【CSP2019模拟】题解

T1：

本场送分题 建个图求最长路即可 由于$T2$花了太久并没有来的及写

被踩爆了

#include<bits/stdc++.h> using namespace std; const int RLEN=1<<20|1; inline char gc(){ static char ibuf[RLEN],*ib,*ob; (ob==ib)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin)); return (ob==ib)?EOF:*ib++; } #define gc getchar inline int read(){ char ch=gc(); int res=0,f=1; while(!isdigit(ch))f^=ch=='-',ch=gc(); while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc(); return f?res:-res; } #define ll long long #define re register #define pii pair<int,int> #define pic pair<int,char> #define fi first #define se second #define pb push_back #define cs const #define bg begin #define poly vector<int> #define chemx(a,b) ((a)<(b)?(a)=(b):0) #define chemn(a,b) ((a)>(b)?(a)=(b):0) cs int N=1e5,M=31; int n,m,tot,in[N]; vector<int> e[N],E[N]; inline void addedge(int u,int v){ e[u].pb(v); } inline void add(int u,int v){ E[u].pb(v),in[v]++; } int pos[M][M][M][M]; struct node{ int a,b,c,d; node(int _1=0,int _2=0,int _3=0,int _4=0):a(_1),b(_2),c(_3),d(_4){} friend inline bool operator <(cs node &a,cs node &b){ return a.a<=b.a&&a.b<=b.b&&a.c<=b.c&&a.d<=b.d; } friend inline node operator +(cs node &a,cs node &b){ return node(a.a+b.a,a.b+b.b,a.c+b.c,a.d+b.d); } friend inline node operator -(cs node &a,cs node &b){ return node(a.a-b.a,a.b-b.b,a.c-b.c,a.d-b.d); } }s[55],t[55],idx[N]; char ss[N]; ll val[N],w[N],mxv[N]; __int128 tval; int dfn[N],low[N],tim,vis[N],bel[N],belnum; stack<int> stk; inline ll calc(int i,int j,int k,int p){ __int128 res=tval; for(int x=1;x<=i;x++)res/=x; for(int x=1;x<=j;x++)res/=x; for(int x=1;x<=k;x++)res/=x; for(int x=1;x<=p;x++)res/=x; return res; } void dfs(int u){ dfn[u]=low[u]=++tim; stk.push(u),vis[u]=1; for(int &v:e[u]){ if(!dfn[v])dfs(v),chemn(low[u],low[v]); else if(vis[v])chemn(low[u],dfn[v]); } if(low[u]==dfn[u]){ belnum++; int tmp; do{ tmp=stk.top(); stk.pop(); vis[tmp]=0; bel[tmp]=belnum; w[belnum]+=val[tmp]; }while(tmp!=u); } } int pp[4]; int main(){ n=read(),m=read(); for(int i=1;i<=m;i++){ scanf("%s",ss+1); memset(pp,0,sizeof(pp)); for(int j=1,l=strlen(ss+1);j<=l;j++) pp[ss[j]-'A']++; s[i]=node(pp[0],pp[1],pp[2],pp[3]); memset(pp,0,sizeof(pp)); scanf("%s",ss+1); for(int j=1,l=strlen(ss+1);j<=l;j++) pp[ss[j]-'A']++; t[i]=node(pp[0],pp[1],pp[2],pp[3]); } tval=1; for(int i=2;i<=n;i++)tval*=i; for(int i=0;i<=n;i++) for(int j=0;i+j<=n;j++) for(int k=0;i+j+k<=n;k++) pos[i][j][k][n-i-j-k]=++tot,val[tot]=calc(i,j,k,n-i-j-k),idx[tot]=node(i,j,k,n-i-j-k); for(int i=1;i<=tot;i++){ node to;for(int j=1;j<=m;j++) if(s[j]<idx[i]){ to=idx[i]-s[j]+t[j]; addedge(i,pos[to.a][to.b][to.c][to.d]); } } for(int i=1;i<=tot;i++)if(!dfn[i])dfs(i); for(int i=1;i<=tot;i++){ for(int &v:e[i]){ if(bel[v]!=bel[i]) add(bel[i],bel[v]); } } queue<int> q; for(int i=1;i<=belnum;i++) if(!in[i])q.push(i); ll ans=0; while(!q.empty()){ int u=q.front();q.pop(); chemx(ans,mxv[u]+w[u]); for(int &v:E[u]){ in[v]--,chemx(mxv[v],mxv[u]+w[u]); if(!in[v])q.push(v); } } cout<<ans; }

