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
nadstratosfer: 2017-08-07 10:48:48

Optimized brute force (about 4M iterations) is enough with Python.

lt: 2017-04-25 20:41:51

Solved in O(N^2 logN), but no doubt it can be easily solved in O(N^2)

cake_is_a_lie: 2017-03-06 16:15:56

You can always brute force and submit as TEXT, or even send in the brute force solution. But it's much more elegant to try and solve it in O(N^2 log N).

suraj_: 2016-11-01 06:46:25

AC!! in one go..use brute force + set;

vineetpratik: 2016-06-27 09:55:30

100th :)

mkfeuhrer: 2016-06-04 13:54:40

print all possible solutions just in sorted order ..... 1 WA ...brute force AC:-)

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.... :)


Added by:Wanderley Guimarăes
Date:2006-06-01
Time limit:0.990s
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