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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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! |
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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 ? |
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e_coder:
2015-11-16 07:05:01
simple brute force. |
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prakash_reddy:
2015-08-22 21:38:10
Easy one.... :) |
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jinkies:
2015-07-12 20:10:56
easy with cube cluster |
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jas.py:
2015-06-23 01:14:19
submitted code->WA
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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 |
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kranti:
2015-06-16 07:52:46
AC in 2nd trial :) |
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GAURAV CHANDEL:
2015-04-23 19:06:06
With TEXT , AC
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Ayushi Srivastava:
2014-12-26 21:20:39
i am getting wa.. but the output i get is correct. wat to do? :(
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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 |