On 12/21/13 13:26, Georgi Guninski wrote:
I am trying to solve the following problem, not necessarily with ppl.
Given positive integers $A0,B0,L$ find integers $A,B$ satisfying:
1 <= A A <= L 1 <= B B <= L 1 <= A0*A - B0*B A0*A - B0*B <= L
Encoded it in PPL by modifying an example (also attached):
Constraint_System cs; cs.insert(A >= 1); cs.insert(A <= Coefficient(L)); cs.insert(B >= 1); cs.insert(B <= Coefficient(L)); cs.insert(Coefficient(A0)*A - Coefficient(B0)*B >= 1); cs.insert(Coefficient(A0)*A - Coefficient(B0)*B <= Coefficient(L) );
// All integer variables. Variables_Set ivs(A, B);
// Cost function. Linear_Expression cost(Coefficient("10"));
MIP_Problem mip(cs.space_dimension(), cs.begin(), cs.end(), ivs, cost, MINIMIZATION);
if (mip.solve() != OPTIMIZED_MIP_PROBLEM) {
======= (reads 3 ints from stdin)
This works for small input, but for:
A0=654013667618 B0=654013667619 L=808711
PPL consumes 6GB RAM very fast and I run out of memory.
Am I doing something wrong?
Other ways to solve the problem?
Attached is the source, function "test10".
Thank you.
ppl-1.1 on x86_64 linux.
Hello Georgi. Thanks for the report.
As far as I can tell you are doing nothing wrong: simply, your constraint system (with A0 = 654013667618, B0 = 654013667619, and L = 808711) has no solution over the integers and the branch-and-bound implementation generates so many LP problems that it fills your memory. Did you try with glpk or lp-solve? Kind regards,
Roberto
P.S. Here is how I concluded there is no solution:
$ swipl Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 7.1.2) Copyright (c) 1990-2013 University of Amsterdam, VU Amsterdam SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software, and you are welcome to redistribute it under certain conditions. Please visit http://www.swi-prolog.org for details.
For help, use ?- help(Topic). or ?- apropos(Word).
?- use_module(library(clpfd)). % library(pairs) compiled into pairs 0.00 sec, 22 clauses % library(lists) compiled into lists 0.01 sec, 122 clauses % library(occurs) compiled into occurs 0.00 sec, 14 clauses % library(apply_macros) compiled into apply_macros 0.01 sec, 168 clauses % library(assoc) compiled into assoc 0.00 sec, 103 clauses % library(clpfd) compiled into clpfd 0.11 sec, 2,769 clauses true.
?- A0=654013667618, B0=654013667619, L=808711, 1 #=< A, A #=< L, 1 #=< B, 1 #=< A0*A - B0*B, A0*A - B0*B #=< L. false.
?-