[Topcoder SRM403 Division I Level Three] TheLuckySum

Topcoder SRM403 Division I Level Three

题解：
错误的解法：
$dp$预处理$n \leq 10^6$的答案，然后迭代加深爆搜，发现无论怎么加优化都会T掉。
正确的解法：
按位搜索，枚举每一位上有几个4和几个7，然后在确定了每一位上4和7的个数后，当前的最优解可以直接$O(9^2)$求得。加上一些可行性剪枝即可轻松通过。

#include<bits/stdc++.h>
#define LL long long
#define ull unsigned long long
#define ULL ull
#define mp make_pair
#define pii pair<int,int>
#define piii pair<int, pii >
#define pll pair <ll,ll>
#define pb push_back
#define big 20160116
#define INF 2147483647
#define pq priority_queue
using namespace std;
inline int read(){
    int x=0,f=1;
    char ch=getchar();
    while (ch<'0'||ch>'9'){if(ch=='-') f=-1;ch=getchar();}
    while (ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
namespace Mymath{
    LL qp(LL x,LL p,LL mod){
        LL ans=1;
        while (p){
            if (p&1) ans=ans*x%mod;
            x=x*x%mod;
            p>>=1;
        }
        return ans;
    }
    LL inv(LL x,LL mod){
        return qp(x,mod-2,mod);
    }
    LL C(LL N,LL K,LL fact[],LL mod){
        return fact[N]*inv(fact[K],mod)%mod*inv(fact[N-K],mod)%mod;
    }
    template <typename Tp> Tp gcd(Tp A,Tp B){
        if (B==0) return A;
        return gcd(B,A%B);
    }
    template <typename Tp> Tp lcm(Tp A,Tp B){
        return A*B/gcd(A,B);
    }
};
namespace fwt{
    using namespace Mymath;
    void FWT(int a[],int n,LL mod)
    {
        for(int d=1;d<n;d<<=1)
            for(int m=d<<1,i=0;i<n;i+=m)
                for(int j=0;j<d;j++)
                {
                    int x=a[i+j],y=a[i+j+d];
                    a[i+j]=(x+y)%mod,a[i+j+d]=(x-y+mod)%mod;
                    //xor:a[i+j]=x+y,a[i+j+d]=x-y;
                    //and:a[i+j]=x+y;
                    //or:a[i+j+d]=x+y;
                }
    }

    void UFWT(int a[],int n,LL mod)
    {
        LL rev=inv(2,mod);
        for(int d=1;d<n;d<<=1)
            for(int m=d<<1,i=0;i<n;i+=m)
                for(int j=0;j<d;j++)
                {
                    int x=a[i+j],y=a[i+j+d];
                    a[i+j]=1LL*(x+y)*rev%mod,a[i+j+d]=(1LL*(x-y)*rev%mod+mod)%mod;
                    //xor:a[i+j]=(x+y)/2,a[i+j+d]=(x-y)/2;
                    //and:a[i+j]=x-y;
                    //or:a[i+j+d]=y-x;
                }
    }
    void solve(int a[],int b[],int n,LL mod)
    {
        FWT(a,n,mod);
        FWT(b,n,mod);
        for(int i=0;i<n;i++) a[i]=1LL*a[i]*b[i]%mod;
        UFWT(a,n,mod);
    }
};
const int Maxn=15;
int w[Maxn],n;
int c4[Maxn],c7[Maxn];
int tc4[Maxn],tc7[Maxn];
int p10[Maxn];
int curans;
vector<int> ans;
int Pc(int &a,int&b){
    if(a){
        a--;
        return 4;
    }
    b--;//assert(b>=0);
    return 7;
}
void check(){
    int Mx=0;
    for (int i=0;i<10;i++) Mx=max(Mx,c4[i]+c7[i]);
    if (Mx>curans) return;
    //cout<<c4[0]<<c7[0]<<endl;
    vector<int> tmp;
    for (int i=0;i<10;i++) tc4[i]=c4[i],tc7[i]=c7[i];
    for (int i=0;i<9;i++){
        int tx=c4[i]+c7[i]-c4[i+1]-c7[i+1];
        for (int j=0;j<tx;j++){
            int t=0;
            for (int k=0;k<=i;k++){
                t+=p10[k]*Pc(c4[k],c7[k]);
            }
            tmp.pb(t);
        }
    }
    for (int i=0;i<10;i++) c4[i]=tc4[i],c7[i]=tc7[i];
    //cout<<c4[0]<<' '<<c7[0]<<endl;
    if (Mx<curans){
        curans=Mx;
        ans=tmp;
        return;
    }
    for (int i=0;i<ans.size();i++){
        if (tmp[i]<ans[i]){
            break;
        }
        if (tmp[i]>ans[i]){
            return;
        }
    }
    ans=tmp;
    return;
}
void Go(int lvl,int cnt){
    //cout<<lvl<<cnt<<endl;
    if (lvl==9){
        if (w[lvl]==0){
            //cout<<c4[0]<<' '<<c7[0]<<endl;
            check();
        }
        return;
    }
    for (int i=0;i<=cnt;i++){
        for (int j=0;j<=cnt-i;j++){
            //if (!i && !j) continue;
            int v=i*4+j*7-w[lvl];
            if (v%10!=0) continue;
            //if (lvl==0) cout<<i<<j<<endl;
            int pv=w[lvl];
            w[lvl]=0;
            w[lvl+1]-=v/10;
            c4[lvl]=i;c7[lvl]=j;
            Go(lvl+1,i+j);
            //c4[lvl]=c7[lvl]=0;
            w[lvl]=pv;
            w[lvl+1]+=v/10;
        }
    }
}
class TheLuckySum{
    public:
        vector<int> sum(int N){
            n=N;curans=1e9;
            p10[0]=1;
            for (int i=1;i<10;i++) p10[i]=p10[i-1]*10;
            for (int i=0;i<10;i++){
                w[i]=N%10;
                N/=10;
            }
            Go(0,14);
            //cout<<curans<<endl;
            return ans;
        }
}tst;
/*
int main(){
    vector<int> as=tst.sum(998244353);
    for (int i=0;i<as.size();i++){
        cout<<as[i]<<endl;
    }
}*/