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Discussion of Problem 1462. Uncle Scrooge's GoldVedernikoff 'Goryinyich' Sergey (HSE: АОП) 2 ADMINS: ban the following user(s) for multiple accounts and flooding testing queue [1] // Problem 1462. Uncle Scrooge's Gold 17 Oct 2015 21:56 Kolega FrigATE Mister IPRIT Jogn Doe Jogn Doe2 Jogn Doe3 John Doe 4 John Doe 5 Vladimir Yakovlev (USU) Re: 2 ADMINS: ban the following user(s) for multiple accounts and flooding testing queue // Problem 1462. Uncle Scrooge's Gold 18 Oct 2015 14:20 Flooding submissions were cleaned out Edited by author 18.10.2015 14:20 Krayev Alexey (PSU) 0.046s. Who's better? (-) [8] // Problem 1462. Uncle Scrooge's Gold 19 Aug 2006 20:30 xurshid_n Re: 0.046s. Who's better? (-) // Problem 1462. Uncle Scrooge's Gold 21 Oct 2006 18:18 Please, send me your solution or algorithm!!! my email: xujand000@rambler.ru Vladimir Yakovlev (USU) Did you use FFT? (-) [4] // Problem 1462. Uncle Scrooge's Gold 23 Oct 2006 15:25 Edited by author 23.10.2006 19:00 Krayev Alexey (PSU) Re: Yes (-) // Problem 1462. Uncle Scrooge's Gold 23 Oct 2006 17:45 xurshid_n What is FFT? (-) [2] // Problem 1462. Uncle Scrooge's Gold 26 Oct 2006 18:40 Todor Tsonkov Re: What is FFT? (-) [1] // Problem 1462. Uncle Scrooge's Gold 3 Nov 2006 02:41 I'm also interested in a c++ solution of this problem, please send to tabledott@gmail.com Vedernikoff Sergey Re: What is FFT? (-) // Problem 1462. Uncle Scrooge's Gold 16 Nov 2006 15:30 Simple problem... FFT can be used to solve it, but for what purpose??? [SPbSU ITMO] WiNGeR Re: 0.046s. Who's better? (-) [1] // Problem 1462. Uncle Scrooge's Gold 28 Nov 2006 09:03 0.031 ;) vindex Re: 0.046s. Who's better? (-) // Problem 1462. Uncle Scrooge's Gold 2 Dec 2010 12:17 [url=http://www.stratomedia.co.il]בניית אתרים[/url] [url=http://www.vindex.co.il]בעלי מקצוע[/url] [url=http://moverexpert.com]moving[/url] [url=http://www.vindex.co.il/%D7%94%D7%95%D7%91%D7%9C%D7%AA_%D7%93%D7%99%D7%A8%D7%95%D7%AA_%D7%94%D7%95%D7%91%D7%9C%D7%95%D7%AA_%D7%9E%D7%A9%D7%A8%D7%93%D7%99%D7%9D_%D7%94%D7%A2%D7%91%D7%A8%D7%AA_%D7%93%D7%99%D7%A8%D7%94/ ]הובלות[/url] Todor Tsonkov How to improve my Algo. I got TL on test 4 [21] // Problem 1462. Uncle Scrooge's Gold 12 Aug 2006 19:35 I try to find fib(2*n-2)/fib(n-2) but I get TL on test 4, my algo is linear so I couldn't pass the TL, I wonder is the direct algo for finding fib(n-2) and fib(2*n-2) better, because I couldn't implement it :) VALERO Re: How to improve my Algo. I got TL on test 4 [13] // Problem 1462. Uncle Scrooge's Gold 12 Aug 2006 19:40 i have tl too, but i find that fib(2*n-2)/fib(n-2)=fib(n+1)+fib(n-1) ^) but i have tl ( Mafia {Toropov, Isenbaev, Oparin} SPb IFMO Re: How to improve my Algo. I got TL on test 4 [12] // Problem 1462. Uncle Scrooge's Gold 12 Aug 2006 19:48 fib(n) could be evaluated in O(log n) multiplication operations. Todor Tsonkov Re: How to improve my Algo. I got TL on test 4 [11] // Problem 1462. Uncle Scrooge's Gold 12 Aug 2006 19:55 Well, my idea was to evaluate fib(n-2) and fib(2*n-2) using the direct formula for fib(n)- as function of n, but I couldn't implement it , while the bruteforce solution was TL, anyway I'm gonna think a bit more about it, btw congrats for the victory, guys, you did a great job, also a great competiton for ACRush as always :) UdH-WiNGeR Re: How to improve my Algo. I got TL on test 4 [10] // Problem 1462. Uncle Scrooge's Gold 12 Aug 2006 20:20 Hint: direct formula is hard to implement, but we can rewrite it using linear algebra like this: .....................................