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
無敵的繁題啊！！！！！！！
200位，寫了個高精度模版。。。
debug了一天。。代碼冗長無比，而且到處都是陷阱，比如前導0等等。。。
但還是艱難AC了。。。
貼出代碼：（7.8KB）
[cpp]
#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;
}
作者：ascii991
