ural 1165 subnumber ------猥琐的超级大繁题

最新推荐文章于 2019-06-06 00:12:14 发布

原创最新推荐文章于 2019-06-06 00:12:14 发布 · 964 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#string #concatenation #c #os #ini

acm_杂题专栏收录该内容

8 篇文章

订阅专栏

本文介绍了一个复杂的算法问题——求解一个特定数字序列首次出现在无限递增整数序列中的位置。通过使用高精度计算技术，文章提供了一个详细的实现方案，并分享了作者在调试过程中的经验。

1165. Subnumber

Time Limit: 1.0 second
Memory Limit: 16 MB

George likes arithmetics very much. Especially he likes the integers series. His most favourite thing is the infinite sequence of digits, which results as the concatenation of all positive integers in ascending order. The beginning of this sequence is 1234567891011121314… Let us call this sequence S. Then S[1] = 1, S[2] = 2, …, S[10] = 1, S[11] = 0, …, and so on.

George takes a sequence of digits A and wants to know when it first appears in S. Help him to solve this difficult problem.

Input

The first line contains A - the given sequence of digits. The number of digits in A does not exceed 200.

Output

Output the only number - the least k such that A[1] = S[k], A[2] = S[k+1], ... A[len(A)] = S[k + len(A) – 1], where len(A) denotes the length of A (i.e. the number of digits in it).

Sample

input	output
101	10

无敌的繁题啊！！！！！！！

200位，写了个高精度模版。。。

debug了一天。。代码冗长无比，而且到处都是陷阱，比如前导0等等。。。

但还是艰难AC了。。。

贴出代码：（7.8KB）

#include <iostream>
#include <cstring>
#include <string>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
using namespace std;

class BigNum
{
private:
    enum {blen=4,MAX=53,base=10000};
    int len;
    int a[MAX];
public:
    explicit BigNum(int num=0);
    BigNum(const BigNum& b);
    BigNum(int x,int b);
    explicit BigNum(string num);
    BigNum operator+ (const BigNum& b)const;
    BigNum operator+ (const int b)const;
    BigNum operator- (const BigNum& b)const;
    BigNum operator- (const int b)const;
    BigNum operator* (const BigNum& b)const;
    BigNum operator* (const int b)const;
    const int& operator[] (int i)const;
    int& operator[] (int i);
    bool operator< (const BigNum& b)const;
    bool operator> (const BigNum& b)const;
    bool operator== (const BigNum& b)const;
    bool operator!= (const BigNum& b)const;
    string toString()const;
    friend ostream& operator<< (ostream& os,const BigNum& a);
};

BigNum::BigNum(int num)
{
    if (num==0)
    {
        len=0;
        memset(a,0,sizeof(a));
        return;
    }
    len=0;
    memset(a,0,sizeof(a));
    while (num>0)
    {
        a[len++]=num%base;
        num/=base;
    }
}

BigNum::BigNum(int x,int b) // x*10^b
{
    if (x==0)
    {
        len=0;
        memset(a,0,sizeof(a));
        return;
    }
    len=(b+1)/blen+1;
    if ((b+1)%blen==0) len--;
    memset(a,0,sizeof(a));
    int i=b%blen,j=1;
    while (i>0)
    {
        j*=10;
        i--;
    }
    a[len-1]=x*j;
}

BigNum::BigNum(string num)
{
    const int nn[blen]={1,10,100,1000};
    if (num==string(num.size(),'0'))
    {
        len=0;
        memset(a,0,sizeof(a));
        return;
    }
    memset(a,0,sizeof(a));
    len=0;
    for (int i=0;i<num.size();i++)
    {
        if (i%blen==0) len++;
        a[len-1]+=(num[num.size()-i-1]-'0')*nn[i%blen];
    }
}

BigNum::BigNum(const BigNum& b)
{
    len=b.len;
    memcpy(a,b.a,sizeof(b.a));
}

int& BigNum::operator[](int i)
{
    return a[i];
}

const int& BigNum::operator[](int i)const
{
    return a[i];
}

BigNum BigNum::operator+(const BigNum& b)const
{
    BigNum c=BigNum();
    int k=0;
    c.len=max(len,b.len);
    for (int i=0;i<c.len;i++)
    {
        c[i]=(a[i]+b[i]+k)%base;
        k=(a[i]+b[i]+k)/base;
    }
    while (k>0)
    {
        c[c.len++]=k%base;
        k/=base;
    }
    return c;
}

BigNum BigNum::operator+(const int b)const
{
    BigNum c=*this;
    int i=0;
    c[0]+=b;
    while (c[i]>=base)
    {
        c[i+1]+=c[i]/base;
        c[i]%=base;
        i++;
    }
    while (c[c.len]>0) c.len++;
    return c;
}

BigNum BigNum::operator-(const BigNum& b)const //ensure that a>b
{
    BigNum c=BigNum();
    c.len=max(len,b.len);
    int k=0;
    for (int i=0;i<len;i++)
        if (a[i]-b[i]-k>=0)
            c[i]=a[i]-b[i]-k;
        else
        {
            k++;
            c[i]=a[i]-b[i]+base;
        }
    while (c.len>0 && c[c.len-1]==0) c.len--;
    return c;
}

BigNum BigNum::operator-(const int b)const
{
    BigNum c=*this;
    int i=0;
    c[i]-=b;
    while (c[i]<0)
    {
        c[i+1]--;
        c[i]+=base;
        i++;
    }
    while (c.len>0 && c[c.len-1]==0) c.len--;
    return c;
}

