(f_{i,u,v},i)位，AC自动机上(u)位置，(v)次匹配的最大值
大菜鸡又去翻题解
两边取对数！！！
[ams=sqrt[c]{prod_{i=1}^cw_i}
]
[lnans=frac1csum_{i=1}^clnw_i
]
分数规划，二分DP即可
#include<bits/stdc++.h>
using namespace std;
inline int read(){
int x=0,f=1;char c=getchar();
while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
while(isdigit(c)){x=(x<<1)+(x<<3)+(c^48);c=getchar();}
return f==1?x:-x;
}
const int N=1504;
const double eps=1e-8,inf=1e9;
vector<int>e[N];
int n,m,tot=1,sz[N],fail[N],ch[N][12],fi[N][N],fu[N][N];
double f[N][N],w[N];
void dfs(int x){
for(auto v:e[x]){
sz[v]+=sz[x];
w[v]+=w[x];
dfs(v);
}
}
#define re register
inline void buildAC(){
for(re int i=0;i<=9;++i)ch[0][i]=1;
queue<int>q;
q.push(1);
while(!q.empty()){
int x=q.front();q.pop();
e[fail[x]].push_back(x);
for(re int i=0,u;i<=9;++i){
u=ch[x][i];
if(!u){
ch[x][i]=ch[fail[x]][i];
continue;
}
fail[u]=ch[fail[x]][i];
q.push(u);
}
}
dfs(1);
}
inline int cmp(double x,double y){
if(fabs(x-y)<eps)return 0;
return (x<y)?-1:1;
}
inline void update(int p,int x,int f1,int f2,double mid){
double v=f[p-1][f1]+w[x]-mid*sz[x];
if(v>f[p][x]){
f[p][x]=v;
fi[p][x]=f1;
fu[p][x]=f2;
}
}
char s[N],c[N];
inline bool check(double mid){
for(re int i=0;i<=n;++i)
for(re int j=1;j<=tot;++j)f[i][j]=-inf;
f[0][1]=0;
for(re int i=0;i<n;++i)
for(re int j=1;j<=tot;++j){
if(!cmp(f[i][j],-inf))continue;
if(s[i+1]=='.')for(int u=0;u<=9;u++)
update(i+1,ch[j][u],j,u,mid);
else update(i+1,ch[j][s[i+1]^48],j,s[i+1]^48,mid);
}
for(re int j=1;j<=tot;++j)
if(cmp(f[n][j],0)==1)return 1;
return 0;
}
void out(int p,int u){
if(!p)return;
out(p-1,fi[p][u]);
putchar(fu[p][u]|48);
}
int main(){
cerr<<log(inf);
n=read();m=read();
scanf("%s",s+1);
for(re int i=1,p,u;i<=m;++i){
scanf("%s",c+1);
p=1;
for(re int j=1,len=strlen(c+1);j<=len;++j){
u=(c[j]^48);
if(!ch[p][u])ch[p][u]=++tot;
p=ch[p][u];
}
w[p]+=log(read());
sz[p]++;
}
buildAC();
double l=0,r=24,mid,ans=0;
for(re int T=1;T<=40;++T){
mid=(l+r)/2;
if(check(mid))ans=l=mid;
else r=mid;
}
check(ans);
int id=1;
for(re int i=2;i<=tot;++i)
if(f[n][i]>f[n][id])id=i;
out(n,id);
return (0-0);
}