T2：

以前考过的一道$CF$原题 不过当时并没有写就是了

结果为了保险写了双取模哈希光荣$T$了，白丢$15$分

#include<bits/stdc++.h> using namespace std; const int RLEN=1<<20|1; inline char gc(){ static char ibuf[RLEN],*ib,*ob; (ob==ib)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin)); return (ob==ib)?EOF:*ib++; } #define gc getchar inline int read(){ char ch=gc(); int res=0,f=1; while(!isdigit(ch))f^=ch=='-',ch=gc(); while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc(); return f?res:-res; } #define ll long long #define re register #define pii pair<int,int> #define pic pair<int,char> #define fi first #define se second #define pb push_back #define cs const #define bg begin #define poly vector<int> #define chemx(a,b) ((a)<(b)?(a)=(b):0) #define chemn(a,b) ((a)>(b)?(a)=(b):0) cs int mod=1e9+7; inline int add(int a,int b){return (a+=b)>=mod?a-mod:a;} inline void Add(int &a,int b){(a+=b)>=mod?a-=mod:0;} inline int dec(int a,int b){return (a-=b)<0?a+mod:a;} inline void Dec(int &a,int b){(a-=b)<0?a+=mod:0;} inline int mul(int a,int b){return 1ll*a*b%mod;} inline void Mul(int &a,int b){a=1ll*a*b%mod;} inline int ksm(int a,int b,int res=1){for(;b;b>>=1,Mul(a,a))(b&1)&&(Mul(res,a),1);return res;} inline int Inv(int x){return ksm(x,mod-2);} cs int N=2005; int n,m; char a[2][N],s[N]; int f[2][N][N]; int pw1[N],pw2[N]; cs int bas1=1331,mod1=1920643713,bas2=233,mod2=771939933; inline void init(){ pw1[0]=pw2[0]=1; for(int i=1;i<N;i++)pw1[i]=1ll*pw1[i-1]*bas1%mod1,pw2[i]=1ll*pw2[i-1]*bas2%mod2; } struct Hash{ int has1[N],has2[N]; inline void init(char *s){ for(int i=1,len=strlen(s+1);i<=len;i++) has1[i]=(1ll*has1[i-1]*bas1+s[i]-'a'+1)%mod1,has2[i]=(1ll*has2[i-1]*bas2+s[i]-'a'+1)%mod2; } inline pii query(int l,int r){ return pii(((has1[r]-1ll*has1[l-1]*pw1[r-l+1])%mod1+mod1)%mod1,((has2[r]-1ll*has2[l-1]*pw2[r-l+1])%mod2+mod2)%mod2); } }S,pre[2],suf[2]; inline bool operator ==(cs pii &a,cs pii &b){ return a.fi==b.fi&&a.se==b.se; } inline int calc(char *s,int dir){ memset(f,0,sizeof(f)); int res=0; for(int i=0;i<=n;i++){ for(int k=2;k*2<=m&&k<=i;k++)if(!dir||k*2!=m){ if(suf[0].query(n-i+1,n-i+k)==S.query(1,k)&&pre[1].query(i-k+1,i)==S.query(k+1,2*k))Add(f[1][i][2*k],1); if(suf[1].query(n-i+1,n-i+k)==S.query(1,k)&&pre[0].query(i-k+1,i)==S.query(k+1,2*k))Add(f[0][i][2*k],1); } f[0][i][0]=1,f[1][i][0]=1; for(int k=2;2*k<=m&&i+k<=n;k++)if(!dir||k*2!=m){ if(pre[0].query(i+1,i+k)==S.query(m-2*k+1,m-k)&&suf[1].query(n-i-k+1,n-i)==S.query(m-k+1,m))Add(res,f[0][i][m-2*k]); if(pre[1].query(i+1,i+k)==S.query(m-2*k+1,m-k)&&suf[0].query(n-i-k+1,n-i)==S.query(m-k+1,m))Add(res,f[1][i][m-2*k]); } for(int j=0;j<m;j++){ if(a[0][i+1]==s[j+1])Add(f[0][i+1][j+1],f[0][i][j]); if(a[1][i+1]==s[j+1])Add(f[1][i+1][j+1],f[1][i][j]); if(j+2<=m){ if(a[1][i+1]==s[j+1]&&a[0][i+1]==s[j+2])Add(f[0][i+1][j+2],f[1][i][j]); if(a[0][i+1]==s[j+1]&&a[1][i+1]==s[j+2])Add(f[1][i+1][j+2],f[0][i][j]); } } Add(res,f[0][i][m]),Add(res,f[1][i][m]); } return res; } int ans; int main(){ init(); scanf("%s",a[0]+1); scanf("%s",a[1]+1); n=strlen(a[0]+1); pre[0].init(a[0]); reverse(a[0]+1,a[0]+n+1); suf[0].init(a[0]); reverse(a[0]+1,a[0]+n+1); pre[1].init(a[1]); reverse(a[1]+1,a[1]+n+1); suf[1].init(a[1]); reverse(a[1]+1,a[1]+n+1); scanf("%s",s+1); m=strlen(s+1); S.init(s); Add(ans,calc(s,0)); if(m==1){cout<<ans;return 0;} reverse(s+1,s+m+1); S.init(s); Add(ans,calc(s,1)); if(m==2){ for(int i=1;i<=n;i++){ if(a[0][i]==s[1]&&a[1][i]==s[2])Dec(ans,1); if(a[1][i]==s[1]&&a[0][i]==s[2])Dec(ans,1); } } cout<<ans<<'\n'; }

