UVA - 10706 Number Sequence

先找到是在哪个集合内,再找到是集合内的哪个元素,最后找到元素的第几位数

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std;
long long table[100010];
long long psum[100010];
int n=100000;
void maketable()
{
int i,flag=1,x=0;
for(i=1;i<=n;i++)
{
if(i%flag==0)
{
flag*=10;
x++;
}
table[i]=table[i-1]+x;
psum[i]+=table[i]+psum[i-1];
}
}
int main()
{
//freopen("in","r",stdin);
//freopen("out","w",stdout);
maketable();
int T,i,t;
long long x;
char s[100];
cin>>T;
while(T--)
{
cin>>x;
i=lower_bound(psum,psum+n,x)-psum;
if(psum[i]==x)
cout<<i%10<<endl;
else
{
x-=psum[i-1];
i=lower_bound(table,table+n,x)-table;
if(table[i]==x)
cout<<i%10<<endl;
else
{
x-=table[i-1];
sprintf(s,"%d",i);
cout<<s[x-1]<<endl;
}
}
}
return 0;
}

UVA - 10706
Number Sequence

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit

Status

Description





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

Problem source: Iranian Contest

Special Thanks: Shahriar Manzoor, EPS.

Source

Root :: AOAPC I: Beginning Algorithm Contests (Rujia Liu) ::
Volume 4. Algorithm Design

Root :: Competitive Programming 2: This increases the lower bound of Programming Contests. Again (Steven & Felix Halim) :: Problem Solving Paradigms ::

Divide and Conquer -Binary Search

Root :: Competitive Programming 3: The New Lower Bound of Programming Contests (Steven & Felix Halim) :: Problem Solving Paradigms :: Divide and Conquer ::

Binary Search