(0, 1)^(n-1) (fib(n), fib(n+1))=(1, 1)*(....) .....................................(1, 1) , so we can use integer arithmetics! Edited by author 12.08.2006 21:05 Edited by author 12.08.2006 21:05 Edited by author 12.08.2006 21:05 Edited by author 12.08.2006 21:06 Edited by author 12.08.2006 21:06 Edited by author 12.08.2006 21:06 VALERO Re: How to improve my Algo. I got TL on test 4 [9] // Problem 1462. Uncle Scrooge's Gold 13 Aug 2006 00:18 Who can you write me om email the algorithm or in what book i can find it? Thanks. adas@simnet.kiev.ua UdH-WiNGeR Re: How to improve my Algo. I got TL on test 4 [8] // Problem 1462. Uncle Scrooge's Gold 13 Aug 2006 14:37 Here is an explanation of the algorithm in Russian: http://algolist.manual.ru/maths/count_fast/fibonacci.php Edited by author 13.08.2006 14:37 Anton [SUrSU] Test data [7] // Problem 1462. Uncle Scrooge's Gold 13 Aug 2006 18:32 What is the answer fo this test? n = 7000 UdH-WiNGeR Re: Test data // Problem 1462. Uncle Scrooge's Gold 13 Aug 2006 20:23 81937319032993876558582070063011262115783024656965723338526424275071630557443673768160691777974344039339079218543821663526642065353277478431909789983160736348837929626796434540999450923786205450782143686270382692873692233405139629109704561270312322297501776980155782647708033073460077811847296059544586515736242655594916292010288630241998587835886957464588315061688674744586049802510938100726026534538639883653835446753146728656928193874140316597540202353213455487305219113003826047850156459479457447951648423579548704045234844929446845423587933723079796158760129023524040519672308404718221125336963212128205511547407802595672777585867901520427711491099757592076124797583476061864630025076181920889182653070760272884159824308542397653852400985696907858408387639956157978706489167805462854368911415071677899319871467455602850964575780531369593561207038707991166116257391616617990142018311285809472372949541001826651548109149596409807197380997932230498982610632747317000197354547509949735065278160290108373521163485352357077038417341404680343430978229222267611931184569548788576280109768575772879672619415599295926884517066063939649588253695834282602632479823971486742422068816044196848224503022646081677385555572595399717609483383203051148447238015528377198350218937442030369055848713320280710524550172256486540262008219704955151944469303730096667265538925353091481286313382299155890271045282453432557272252772046637042581378078908572780035752442042046549675078127 Anton [SUrSU] Re: Test data [5] // Problem 1462. Uncle Scrooge's Gold 13 Aug 2006 23:11 I know how to calc Fn in O(log n). But also i must use long arithmetic and TL in result. Give some hints please Sid Re: Test data [4] // Problem 1462. Uncle Scrooge's Gold 13 Aug 2006 23:25 Just use java.math.BigInteger in Java.=) Todor Tsonkov Re: Test data [3] // Problem 1462. Uncle Scrooge's Gold 14 Aug 2006 01:07 Yup, I used BigInteger but O(n) gave me TL, so does there exist a solution which doesn't use advanced maths techniques such as the described above, because I tried to use BigDecimal but it loses precision when trying to calculate directly Fib(n) Vasilevskiy Boris Re: Test data [2] // Problem 1462. Uncle Scrooge's Gold 14 Aug 2006 14:35 It`s improbable task! While I use quick power raising of matrix, I still got tl Then I tried to calculate it lineary and got AC, c++ Petr Re: Test data [1] // Problem 1462. Uncle Scrooge's Gold 31 Aug 2006 17:45 Hi Boris :) Here my sol: There is sequence a(i)=a(i-1)+a(i-2), a(1)=1,a(2)=3. Ans for this problem is a(n). I tried to calculate it O(n) and it taked ~ 17 sec in n=40000. Then I tried to calculate it o(logN) and it,of course, slower then O(n). Is there any special quick algo for long numbers?