Problem Description
A single positive integer i is given. Write a program to find the digit located in the position i in the sequence of number groups S1S2...Sk. Each group Sk consists 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
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 ≤ 10), 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
2
8
3
Sample Output
2
2
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1 /* 2 一个数的位数可用log10((double)value)+1表示 3 a[]表示子串的长度，b[]表示到第i个子串时的总长度 4 */ 5 #include<iostream> 6 #include<string> 7 #include<cstring> 8 #include<cmath> 9 #include<cstdio> 10 #include<queue> 11 #include<cstdlib> 12 #define maxn 32000 13 using namespace std; 14 typedef long LL; 15 unsigned int a[maxn],b[maxn]; 16 unsigned int n,m,j,k; 17 unsigned int cas; 18 int main() 19 { 20 a[0]=0; 21 b[0]=0; 22 a[1]=1; 23 b[1]=1; 24 LL i; 25 for(i=2;i<maxn;i++) 26 { 27 a[i]=a[i-1]+log10((double)i)+1; 28 b[i]=b[i-1]+a[i]; 29 } 30 scanf("%u",&cas); 31 while(cas--) 32 { 33 scanf("%u",&n); 34 for(j=0;j<maxn;j++) 35 { 36 if(n<=b[j]) 37 break; 38 } 39 unsigned int remain=n-b[j-1]; 40 unsigned int sum=0,value; 41 for(value=1;value<maxn;value++) 42 { 43 sum+=(1+log10((double)value)); 44 if(sum>=remain) 45 break; 46 } 47 unsigned int value_bit=1+log10((double)value); 48 unsigned int position=remain-(sum-value_bit); 49 unsigned int temp1=value; 50 char* str = (char*)malloc(10*sizeof(char)); 51 unsigned int num=0; 52 while(temp1) 53 { 54 unsigned int temp=temp1%10; 55 str[num++]=temp+'0'; 56 temp1/=10; 57 } 58 str[num]=' '; 59 if(position==value_bit) 60 printf("%c ",str[0]); 61 else 62 printf("%c ",str[position-1]); 63 64 } 65 return 0; 66 }