UVA - 10706 Number Sequence

Problem B

Number Sequence

Input: standard input
Output: standard output
Time Limit: 1 second

A single positive integer iis given. Write a program to find the digit located in the position iin the sequence of number groups S1S2…Sk. Each group Skconsists
of a sequence of positive integer numbers ranging from 1 to k, written one after another. For example, the first 80 digits of the sequence are as follows:

11212312341234512345612345671234567812345678912345678910123456789101112345678910

Input

The first line of the input file contains a single integer t (1 <=t <=25), the number of test cases, followed by one line for each test case. The line for a test case contains the single integer i (1 <=i <=2147483647)

 

Output

There should be one output line per test case containing the digit located in the position i.

 

Sample Input                           Output for Sample Input

2 8 3

2 2

题意：

第一，每个通项中有多少个数字，

第二，根据第一组数据算出从第一项开始至第n项一共有多数字；

这样我们就可以算出第i位是在第n+1项中的i-sum
项，其中sum[]代表的就是第二组数据。

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
#define long long ll;
ll n;
int getlen(int x)
{
int cnt=0;
while(x)
{
x/=10;
cnt++;
}
return cnt;
}
void getans(int p)
{
for(int j=1; j<=p; j++)
{
int x=getlen(j);
if(n-x>0)
n-=x;
else
{
char a[10000];
sprintf(a,"%d",j);
cout<<a[n-1]<<endl;
return ;
}
}
}
void solve()
{
int len=0;
for(int i=1;; i++)
{
len+=getlen(i);
if(n>len)
n-=len;
else
{
getans(n);
return ;
}
}
}
int main()
{
int t;
cin>>t;
while(t--)
{
cin>>n;
solve();
}
return 0;
}