FACT2 - Integer Factorization (29 digits)

This is a problem to test the robustness of your Integer Factorization algorithm.

Given some integers, you need to factor them into product of prime numbers.

The largest integer given in the input file has 29 digits.

You may need to use a general factorization algorithm since no special numbers (e.g. Fermat numbers) are considered when designing the input data.


There are several numbers given, each one in a line.

The input ends with a number 0.

The number of test cases is about 10.


For each number, print in a line the factorization of it. See examples below for the output format.



317^1 9817^1
17^2 89^1 509^1
2^18 3^8 5^4 7^2 11^1 13^1 17^1 19^1
328439^1 234884407^1

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cjn2007: 2022-01-13 05:23:10

final AC :D

nurbijoy: 2020-05-18 16:26:26

I can't get how can I combine them. I solve FAC0 easily using basic factorization

Scape: 2019-12-28 09:41:22

@Lakshman, this is interesting. I tried different variations of brent pollard rho but was unable to pass. Then I modified my code to implement the pollard rho in exactly your way and got accepted in 1.87. If I optimize the pollard rho it gets TLE and with srand(time(0)), it also gets TLE.

Looks like this is not supposed to pass and you only got lucky since the algorithm is randomized :D

mrmajumder: 2019-11-27 07:21:33

Any hints for C++ about how to handle such a big number?

[Lakshman]: 2018-09-23 10:57:36

Surprised to see even my Brent RollardRho also got AC here. In my system, my code is unable to factor 29996186117636068716616424167 in given time don't how it got accepted here.

liouzhou_101: 2018-09-11 10:28:35

Why does my AC code for FACT1 using Brent Pollard Rho still get AC here? I thought it would get TLE instead.

Howard Roark: 2017-10-22 17:48:10

Meeting the time constraints in a language like Java or python will be a real challenge. I have seen pure Java implementations of the quadratic sieve that can do it, but they represent a ton of code and years of effort. Pollard-rho is just a little bit too slow I think, not sure about lenstra's elliptic curve method variants.

[Lakshman]: 2017-02-10 20:21:48

Why java solutions are taking more time than earlier one. Even though Cluster has been upgraded to faster one.

[Lakshman]: 2015-12-08 04:42:46

Finally factored it.Used combination of Quadratic sieve + Fermat + Brent Pollard Rho.

Quadratic Sieve is enough for this.

Last edit: 2015-12-08 08:22:15
black MaMbA: 2014-08-27 15:01:07

is there any specific set of algorithms that we have to implement like lenstra elliptic curve,quadratic sieve because algorithms for first two versions of the problem get TLE in this version

Added by:Jimmy
Time limit:2.014s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL NODEJS PERL6 VB.NET