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Discussion of Problem 1206. Sum of Digits of the Sum of Numbersajay jadhav DP? [1] // Problem 1206. Sum of Digits of the Sum of Numbers 30 Apr 2020 12:20 Can anybody post DP approach, if any exists? Anier Velasco Sotomayor Re: DP? // Problem 1206. Sum of Digits of the Sum of Numbers 21 Dec 2020 06:01 Dp[i][diff][c]: amount of pairs of numbers (A, B) of size i where S(A+B)-S(A)-S(B)=diff and we carry c from the sum of A and B Here we consider also number with leading zeroes, we can notice that **diff** is in the range [-460, 900] -maybe we can make it narrower- and that **c** is either 0 or 1. Arrias very good tusk // Problem 1206. Sum of Digits of the Sum of Numbers 22 Sep 2018 14:01 Edited by author 22.09.2018 14:02 Mikhail accepted [1] // Problem 1206. Sum of Digits of the Sum of Numbers 11 May 2018 00:55 ans1 = 0 ans2 = 0 for i in range(1, 10) : for j in range(1, 10) : if i + j < 10 : ans1 += 1 for i in range(0, 10) : for j in range(0, 10) : if i + j < 10 : ans2 += 1 n = int(input()) for i in range (1, n) : ans1 *= ans2 print(ans1) Artem Re: accepted // Problem 1206. Sum of Digits of the Sum of Numbers 16 Jun 2018 15:43 How this work? Axmadjon Wrong answer test 4 in Java 1.7 please help me [1] // Problem 1206. Sum of Digits of the Sum of Numbers 5 May 2014 17:02 import java.util.Scanner; public class _1206 { public static void main(String[] args) { Scanner s = new Scanner(System.in); int n = 36; long k = s.nextInt(); while (k > 1) { n *= 55; k--; } System.out.println(n); } } Edited by author 05.05.2014 17:02 mberdyshev Re: Wrong answer test 4 in Java 1.7 please help me // Problem 1206. Sum of Digits of the Sum of Numbers 9 Jun 2017 14:32 Use BigInteger Noob Proof [3] // Problem 1206. Sum of Digits of the Sum of Numbers 12 May 2012 03:16 I've solved it using bruteforce for small K and then guessing the formula. But I still don't know the proof. Can anybody write it? balandini Re: Proof [2] // Problem 1206. Sum of Digits of the Sum of Numbers 7 Jun 2012 18:20 S(A + B) = S(A) + S(B) is equal to that that for every pair of corresponding digits of A and B their sum is lower then 10 (1). For example: 12 and 13 :1+1<10;2+3<10 it means S(A + B) = S(A) + S(B) 18 and 19: 8+9>10 it means S(A + B) = S(A) + S(B) is wrong here. Then for every pair of digits from A and B you just count how many varints of pair suits (1) and multiply these quantities for all pairs. Dmitri Belous Re: Proof [1] // Problem 1206. Sum of Digits of the Sum of Numbers 2 Sep 2012 15:22 thanks Kuros Re: Proof // Problem 1206. Sum of Digits of the Sum of Numbers 7 Feb 2014 01:51 Another way to go at it is to think of the number (A+B) as a bunch of stacked blocks, each stack representing a digit. Here is 43 for example: _ |_| _ |_||_| |_||_| |_||_| Now, to find all the A's and B's that can form S(A+B) = S(43), for example 12+31 or 22+21, etc, we can represent this as chopping each stack into two parts, for example in the case of 12+31: _ |_| _ _ |_| |_||_| |_| _ |_||_| Now, if we take the general case of having two digits, if the first digit is 1, we can't split the first digit in two since the first digit of A or B can't be 0. However, if the first digit is 2, we can split it in one way (in the middle), and then we can split the second digit depending on what digit it is. If it is 2, we can split it in 3 different ways ( (0,2),(1,1),(2,0) ). If it is 3, we can split it in 4 different ways, etc. So, if the first digit of the two-digit number is 2, we can split the whole number in 1*(1+2+3+4+5+6+7+8+9+10)=1+(10*11/2) different ways. If the first digit is 3, we can split the whole number in 2*(1+2+3+4+5+6+7+8+9+10)=2*(10*11/2) different ways, etc. If we sum everything we get (8*9)/2*(10*11)/2 ways to split a two digit number. For an n digit number continuing the same way we get (8*9)/2*((10*11)/2)^(n-1). svg2003 No subject // Problem 1206. Sum of Digits of the Sum of Numbers 13 Dec 2013 11:25 Edited by author 13.12.2013 11:36 Edited by author 13.12.2013 11:36 Adhambek You use BigIntegers or strings // Problem 