

334887 1506 17859926

output:

503264679

result:

ok 1 number(s): "503264679"

Test #27:

score: 0
Accepted
time: 103ms
memory: 40232kb

input:

936048 544 53978328

output:

548647866

result:

ok 1 number(s): "548647866"

Test #28:

score: 0
Accepted
time: 192ms
memory: 63528kb

input:

152789 1264 792983073

output:

839541707

result:

ok 1 number(s): "839541707"

Test #29:

score: 0
Accepted
time: 274ms
memory: 67684kb

input:

714493 1392 91796331

output:

721071046

result:

ok 1 number(s): "721071046"

Test #30:

score: 0
Accepted
time: 98ms
memory: 49072kb

input:

269571 816 830801077

output:

330064211

result:

ok 1 number(s): "330064211"

Test #31:

score: 0
Accepted
time: 173ms
memory: 52976kb

input:

845120 944 424581630

output:

348960190

result:

ok 1 number(s): "348960190"

Test #32:

score: 0
Accepted
time: 60ms
memory: 32772kb

input:

533990 368 163586376

output:

522092095

result:

ok 1 number(s): "522092095"

Test #33:

score: 0
Accepted
time: 384ms
memory: 80012kb

input:

181707 1792 462399634

output:

373795106

result:

ok 1 number(s): "373795106"

Test #34:

score: 0
Accepted
time: 459ms
memory: 82128kb

input:

417349 1920 761212891

output:

587051329

result:

ok 1 number(s): "587051329"

Test #35:

score: 0
Accepted
time: 253ms
memory: 65564kb

input:

526583 1344 500217637

output:

108767800

result:

ok 1 number(s): "108767800"

Test #36:

score: 0
Accepted
time: 127ms
memory: 46892kb

input:

867054 769 93998191

output:

239123369

result:

ok 1 number(s): "239123369"

Extra Test:

score: 0
Extra Test Passed