【HDOJ6659】Acesrc and Good Numbers（dfs）

题意：定义f(n,d)为数码d在1到n中出现的次数，其中d=0..9

如果f(d,k)=k，则称k是d好数

给定x和d，求不大于x的最大的d好数

x<=1e18

思路：考虑f的增长率主要和位数有关

各种位数，上限，下限剪枝……

事实上所有d好数不会超过1e11

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef pair<ll,ll> Pll;
 typedef vector<int> VI;
 typedef vector<PII> VII;
 #define N  210000
 #define M  4100000
 #define fi first
 #define se second
 #define MP make_pair
 #define pi acos(-1)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
 #define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
 #define lowbit(x) x&(-x)
 #define Rand (rand()*(1<<16)+rand())
 #define id(x) ((x)<=B?(x):m-n/(x)+1)
 #define ls p<<1
 #define rs p<<1|1

 const ll MOD=1e9+,inv2=(MOD+)/;
       double eps=1e-;
       ll INF=1e18;
       int dx[]={-,,,};
       int dy[]={,,-,};

 ll a[N],b[N],ans,n,k,mi[N];
 int len;

 ll read()
 {
    ll v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 ll calc(ll n)
 {
     if(n<) return ;
     int len=;
     while(n)
     {
         b[++len]=n%;
         n/=;
     }
     ll t=,re=;
     per(i,len,)
     {
         rep(j,,b[i]-)
         {
             if(i>=) re+=mi[i-]*(i-);
             if(j==k) re+=mi[i-];
             re+=mi[i-]*t;
         }
         if(b[i]==k) t++;
     }
     return re+t;
 }

 void dfs(int u,ll now,ll now_,int flag,int s)
 {
     if(u==)
     {
         if(calc(now)==now)
         {
             ans=now;
             return;
         }
     }
     if(s>=)
     {
         if(calc(now)-now<=&&calc(now_)-now_>=)
         {
             ll l=now,r=now_,last=now;
             while(l<=r)
             {
                 ll mid=(l+r)>>;
                 if(calc(mid)-mid<=){last=mid; l=mid+;}
                  else r=mid-;
             }
             if(calc(last)-last==) ans=max(ans,last);
         }
         return;
     }
     ll x=calc(now)-now,y=calc(now_)-calc(now),z=now-now_;
     if(x<&&x+y<) return;
     if(x>&&x+z>) return;
     if(flag)
     {
         per(i,,)
         {
             dfs(u-,now+mi[u-]*i,now+mi[u-]*(i+)-,,s+(i==k));
             if(ans!=-INF) return;
         }
     }
      else
      {
          dfs(u-,now+mi[u-]*a[u],now_,,s+(a[u]==k));
          if(ans!=-INF) return;
          per(i,a[u]-,)
          {
              dfs(u-,now+mi[u-]*i,now+mi[u-]*(i+)-,,s+(i==k));
              if(ans!=-INF) return;
          }
      }

 }

 int main()
 {
     //freopen("1.in","r",stdin);
     //freopen("1.out","w",stdout);

     int cas;
     scanf("%d",&cas);
     mi[]=;
     rep(i,,) mi[i]=mi[i-]*;
     while(cas--)
     {
         k=read(),n=read();
         ll n_=n;
         if(n==)
         {
             printf("0\n");
             continue;
         }
         len=;
         while(n)
         {
             a[++len]=n%;
             n/=;
         }
         ans=-INF;
         n=n_;
         dfs(len,,n,,);
         printf("%I64d\n",ans);

     }

     return ;
 }