CUBES - Perfect Cubes


For hundreds of years Fermat's Last Theorem, which stated simply that for n > 2 there exist no integers a, b, c > 1 such that a^n = b^n + c^n, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It is possible, however, to find integers greater than 1 that satisfy the "perfect cube" equation a^3 = b^3 + c^3 + d^3 (e.g. a quick calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true). This problem requires that you write a program to find all sets of numbers {a,b,c,d} which satisfy this equation for a <= 100.

The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.

Note that the programmer will need to be concerned with an efficient implementation. The official time limit for this problem is 2 minutes, and it is indeed possible to write a solution to this problem which executes in under 2 minutes on a 33 MHz 80386 machine. Due to the distributed nature of the contest in this region, judges have been instructed to make the official time limit at their site the greater of 2 minutes or twice the time taken by the judge's solution on the machine being used to judge this problem.

The first part of the output is shown here:

Cube = 6, Triple = (3,4,5)
Cube = 12, Triple = (6,8,10)
Cube = 18, Triple = (2,12,16)
Cube = 18, Triple = (9,12,15)
Cube = 19, Triple = (3,10,18)
Cube = 20, Triple = (7,14,17)
Cube = 24, Triple = (12,16,20)

hide comments
akshayvenkat: 2016-03-07 18:37:19

Brute Force accepted.. 9 = (1,6,8) case fetched me the wrong answer. make sure a,b,c are greater than one, and only then print! Easy stuff!

dwij28: 2016-01-13 02:58:27

Python results in TLE but got AC with C, C++ and TEXT.. Would love to hear from someone who has an AC python solution.. Did you guys use binary search or something of that sort ?

e_coder: 2015-11-16 07:05:01

simple brute force.

prakash_reddy: 2015-08-22 21:38:10

Easy one.... :)

jinkies: 2015-07-12 20:10:56

easy with cube cluster

jas.py: 2015-06-23 01:14:19

submitted code->WA
submitted the output of same code as TEXT->AC
dont know why??

iharsh234: 2015-06-18 12:17:13

it tahe 2.2 sec for python to do this.I could i reduce it to 0.9.somebody help

Last edit: 2015-06-18 14:15:25
kranti: 2015-06-16 07:52:46

AC in 2nd trial :)

GAURAV CHANDEL: 2015-04-23 19:06:06

With TEXT , AC
but c++ gives WA

Ayushi Srivastava: 2014-12-26 21:20:39

i am getting wa.. but the output i get is correct. wat to do? :(


Added by:Wanderley Guimarăes
Date:2006-06-01
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Mid Central Regionals 1995