T3：

卷一个$i{d}_k$ 就是相当于要求${\sum }_{i=1}^n{i}^m$这样一个东西 先快速插值后多点求值完杜教筛即可

本机跑了$30s$交$oj$上只跑了$4s$ 什么鬼

#include<bits/stdc++.h> using namespace std; const int RLEN=1<<20|1; inline char gc(){ static char ibuf[RLEN],*ib,*ob; (ob==ib)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin)); return (ob==ib)?EOF:*ib++; } #define gc getchar inline int read(){ char ch=gc(); int res=0,f=1; while(!isdigit(ch))f^=ch=='-',ch=gc(); while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc(); return f?res:-res; } #define ll long long #define re register #define pii pair<int,int> #define pic pair<int,char> #define fi first #define se second #define pb push_back #define cs const #define bg begin #define poly vector<int> #define chemx(a,b) ((a)<(b)?(a)=(b):0) #define chemn(a,b) ((a)>(b)?(a)=(b):0) cs int mod=998244353,G=3; inline int add(int a,int b){return (a+=b)>=mod?a-mod:a;} inline void Add(int &a,int b){(a+=b)>=mod?a-=mod:0;} inline int dec(int a,int b){return (a-=b)<0?a+mod:a;} inline void Dec(int &a,int b){(a-=b)<0?a+=mod:0;} inline int mul(int a,int b){return 1ll*a*b%mod;} inline void Mul(int &a,int b){a=1ll*a*b%mod;} inline int ksm(int a,int b,int res=1){for(;b;b>>=1,Mul(a,a))(b&1)&&(Mul(res,a),1);return res;} inline int Inv(int x){return ksm(x,mod-2);} cs int C=19; poly w[C+1]; int rev[(1<<20)|5]; inline void init_w(){ for(int i=1;i<=C;i++)w[i].resize(1<<(i-1)); w[C][0]=1; int wn=ksm(G,(mod-1)/(1<<C)); for(int i=1;i<1<<(C-1);i++)w[C][i]=mul(w[C][i-1],wn); for(int i=C-1;i;i--) for(int j=0;j<1<<(i-1);j++) w[i][j]=w[i+1][j<<1]; } inline void init_rev(int lim){ for(int i=0;i<lim;i++)rev[i]=(rev[i>>1]>>1)|((i&1)*(lim>>1)); } inline void ntt(poly &f,int lim,int kd){ for(int i=0;i<lim;i++)if(i>rev[i])swap(f[i],f[rev[i]]); for(int mid=1,l=1,a0,a1;mid<lim;mid<<=1,l++) for(int i=0;i<lim;i+=(mid<<1)) for(int j=0;j<mid;j++) a0=f[i+j],a1=mul(w[l][j],f[i+j+mid]),f[i+j]=add(a0,a1),f[i+j+mid]=dec(a0,a1); if(kd==-1){ reverse(f.bg()+1,f.bg()+lim); for(int i=0,iv=Inv(lim);i<lim;i++)Mul(f[i],iv); } } inline poly operator +(poly a,poly b){ if(a.size()<b.size())a.resize(b.size()); for(int i=0;i<b.size();i++)Add(a[i],b[i]); return a; } inline poly operator -(poly a,poly b){ if(a.size()<b.size())a.resize(b.size()); for(int i=0;i<b.size();i++)Dec(a[i],b[i]); return a; } inline poly operator *(poly a,poly b){ int deg=a.size()+b.size()-1,lim=1; if(deg<=32){ poly c(deg,0); for(int i=0;i<a.size();i++) for(int j=0;j<b.size();j++) Add(c[i+j],mul(a[i],b[j])); return c; } while(lim<deg)lim<<=1; init_rev(lim); a.resize(lim),ntt(a,lim,1); b.resize(lim),ntt(b,lim,1); for(int i=0;i<lim;i++)Mul(a[i],b[i]); ntt(a,lim,-1),a.resize(deg); return a; } inline poly Inv(poly a,int deg){ poly b(1,Inv(a[0])),c; for(int lim=4;lim<(deg<<2);lim<<=1){ c=a,c.resize(lim>>1); init_rev(lim); b.resize(lim),ntt(b,lim,1); c.resize(lim),ntt(c,lim,1); for(int i=0;i<lim;i++)Mul(b[i],dec(2,mul(b[i],c[i]))); ntt(b,lim,-1),b.resize(lim>>1); } b.resize(deg);return b; } inline poly operator /(poly a,poly b){ int deg=a.size()-b.size()+1; reverse(a.bg(),a.end()); reverse(b.bg(),b.end()); a=a*Inv(b,deg),a.resize(deg); reverse(a.bg(),a.end()); return a; } inline poly operator %(poly a,poly b){ if(a.size()<b.size())return a; a=a-(a/b)*b; a.resize(b.size()-1);return a; } inline poly integ(poly a){ for(int i=0;i<(int)a.size()-1;i++)a[i]=mul(a[i+1],i+1); a.pop_back();return a; } cs int N=1000005; namespace fastcalc{ poly f[N<<2]; #define lc (u<<1) #define rc ((u<<1)|1) #define mid ((l+r)>>1) void build(int u,int l,int r,int *v){ if(l==r){f[u].clear(),f[u].pb(dec(0,v[l]%mod)),f[u].pb(1);return;} build(lc,l,mid,v),build(rc,mid+1,r,v); f[u]=f[lc]*f[rc]; } void calc(int u,int l,int r,poly g,int *v){ if(l==r){v[l]=g[0];return;} calc(lc,l,mid,g%f[lc],v),calc(rc,mid+1,r,g%f[rc],v); } inline void calc(poly coef,int n,int *v){ build(1,1,n,v); calc(1,1,n,coef,v); } #undef lc #undef rc #undef mid } namespace interpolation{ poly f[N<<2]; int val[N]; #define lc (u<<1) #define rc ((u<<1)|1) #define mid ((l+r)>>1) void build(int u,int l,int r){ if(l==r){f[u].clear(),f[u].pb(dec(0,l)),f[u].pb(1);return;} build(lc,l,mid),build(rc,mid+1,r); f[u]=f[lc]*f[rc]; } poly calc(int u,int l,int r,int *v){ if(l==r){return poly(1,v[l]);} return calc(lc,l,mid,v)*f[rc]+f[lc]*calc(rc,mid+1,r,v); } inline poly calc(int n,int *v){ build(1,1,n); for(int i=1;i<=n;i++)val[i]=i; fastcalc::calc(integ(f[1]),n,val); for(int i=1;i<=n;i++)val[i]=mul(Inv(val[i]),v[i]); return calc(1,1,n,val); } #undef lc #undef rc #undef mid } int n,m,tot; int pr[N],s1[N],s2[N],g1[N],g2[N],mu[N]; int all[N],num,idx[N]; bitset<N> vis; inline int get(int x){ return x<=N-5?g1[x]:g2[n/x]; } int du(int x){ if(x<=N-5)return s1[x]; if(vis[n/x])return s2[n/x]; vis[n/x]=1; int res=1; for(int i=2,nxt;i<=x;i=nxt+1){ nxt=x/(x/i); Dec(res,mul(dec(get(nxt),get(i-1)),du(x/i))); } return s2[n/x]=res; } inline void init(){ cs int len=N-5; s1[1]=g1[1]=mu[1]=1; for(int i=2;i<=len;i++){ if(!vis[i])pr[++tot]=i,mu[i]=mod-1,g1[i]=ksm(i,m); s1[i]=mul(g1[i],mu[i]); for(int j=1;i*pr[j]<=len&&j<=tot;j++){ vis[i*pr[j]]=1,g1[i*pr[j]]=mul(g1[i],g1[pr[j]]); if(i%pr[j]==0)break; mu[i*pr[j]]=mod-mu[i]; } } for(int i=2;i<=len;i++)Add(s1[i],s1[i-1]),Add(g1[i],g1[i-1]); vis.reset(); } int main(){ init_w(); n=read(),m=read(); init(); if(n>N-5){ for(int i=1,nxt;i<=n;i=nxt+1){ nxt=n/(n/i); if(nxt>N-5)all[++num]=nxt,idx[num]=nxt; } poly res=interpolation::calc(m+2,g1); fastcalc::calc(res,num,all); for(int i=1;i<=num;i++)g2[n/idx[i]]=all[i]; } cout<<du(n); }