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)
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aejaz_ahmed9:
2020-10-23 14:25:50
c++ will give you wrong answer;
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ratnasingh:
2019-10-16 15:57:20
when Submitted as TEXT of same code output accepted, C++ code giving WA.Dont know why
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dev_harsh1998:
2019-05-05 12:44:40
lol bruteforce Last edit: 2019-05-05 12:45:03 |
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kass_97:
2017-12-15 18:59:28
Back to SPOJ after a long time, solved this one first |
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nadstratosfer:
2017-08-07 10:48:48
Optimized brute force (about 4M iterations) is enough with Python. |
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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) |
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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). |
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suraj_:
2016-11-01 06:46:25
AC!! in one go..use brute force + set; |
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vineetpratik:
2016-06-27 09:55:30
100th :) |
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mkfeuhrer:
2016-06-04 13:54:40
print all possible solutions just in sorted order ..... 1 WA ...brute force AC:-) |
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 |