1206. Sum of Digits of the Sum of Numbers 21 Jun 2013 21:05 because , input: n = 50 Length of output is 87 digits output : 682455418022864824778975492858747729001539122984270520078098343219608068466186523437500 Edited by author 21.06.2013 21:07 Phil WA5... [1] // Problem 1206. Sum of Digits of the Sum of Numbers 18 Oct 2011 18:00 I used long arithmetics and calculated "36*pow(55,k-1);". But I have WA5. Please, say why or give that test... Vetriti Re: WA5... // Problem 1206. Sum of Digits of the Sum of Numbers 11 Feb 2013 19:48 Maybe you write wrong long arithmetics. I think you forgot leading zeroes. I had the same mistake. Use this test: 9 3014421764062500 Sorry for my poor English. Vladimir Yakovlev (USU) Problem 1206 "Sum of digits". New tests have been added (+) [3] // Problem 1206. Sum of Digits of the Sum of Numbers 2 Jan 2007 04:51 New tests were added to the problem. All possible inputs are checked now :) Problem statement was updated: limitation "0 < K <= 50" was replaced by "2 <= K <= 50". There wasn't a case K=1 in the tests. AC submissions were rejudged, 44 of them lost AC. [SSAU_#617]snipious aka Pimenov Sergey Nikolaevich Re: Problem 1206 "Sum of digits". New tests have been added (+) [1] // Problem 1206. Sum of Digits of the Sum of Numbers 2 Jan 2007 13:17 I think who write true program with long arithmetics hasn,t lost ACC!!! Vladimir Yakovlev (USU) Yes, those who had tried to cheat or had mistaken in long arithmetics have lost AC (-) // Problem 1206. Sum of Digits of the Sum of Numbers 2 Jan 2007 14:56 Test Re: Problem 1206 "Sum of digits". New tests have been added (+) // Problem 1206. Sum of Digits of the Sum of Numbers 17 Oct 2012 10:41 Thanks. I know why I wa 1 Anastas Easytask!!!!!! [7] // Problem 1206. Sum of Digits of the Sum of Numbers 1 Sep 2007 14:07 Just use long arithmetics and calculate 36*pow(55,k-1); jagatsastry Re: Easytask!!!!!! [4] // Problem 1206. Sum of Digits of the Sum of Numbers 16 Oct 2007 00:45 How did u get the formula jagatsastry Re: Easytask!!!!!! [3] // Problem 1206. Sum of Digits of the Sum of Numbers 16 Oct 2007 01:02 What are the libraries and functions u use for long arithmetic in c++. MAT Re: Easytask!!!!!! // Problem 1206. Sum of Digits of the Sum of Numbers 23 Feb 2008 23:52 There are no such libraries! You must write long arithmetics by yourself ;) Orlangur [KNU] Or find somewhere... (+) [1] // Problem 1206. Sum of Digits of the Sum of Numbers 24 Feb 2008 01:22 Aleksa_Markoni Re: Or find somewhere... (+) // Problem 1206. Sum of Digits of the Sum of Numbers 27 Nov 2008 03:44 Thank finaly something extra ordinary good. Thanks allot. I was searching for this for so long time. Thanks, thanks, thanks... IgorKoval(from Pskov) Re: Easytask!!!!!! [1] // Problem 1206. Sum of Digits of the Sum of Numbers 23 Nov 2011 03:01 This program explain how get 36 and 55. #include <iostream> using namespace std; __int64 s( __int64 x ){ __int64 ans = 0; while( x ){ ans += x % 10; x /= 10; } return ans; } int main(){ __int64 kol = 0; for( __int64 i = 0; i <= 9; ++i ){ for( __int64 j = 0; j <= 9; ++j ){ if( s(i+j) == s(i)+s(j) && i+j<=9 ){ cout << " " << i << " " << j << " s=" << s(i+j) << endl; ++kol; } } cout << "-------------------------" << endl; } cout << "kol = " << kol << endl; kol = 0; for( __int64 i = 1; i <= 9; ++i ){// последний разряд без нулей т.к. число must be без ведущих нулей for( __int64 j = 1; j <= 9; ++j ){ if( s(i+j) == s(i)+s(j) && i+j<=9 ){ cout << " " << i << " " << j << " s=" << s(i+j) << endl; ++kol; } } cout << "-------------------------" << endl; } cout << "kol = " << kol << endl; return 0; } Edited by author 23.11.2011 03:11 Edited by author 23.11.2011 03:12 Edited by author 23.11.2011 03:12 Pegasus Re: Easytask!!!!!! // Problem 1206. Sum of Digits of the Sum of Numbers 15 Oct 2012 20:41 Thanks for your code. Qafqaz_Ferhad Cebiyev And is it very easy to use long arithmetic. I was writing it.But then I saw that this is going to be very long.And I thought to myself this way isn't true. // Problem 1206. Sum of Digits of the Sum of Numbers 15 Jul 2010 21:38 