BigNum BigNum::operator*(const BigNum& b)const
{
    BigNum c=BigNum();
    c.len=0;
    int t;
    for (int j=0;j<b.len;j++)
        for (int i=0;i<len;i++)
        {
            t=c[i+j]+a[i]*b[j];
            c[i+j]=t%base;
            c[i+j+1]+=t/base;
            if (c[i+j]>0) c.len=max(c.len,i+j);
            if (c[i+j+1]>0) c.len=max(c.len,i+j+1);
        }
    c.len++;
    return c;
}

BigNum BigNum::operator*(const int b)const
{
    BigNum c=BigNum();
    c.len=len;
    int k=0;
    for (int i=0;i<len;i++)
    {
        c[i]=(a[i]*b+k)%base;
        k=(a[i]*b+k)/base;
    }
    while (k>0)
    {
        c[c.len++]=k%base;
        k/=base;
    }
    return c;
}

bool BigNum::operator< (const BigNum& b)const
{
    if (len<b.len) return true;
    if (len>b.len) return false;
    for (int i=len-1;i>=0;i--)
        if (a[i]<b[i]) return true;
        else if (a[i]>b[i]) return false;
    return false;
}

bool BigNum::operator> (const BigNum& b)const
{
    if (len>b.len) return true;
    if (len<b.len) return false;
    for (int i=len-1;i>=0;i--)
        if (a[i]>b[i]) return true;
        else if (a[i]<b[i]) return false;
    return false;
}

bool BigNum::operator== (const BigNum& b)const
{
    if (len!=b.len) return false;
    for (int i=0;i<len;i++)
        if (a[i]!=b[i]) return false;
    return true;
}

bool BigNum::operator!= (const BigNum& b)const
{
    return !(*this==b);
}

ostream& operator<< (ostream& os,const BigNum& a)
{
    int i=a.len-1;
    os << a[i];
    for (i-=1;i>=0;i--)
    {
        if (a[i]<a.base/10) os << '0';
        if (a[i]<a.base/100) os << '0';
        if (a[i]<a.base/1000) os << '0';
        os << a[i];
    }
    return os;
}

string BigNum::toString()const
{
    int i=len-1;
    char s[MAX*blen+1];
    sprintf(s,"%d",a[i]);
    for (i-=1;i>=0;i--)
    {
        if (a[i]<base/10) sprintf(s+strlen(s),"%d",0);
        if (a[i]<base/100) sprintf(s+strlen(s),"%d",0);
        if (a[i]<base/1000) sprintf(s+strlen(s),"%d",0);
        sprintf(s+strlen(s),"%d",a[i]);
    }
    return string(s,s+strlen(s));
}

BigNum cal(BigNum a)
{
    string s=a.toString();
    int x=s[0]-'0';
    int b=s.size();
    if (b==1) return BigNum(x);
    BigNum tmp;
    for (int i=0;i<b-1;i++)
        tmp=tmp+BigNum(9,i)*(i+1);
    tmp=tmp+(a-BigNum(1,b-1)+1)*b;
    return tmp;
}

int get(string s1,string s2)
{
    int i,ans=0;
    for (i=1;i<=min(s1.size(),s2.size());i++)
    {
        string ss1=s1.substr(0,i);
        string ss2=s2.substr(s2.size()-i,i);
        if (ss1==ss2) ans=i;
    }
    return ans;
}

int main()
{
    freopen("in.txt","r",stdin);

    int i,j,len,n,k,slen;
    bool ff;
    BigNum ans,tmp;
    string s,ss,st,sp,s1,s2;

    cin >> s;
    n=s.size();
    if (s==string(n,'0'))
    {
        ans=cal(BigNum(1,n))-n+1;
        cout << ans << endl;
        return 0;
    }
    if (n==1)
    {
        cout << s << endl;
        return 0;
    }
    for (len=1;len<n;len++)
        for (i=0;i+len-1<n;i++)
        {
            j=i+len-1;
            if (j>=n) continue;
            ff=true;
            st=s.substr(i,len);
            if (st[0]=='0') continue;
            if (i>0)
            {
                sp=(BigNum(st)-1).toString();
                ss=s.substr(0,i);
                if (ss.size()>sp.size()) continue;
                if (sp.rfind(ss)!=sp.size()-ss.size()) ff=false;
            }
            if (!ff) continue;
            slen=len;
            for (k=j+1;k+slen-1<n;k+=slen)
            {
                st=(BigNum(st)+1).toString();
                slen=st.size();
                if (k+slen-1>=n) break;
                if (st!=s.substr(k,slen))
                {
                    ff=false;
                    break;
                }
            }
            if (!ff) continue;
            if (k<n)
            {
                st=(BigNum(st)+1).toString();
                ss=s.substr(k,n-k);
                if (st.find(ss)!=0) ff=false;
            }
            if (ff)
            {
                st=s.substr(i,len);
                ans=cal(BigNum(st))-i-st.size()+1;
                goto ppp;
            }
        }
    ppp:
    for (i=0;i<n;i++)
    {
        st=s.substr(0,i);
        st=(BigNum("1"+st)+1).toString();
        st=st.substr(1,st.size()-1);
        s2=s.substr(i,n-i);
        k=get(st,s2);
        if (k>=s2.size()) continue;
        st=s.substr(i,n-i-k)+st;
        if (st[0]=='0') continue;
        tmp=cal(BigNum(st)-1)-i+1;
        if (ans==BigNum(0)) ans=tmp;
        else if (tmp<ans) ans=tmp;
    }
    if (s[0]>'0')
    {
        tmp=cal(BigNum(s))-n+1;
        if (ans==BigNum(0)) ans=tmp;
        else if (tmp<ans) ans=tmp;
    }
    else
    {
        s="1"+s;
        tmp=cal(BigNum(s))-n;
        if (ans==BigNum(0)) ans=tmp;
        else if (tmp<ans) ans=tmp;
    }
    cout << ans << endl;
}