米哈游4-15 笔试第三题 数位dp

一、题意：找到第k（k上限1e12）大的，不包括4并且能被7整除的数。
题解：二分+数位dp。

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

typedef long long LL;

const int MAXN = 100;
LL dp[MAXN][7], digit[MAXN];

LL dfs(int pos, int mod, bool limit){
    if (pos == -1){
        return mod==0;
    }
    
    if (!limit && dp[pos][mod] != -1){
        return dp[pos][mod];
    }

    int up = limit ? digit[pos] : 9;
    LL ans = 0;
    for (int i = 0; i <= up; ++i)
    {
        if (i == 4)continue;
        int newmod = (mod * 10 + i) % 7;
        LL tmp = dfs(pos - 1, newmod, limit && (i == up));
        ans += tmp;
    }

    if (!limit)dp[pos][mod] = ans;

    return ans;
}

LL solve(LL x){
    memset(dp, -1, sizeof(dp));
    int pos=0;
    while(x){
        digit[pos++]=x%10;
        x/=10;
    }
    return dfs(pos-1, 0, true) - 1;
}

int main(){
    LL k;
    cin >> k;
    LL l=1, r=1e18;
    while(l<=r){
        LL mid=(l+r)>>1;
        LL tmp=solve(mid);
        if(tmp<k)l=mid+1;
        else r=mid-1;
    }
    
    cout<<l<<endl;
    return 0;
}