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
Tanmay Sinha:
2014-08-06 13:35:21
is there any other method apart from brute force???
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Priyanshu:
2013-06-21 18:22:18
My 100th classical..!!! :D
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mridul:
2013-05-20 19:48:28
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Muhammad Ichsan Abdillah:
2013-01-02 23:55:00
i've got the same problem as abby, and the spelling of Cube ama Triple is correct, why? |
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viraj:
2012-12-30 13:24:07
@Abby check the spelling of Cube and Triple in the output. I made a silly mistake there. |
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Abby:
2012-07-11 09:14:18
Need help. Getting the correct output, at least from the first 7 sample outputs. And I'm still getting Wrong Answer. Any ideas? |
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ASK:
2011-12-15 12:13:39
@aman kumar as we have to find integers greater than 1 that satisfy the "Perfect cubes" |
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Aman Kumar:
2011-12-14 15:07:09
Cube = 9, Triple = (1,6,8)
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Ankit Paharia:
2011-12-10 21:12:24
@~
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~:
2011-06-07 14:19:46
is the given limit that a<=100 should be for b,c,d also?? |
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 |