Qafqaz_Ferhad Cebiyev How to use long aritmetics in C++? I haven't use it before. // Problem 1206. Sum of Digits of the Sum of Numbers 15 Jul 2010 21:26 How to use long aritmetics in C++? I haven't use it before. Mansurov Artur non correct statement? [2] // Problem 1206. Sum of Digits of the Sum of Numbers 9 Jul 2008 10:22 for K=2 we can get 1980 only if we assume that pairs A=12 B=12 A=12 B=12 are two different pairs like A=11 B=12 A=12 B=11 Chmel_Tolstiy Re: non correct statement? [1] // Problem 1206. Sum of Digits of the Sum of Numbers 9 Jul 2008 14:44 I think u are not right. bsu.mmf.team Re: non correct statement? // Problem 1206. Sum of Digits of the Sum of Numbers 17 Sep 2008 21:46 Yes, see this programm: #include <iostream> #include <math.h> using namespace std; int Sum (int n) { int s=0; while (n) { s+=n%10; n/=10; } return s; } int main() { int k=0; for (int i=10; i<100; i++) { for (int j=10; j<100; j++) { if (Sum(i)+Sum(j)==Sum(i+j)) { k++; cout<<i<<" "<<j<<"\n"; } } } cout<<k; return 0; } It returns 1980, but you can easily see that if i=j this pair wasn't counted twice sim40 WHY WA on TEST 5 ?!?!? C++ [1] // Problem 1206. Sum of Digits of the Sum of Numbers 28 Mar 2008 18:57 #include<iostream> using namespace std; unsigned long long n=36; int k; int main() { cin>>k; while(k>1) { n*=55; k--; } cout<<n<<endl; } ENick(TNU) Re: WHY WA on TEST 5 ?!?!? C++ // Problem 1206. Sum of Digits of the Sum of Numbers 26 Apr 2008 22:45 Use long arifmetic. jagatsastry long arithmetic [2] // Problem 1206. Sum of Digits of the Sum of Numbers 19 Nov 2007 02:01 How do we perform long arithmetic calculations in c++? Is there any builtin library with g++? I'd googled for it only to find all external(out of standard g++) libraries. If anyone has written a class for this purpose, please share the code here or mail it to me. Thanks. denton Re: long arithmetic // Problem 1206. Sum of Digits of the Sum of Numbers 17 Feb 2008 18:46 No, such library doesn't exist. You've got three options: 1. Write it yourself. 2. Use Java, if you know it well. 3. Say «Well, it is definitely not my problem». I would recommend option number two ;) Fokysnik Some hints (DONT read this if you want to think yourself) [1] // Problem 1206. Sum of Digits of the Sum of Numbers 14 Aug 2006 18:20 The equality holds when the sum of i-th digits of numbers A and B (A[i]+B[i]<=9) Using this write a simple program. It will be a TL program but... try running it for k=1,2,3,4,5,6,7 and you should notice a rule how the answer for k+1 is formed. And one more thing. You should use long arithmetics. For k=50 answer has 87 digits. Good luck. ылбλщ Arςhiτo伊シξdeΡφςォмгбй Re: Some hints (DONT read this if you want to think yourself) // Problem 1206. Sum of Digits of the Sum of Numbers 23 Jul 2007 17:54 Thanks! Black^n^White AC in 0.001 (with precalculations) [2] // Problem 1206. Sum of Digits of the Sum of Numbers 2 Jan 2007 01:09 [code deleted] Edited by moderator 02.01.2007 18:52 [SSAU_#617]snipious aka Pimenov Sergey Nikolaevich Re: AC in 0.001 (with precalculations) // Problem 1206. Sum of Digits of the Sum of Numbers 2 Jan 2007 13:00 I have ACC 0.015 204 КБ, but I use long arithmetics, that's why my program is more universal!!! Edited by author 02.01.2007 13:00 Roma Labish[Lviv NU] Re: AC in 0.001 (with precalculations) // Problem 1206. Sum of Digits of the Sum of Numbers 2 Jan 2007 15:16 And now your program sucks ...:) Darth Niculus The text is wrong!!!!! // Problem 1206. Sum of Digits of the Sum of Numbers 11 May 2003 18:47 What is K's role in this problem because it has no link to the rest of the problem. hongyan What's the mean of K? [1] // Problem 1206. Sum of Digits of the Sum of Numbers 26 Nov 2002 06:00 Leonid Volkov Re: What's the mean of K? // Problem 1206. Sum of Digits of the Sum of Numbers 26 Nov 2002 13:04 It is the number of digits. In the output specification, there was erroneously placed the russian letter "K", which looks exactly like the latin one, but has another code and may be displayed as "К".
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