(sum or product) Edited by author 31.08.2006 17:50 Kaliningrad SU -J_A_MES-HeadLiner Re: Test data // Problem 1462. Uncle Scrooge's Gold 31 Aug 2006 20:45 Of course there are fast algorithms for long multiplication. Try to find FFT or FHT. SPIRiT Your formula is incorrect! [6] // Problem 1462. Uncle Scrooge's Gold 14 Sep 2006 18:48 The actual answer is fib(2*n-1)/fib(n-1). Just check the sample answer.... Todor Tsonkov Re: Your formula is incorrect! [5] // Problem 1462. Uncle Scrooge's Gold 14 Sep 2006 23:59 Yup, but if you use some math knowledge you will find that the result is fib(n-1)+fib(n+1), during the competition as far as I got was the result you mentioned, but I think implementing it is improbable task, anyway can someone send accepted C++ solution to me at ttsonkov [at] gmail.com, I'd be very grateful, cos I implemented the algo with the matrix but I still get TL. Todor Tsonkov Re: Your formula is incorrect! // Problem 1462. Uncle Scrooge's Gold 15 Sep 2006 18:21 Anyway, Java rulez!!! O(logn) got accepted in about 0.7s. ,yet it would be interesting to see some C++ solutions SPIRiT Re: Your formula is incorrect! [3] // Problem 1462. Uncle Scrooge's Gold 15 Sep 2006 19:50 What do you mean result is fib(n-1)+fib(n+1)? For sample (n=3) fib(2)+fib(4)=2+5=7, but real answer is 4. Check that yourself Todor Tsonkov Re: Your formula is incorrect! [2] // Problem 1462. Uncle Scrooge's Gold 15 Sep 2006 23:26 @spirit: It depends on how you get the Fibbonacci sequence if fib(1)=1, fib(2)=1, fib(3)=2 and etc. you get the desired result :) SPIRiT Oh I get it // Problem 1462. Uncle Scrooge's Gold 18 Sep 2006 18:15 Well, then my formula is fib(n-2)+fib(n) 3a[3.141592..]Jlu No subject // Problem 1462. Uncle Scrooge's Gold 18 Mar 2009 15:10 I use linear algo O(N) + long addition (10^18), but I got TL#4 :( Please help me. Search How to more optimize~Code here...Thank you!!! [1] // Problem 1462. Uncle Scrooge's Gold 25 Sep 2008 01:10 #include <cstdio> #include <string> #include <memory> using namespace std; class BigInteger{ private: enum{MAXLENGTH=14900}; int m[MAXLENGTH]; int len; public: BigInteger(int n) { memset(m,0,sizeof(m)); len=0; if (n == 0) len++; while (n > 0) { m[len++] = n % 10; n = n / 10; } } BigInteger(void) { memset(m,0,sizeof(m)); len=1; } void print(void) { int temp = len-1; while(temp>=0) printf("%d",m[temp--]); } BigInteger operator+ (const BigInteger &a) { int i,carry = 0; BigInteger Temp(*this); if (a.len > Temp.len) Temp.len = a.len; for(i=0;i<Temp.len;i++) { Temp.m[i] += (a.m[i] + carry); carry = Temp.m[i] / 10; Temp.m[i] %= 10; } if (carry > 0) {Temp.m[i] = carry; Temp.len++;} return Temp; } int operator> (const BigInteger &a) { int i; if (len > a.len) return 1; if (len < a.len) return 0; for(i=len-1;(m[i] == a.m[i]) && (i>0);i--); if (m[i] > a.m[i]) return 1; return 0; } int operator== (const BigInteger &a) { int i; if (len != a.len) return 0; for(i = len-1;i>=0;i--) if (m[i] != a.m[i]) return 0; return 1; } }; int main() { int n; scanf("%d",&n); BigInteger r1;int i; BigInteger previous = -1; BigInteger result = 1; for (i = 0; i<n; i++) { BigInteger const sum = result + previous; previous = result; result = sum; if(i==n-3){ r1=result; } } (r1+result).print(); return 0; } Edited by author 25.09.2008 01:10 3a[3.141592..]Jlu Re: How to more optimize~Code here...Thank you!!! // Problem 1462. Uncle Scrooge's Gold 18 Mar 2009 14:59 Use long ariphmetics on base 10^9 or 10^18, but not 10^1 :) Alexey How to make it fast? Is my formula correct? [2] // Problem 1462. Uncle Scrooge's Gold 23 Aug 2006 19:59 I use Fib(n-1)+Fib(n+1). I can find Fib(n) in O(log n). But the long arithmetics makes my programm too slow. Help, please. Cybernetics Team Re: How to make it fast? Is my formula correct? [1] // Problem 1462. Uncle Scrooge's Gold 30 Aug 2006 16:52 Read below some solutions. Your formula is correct, I used it too and recursevly computed the F[n]. I used long arithmetics in base 1.000.000 and it runs quick enough. Denis Koshman Re: How to make it fast? Is my formula correct? // Problem 1462. Uncle Scrooge's Gold 12 Aug 2008 05:33 Better use long arithmetics base 2^P, and then fetch decimal answer by sequential divisions by 1'000'000 or something like that. Alexey How many digits are there in the output if N=70000? (-) [4] // Problem 1462. Uncle Scrooge's Gold 21 Aug 2006 17:23 Cybernetics Team Re: How many digits are there in the output if N=70000? (-) [1] // Problem 1462. Uncle Scrooge's Gold 21 Aug 2006 19:17 14630 digits Alexey Thanks // Problem 1462. Uncle Scrooge's Gold 22 Aug 2006 15:56 10x Abid Re: How many digits are there in the output if N=70000? (-) [1] // Problem 1462. Uncle Scrooge's Gold 7 Feb 2007 12:49 2072801145996145261520530447408850863428513339377208014386060985843763728990950560338251079604581881 2761764843963097882756899306880632339149624457792521065549662450746982954629516070098764978344151183 5995330030762779087743459391817243909019805275976633115556130331941538448665875113367934989079027834 0569811790271945906685562735304733743410753082978063360291190842638975525282371376255146251390737707 7479794770248229483843646633681833549215123470585482715472809087383941758904346522640847918233307726 9328866108345114427090779695990005117224442643471755382945481853638762026546985115627193770965426310 5394352702808301103424957405054432898553516895529167136603624447915874323780327952040118805325278847 0288847800035137267512317663342926011439333402801452136904199295820198703432837127533865033077917441 0100898022841492469103704073386054730663565822108884580528522055691701523568506284269126884159083365 2981898449962724562358921065055713479149834483505479477562321118755467916998143411260891457484332466 8332643775010924705690019102274575145613483922681596385654759233269444264241619526680808134173728034 9475872783233388450598439414037223575558750012302913355794850648784308559343577303219076693667107597 3043115850209464408267038946442563894220187739318055364751537731743362821609888945133271851672020727 6058883659104584529812229076091130643430114436305262385420314059450210042195431947096493318081320875 {AESC USU} Evgeny Kurpilyanskij Re: How many digits are there in the output if N=70000? (-) // Problem 1462. Uncle Scrooge's Gold 23 May 2007 19:36 You are wrong. My AC program write answer with length equal 14630 1364009824826097138409874727232071592670236676434661436958625067025953048160195316590256042336050799 9240285236943998597755517864435051077996983326191535648244715055632646494475836054016954249495840368 9429773910248895618431459625704116289808535035391530034504604812315114781580074061315294350832017537 