Find the nth digit (two-point search)

Topic Connection: http://acm.hdu.edu.cn/showproblem.php?pid=1597Find the nth digit

Time limit:1000/1000 MS (java/others) Memory limit:32768/32768 K (java/others)
Total submission (s): 9517 Accepted Submission (s): 2757

Problem description hypothesis:
S1 = 1
S2 = 12
S3 = 123
S4 = 1234
.........
S9 = 123456789
S10 = 1234567891
S11 = 12345678912
............
S18 = 123456789123456789
..................
Now we're going to connect all the strings together.
S = 1121231234.......123456789123456789112345678912 .....
So can you tell me what the nth number is in the s string?

Input inputs are first a number k and represent a K-inquiry.
The next K line has an integer n (1 <= n < 2^31) per line.

Output for each n, the number of the nth corresponding to the outputs S.

Sample Input61234510

Sample Output112124

AUTHOR8600 Solution: You can use two decomposition, you can also use two equation formula solutions, pay attention to using long Long Binary lookup code:

1#include <cstdio>2#include <cstring>3#include <cmath>4 using namespacestd;5 #definell Long Long6 ll F (ll X)7 {8ll ans = x* (x+1)/2 ;9     returnans;Ten } One intMain () A { -     intT; -scanf"%d",&T); the      for(inti =0; i < T; i++) -     { - ll N; -scanf"%lld",&n); +         if(n==1) -         { +Puts"1"); A             Continue; at         } -ll L =1; -ll r =N; -ll mid = (l+r)/2; -         intTM =0; -          while(r-l>1) in         { -             if(f (Mid) <N) to             { +L =mid; -Mid = (l+r)/2; the             } *             Else if(f (Mid) >N) $             {Panax NotoginsengR =mid; -Mid = (l+r)/2; the             } +             Else if(f (mid) = =N) A             { theTM =mid; +                  Break; -             } $         } $         if(tm!=0) -         { -             if(tm%9==0) puts ("9"); the             Else  -printf"%d\n", tm%9);Wuyi         } the         Else  -         { WuLL flag =l; -ll tt = flag* (flag+1)/2; About             intsum = ntt;  $             if(sum%9==0) puts ("9"); -             Else  -printf"%d\n", sum%9); -         } A     } +     return 0; the}

Formula Code:

1#include <cstdio>2#include <cmath>3 using namespacestd;4 #definell Long Long5 #defineEPS 1e-86 7 intMain ()8 {9     intT;Tenscanf"%d",&T); One      for(inti =0; I < t;i++) A     { -         DoubleN; -scanf"%LF",&n); the         Doublem = (sqrt (1+8*n)-1)/2; -ll mm =m; -LL TM = mm* (mm+1)/2; -ll flag = NTM; +         if(Flag = =0){if(mm%9==0) printf ("9\n");Elseprintf"%lld\n", mm%9);} -         Else +         { A             if(flag%9==0) printf ("9\n"); at             Else  -printf"%lld\n", flag%9); -         } -     } -     return 0 ; -}

Find the nth digit (two-point search)