UVA - 10706 Number Sequence

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本文提供了一种解决UVA-10706 Number Sequence问题的方法，通过预处理和二分查找算法快速定位并输出特定位置上的数字。

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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…S_k. Each group S_kconsists 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

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