0075316588558621037290575768717973347211695376764733809184842518679512635211464818187929679448162171 4120419822770736842403909341535418889602295980606749453924444722749831991886615203317279082083644209 5859240299070567565865919703493001702802472903786299155673454789689666667376454899780585080004575093 5051125493829019415429695413340276560732927987519009397229769042454790699842227702861077089955276947 9789770809912699679036724558045302233243433525289535479438177687342796156957246446368380611154909281 6665987538395900320557483881627165663456662023298993638270329837346030637435609378930404319693647318 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1493574224008823555824663541639323982500024724974619422821107032679079238129469074783622772447564421 0140370675263534155544266070818807822602135897840220998786574507877939665444757459302334027296817191 4683677640077995437590798828127 Edited by author 23.05.2007 19:43 Edited by author 23.05.2007 19:45 SPIRiT WHY WA at test 4 [3] // Problem 1462. Uncle Scrooge's Gold 19 Sep 2006 19:02 I use this formula: f(N)+f(n-2) where F(0)=1, F(1)=1, F(N)=F(N-1)+F(N-2). But wa. What is in the test 4. I checked the answer for N=7000 at the forum and it matches the answer that my program gives. Can anybody give me a test for 4. SPIRiT This problem does not need log(N) methods [2] // Problem 1462. Uncle Scrooge's Gold 25 Sep 2006 12:39 We can state that f(21)=4181*f(1)+6765*f(2), f(22)=6765*f(1)+10946*f(2). Wherefore we can calculate f(i),f(i+1) with N/20 operations. All we need is addition of two long numbers (I used base 10000 for them) and multiplication of long number and simple one, that's all. The usage of recursion formula f(2n)=f^2(n)+f^(n+1) (or something like that) is overridden here by the cost of multiplication of two long numbers. Todor Tsonkov Re: This problem does not need log(N) methods [1] // Problem 1462. Uncle Scrooge's Gold 25 Sep 2006 14:07 @Spirit: If you want to I can give you my accepted Java source, please give me your mail, but I'm interested in any accepted C++ solutions, please send to tabledott@gmail.com, cause all my C++ efforts were unsucessful, btw I used base 10^9 and I was losing accuracy :) Olly Re: This problem does not need log(N) methods // Problem 1462. Uncle Scrooge's Gold 25 Feb 2007 17:04 I'll send you my C++ solution. I made it in O(n) with only + in long arithmetics, but it's well optimized. If anybode else is interested in my solution mail to me alutsenko[at]bk[dot]ru Cybernetics Team Recursion [2] // Problem 1462. Uncle Scrooge's Gold 21 Aug 2006 19:38 Today I solved this problem using some nice (and easy to find) formulas for computing F[n]: F[2n] = F[n]*(F[n-1] + F[n+1]) and F[2n-1] = F^2[n-1] + F^2[n] with these you cand recursevly compute F[n] fast enough (~0.25 sec). I also precalculated a table with first 2000 Fibonacci and when the recursion dropped below 2000 it returned the computed value. I see some nice times on the best AC list. Will you please tell us how you did it? What formulas, optimizations... Thank you Kaliningrad SU -J_A_MES-HeadLiner Re: Recursion // Problem 1462. Uncle Scrooge's Gold 22 Aug 2006 01:32 Where can I find fast(n*log(n))long multiplication in acceptable form? SPIRiT Re: Recursion // Problem 1462. Uncle Scrooge's Gold 18 Sep 2006 18:33 From what index do you start? F(0)=1 and F(1)=1 or not? Cause I have such formulas: F(2n+1)=F(N)*(F(n-1)+F(n+1)); F(2n)=F^2(N)+F^(N-1)
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