langford.c
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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <paccs.h>
// Langford's number problem (CSPLib 024)
/*
Problem:
- sorting K sets {1, ..., N} such that:
- between each consecutive pair of 1's there is one other number
- between each consecutive pair of 2's there are two other numbers
- ...
- between each consecutive pair of N's there are N other numbers
Modelling:
- K * N variables representing the positions of the numbers
- the first K variables represent the position of the 1's
- the next K variables represent the position of the 2's
- ...
- the last K variables represent the position of the N's
Solution:
- the variables contain a permutation of 1..N * K (the positions)
- each pair of adjacent variables from the first K differ by 1 + 1
- each pair of adjacent variables from the second K differ by 2 + 1
- ...
- each pair of adjacent variables from the last K differ by N + 1
*/
#define MAX_K 10 // sets
#define MAX_N 100 // 1..N
static int K = 3; // default sets
static int N = 9; // default elements
int main(int argc, char *argv[])
{
int arg;
fd_int numbers[MAX_K * MAX_N];
int ordered[MAX_K * MAX_N];
int solutions = 0, one_solution = 1;
int use_label = 0;
int i, j;
int seed;
fd_init(&argc, &argv);
for (arg = 1; arg < argc; ++arg)
if (!strcmp(argv[arg], "--all"))
one_solution = 0;
else if (!strcmp(argv[arg], "--label"))
use_label = 1;
else if (isdigit(*argv[arg]))
break;
else
{
fd__error("%s: invalid argument `%s'\n", argv[0], argv[arg]);
return 2;
}
if (argc > arg)
{
K = atoi(argv[arg++]);
N = atoi(argv[arg++]);
}
#ifdef LOCAL_SEARCH
seed = time(0);
//seed = 1206468701;
//seed = 1208196137; // converges to a local minimum with MCH
srandom(seed);
fd__trace("seed = %u\n", seed);
#endif
for (i = 0; arg < argc; ++arg, ++i)
{
int lb, ub;
char *s;
lb = ub = atoi(argv[arg]);
if (s = strchr(argv[arg], '-'))
ub = atoi(s + 1);
numbers[i] = fd_new(lb, ub);
}
for (; i < K * N; ++i)
numbers[i] = fd_new(0, K * N - 1);
fd_all_different(numbers, K * N);
if (use_label)
fd_label(numbers, K * N);
// don't generate solutions which correspond to exchanging the
// positions of a number (and are, therefore, identical)
for (i = 0; i < N; ++i)
for (j = 0; j < K - 1; ++j)
fd_minus_eq(numbers[i * K + j + 1], numbers[i * K + j], i + 2);
// printf("%d %d %d\n", i * K + j + 1, i * K + j, i + 2);
// don't generate symmetrical solutions
{
fd_int first, last;
first = fd_new(0, K * N - 1);
last = fd_new(0, K * N - 1);
fd_element(numbers, K * N, first, 0);
fd_element(numbers, K * N, last, K * N - 1);
fd_lt(first, last);
}
#ifndef COUNT_SOLUTIONS
while (fd_solve() == FD_OK)
{
printf("solution %d:\n", ++solutions);
for (i = 0; i < K * N; ++i)
{
fd_print(numbers[i]);
putchar(' ');
}
putchar('\n');
for (i = 0; i < K * N; ++i)
{
fd_var_single(numbers[i], &j);
ordered[j] = i / K + 1;
}
for (i = 0; i < K * N; ++i)
printf("%d ", ordered[i]);
putchar('\n');
#if !(defined(LOCAL_SEARCH) || defined(DISTRIBUTED_SOLVER))
if (one_solution)
#endif
break;
}
if (solutions)
printf("%d solutions found\n", solutions);
else
printf("inconsistent CSP\n");
fd_end();
return !solutions;
#else /* COUNT_SOLUTIONS */
fd_solve();
fd_end();
return 0;
#endif /* COUNT_SOLUTIONS */
}