/* 23.11.2011 last modification: 26.06.2013
Copyright (c) 2011-2013 by Siegfried Koepf
This file is distributed under the terms of the GNU General Public License
version 3 as published by the Free Software Foundation.
For information on usage and redistribution and for a disclaimer of all
warranties, see the file COPYING in this distribution.
k-compositions in colexicographic order
Algorithm by Siegfried Koepf
Functions:
int gen_k_comp_colex_init(unsigned char *vector, const unsigned char n, const unsigned char k)
Test for special cases
Initialization of vector
Possible return values are: GEN_ERROR, GEN_EMPTY, GEN_NEXT
int gen_k_comp_colex_next(unsigned char *vector, const unsigned char k)
Transforms current figure in vector into its successor
Possible return values are: GEN_NEXT, GEN_TERM
Arguments:
unsigned char *vector; //pointer to the array where the current figure is stored
const unsigned char n; //length of alphabet
const unsigned char k; //length of figures
Usage and restrictions:
Arguments and elements in vector are restricted to the interval (0, 255)
Memory allocation for vector must be provided by the calling process
k must be <= n
Cardinality:
Binomial(n - 1, k - 1)
*/
#include "_generate.h"
int gen_k_comp_colex_init(unsigned char *vector, const unsigned char n, const unsigned char k)
{
int j; //index
//test for special cases
if(k > n)
return(GEN_ERROR);
if(n == 0)
return(GEN_EMPTY);
if(k == 0)
return(GEN_ERROR);
//initialize: vector[0] = n - k + 1, vector[1, ..., k - 1] are 1
vector[0] = n - k + 1;
for(j = 1; j < k; j++)
vector[j] = 1;
return(GEN_NEXT);
}
int gen_k_comp_colex_next(unsigned char *vector, const unsigned char k)
{
int j; //index
//terminate, this is only needed to allow k == 1
if(k <= 1)
return(GEN_TERM);
//easy case
if(vector[0] > 1)
{
vector[0]--;
vector[1]++;
return(GEN_NEXT);
}
//find leftmost element to increase
for(j = 1; j < k; j++)
if(vector[j] > 1)
break;
//terminate if the first k - 1 parts are 1
if(j >= k - 1)
return(GEN_TERM);
//increase
vector[j + 1]++;
//set left-hand elements
vector[0] = vector[j] - 1;
vector[j] = 1;
return(GEN_NEXT);
}