Reading the question, I guess we can define n = 10^10 and m = 10^15 - 1, and it will broke this idea, because the maximum is not 10^15 - 1 anymore.
2009/7/23 Hawston LLH <[email protected]> > "long long" arithmetic calculation (+ - x /) is fully supported by most > machines, so this should not be a problem. :) > > 2009/7/23 周游弋 <[email protected]> > > Because any number bigger than 162 can be eventually summed back to a >> value less than 162, 999 -> 243 -> 29, 9999 -> 324 -> 29 etc. Thus if we >> could find determine the clear numbers in [1,162], then all integers can be >> deducted eventually by (or “to”) these determined numbers. >> >> >> >> As for finding S(n), it is just a counting problem. Starting from n, try >> n+1, n+2, n+2 …. And for S(n, m), just start from n+m, try n+m+1, n+m+2… As >> I said, no matter how big the number is, it will eventually fall in between >> [1,162] in four or five steps. >> >> >> >> As for the concrete implementation, there is an issue. The data scale is >> too big for long integer. Though a “double” variable could do, there will be >> precision problems with “double” values. In GNU extension we could use a >> “long long” type but it destroy the portability of the solution. So, we may >> need to write a function to sum two big integers together, digit by digit, >> to compute n+m when n or m are rather large. >> >> >> >> For this specific problem, first build a look-up table T[i] (i = 1, 2, 3, >> … , 1215) using the method we discussed, T[i] denotes whether i is a clear >> number. Now compute n+m by the “big integer adding function”. Starting from >> n+m+1, sum all its digits up and look it up in T. >> >> >> ------------------------------ >> >> *发件人:* [email protected] [mailto:[email protected]] >> *代表 *Hawston LLH >> *发送时间:* 2009年7月22日 15:58 >> *收件人:* [email protected] >> *主题:* Re: 答复: Clear Numbers exercise >> >> >> >> i think either you misunderstood the S(n) which is the minimum clear >> number greater than n or i have misunderstood your purpose of "the largest >> possible sum of all digits". Could you elaborate your purpose to find "162"? >> >> >> >> >> >> On Wed, Jul 22, 2009 at 3:35 PM, 周游弋 <[email protected]> wrote: >> >> >> For the largest possible value is 10^15, thus the largest possible sum of >> all digits comes from 999999999999999, which gives 15*81 = 1215 >> For 1215, the largest possible sum of all digits comes from 999 --> 243. >> For 243, the largest possible sum of all digits comes from 199 --> 163 >> For 163, it's 162. And it ends here. >> >> Finding the clear numbers in [1,162] is trival. >> >> -----邮件原件----- >> 发件人: [email protected] [mailto:[email protected]] >> 代表 FameofLight >> 发送时间: 2009年7月22日 15:00 >> 收件人: google-codejam >> 主题: Re: Clear Numbers exercise >> >> >> >> Anybody please give me some clue on How to Solve this problem. >> >> On Jul 22, 5:26 am, khanh le <[email protected]> wrote: >> > Dear people, >> > i have a exercise, so i want to you solve it. you must code by C++ >> langguage >> > now, read the exercise below: >> > >> > Peter has just found a definition of *clear numbers* as the following: >> for >> > each positive integer n, we form another number by summing the squares >> of >> > the digits of n. We repeat this procedure. If at some step, we obtain >> the >> > number 1 then n is called a *clear number*. For example, for n=19, we >> have: >> > >> > 19 → 82 (= 12 +92) → 68 → 100 → 1 >> > >> > Thus, 19 is a clear number. >> > >> > Not all numbers are clear numbers. For example, for n=12, we have: >> > >> > 12 → 5 → 25 → 29 → 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 → 145 >> > >> > Peter is very interested in this definition of clear numbers. He issued >> a >> > challenge to the landlord: given a positive integer n, find S(n), the >> clear >> > number succeeding n, i.e. S(n) is the minimum clear number greater than >> n. >> > However, this question is so easy for the landlord that he challenged >> Peter >> > with another problem: given two positive integers n and m (1 ≤ n, m ≤ >> 1015), >> > find the number Sm(n)=S(S(…S(n) )) which is the mth clear number >> succeeding >> > n. >> > >> > Please help Peter to solve the task! >> > Input >> > >> > The first line contains t (0 < t ≤ 20) , the number of test cases. >> > >> > Each line in the next t lines contains two positive integers n and m. >> > Output >> > >> > Print t lines, each line contains the result of the corresponding test >> case. >> > Example >> > >> > *Input* >> > 2 >> > 18 1 >> > 1 145674807 >> > >> > *Output* >> > 19 >> > 1000000000 >> > >> > Notes >> > >> > There are 50% of the test cases in which 1 ≤ n, m ≤ 107. >> > >> > -- >> > Regard! >> > Khanh >> >> >> >> >> >> >> >> > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "google-codejam" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/google-code?hl=en -~----------~----~----~----~------~----~------~--~---
