Functions and CALL Routines

LEXCOMBI Function

Generates all combinations of the indices of n objects taken k at a time in lexicographic order.

Category:	Combinatorial
Restriction:	The LEXCOMBI function cannot be executed when you use the %SYSFUNC macro.

Syntax
Arguments
Details
Comparisons
Examples
See Also

Syntax

LEXCOMBI(n, k, index-1, ..., k)

Arguments

n

is a numeric constant, variable, or expression that specifies the total number of objects.

K

is a numeric constant, variable, or expression that specifies the number of objects in each combination.

index

is a numeric variable that contains indices of the objects in the combination that is returned. Indices are integers between 1 and n inclusive.

Tip:	If index-1 is missing or zero, then the LEXCOMBI function initializes the indices to index-1=1 through index-k=k . Otherwise, LEXCOMBI creates a new combination by removing one index from the combination and adding another index.

Details

Before the first execution of the LEXCOMBI function, complete one of the following tasks:

Set index-1 equal to zero or to a missing value.
Initialize index-1 through index-k to distinct integers between 1 and n inclusive.

The number of combinations of n objects taken k at a time can be computed as COMB(n,k). To generate all combinations of n objects taken k at a time, execute the LEXCOMBI function in a loop that executes COMB(n,k) times.

In the LEXCOMBI function, the returned value indicates which, if any, indices changed. If index-1 through index-i did not change, but index-j did change, wherej=i+1, then LEXCOMBI returnsi. If LEXCOMBI is called after the last combinations in lexicographic order have been generated, then LEXCOMBI returns -1.

Comparisons

The LEXCOMBI function generates all combinations of the indices of n objects taken k at a time in lexicographic order. The ALLCOMBI function generates all combinations of the indices of n objects taken k at a time in a minimum change order.

Examples

The following example uses the LEXCOMBI function to generate combinations of indices in lexicographic order.

data _null_;
   array x[5] $3 ('ant' 'bee' 'cat' 'dog' 'ewe');
   array c[3] $3;
   array i[3];
   n=dim(x);
   k=dim(i);
   i[1]=0;
   ncomb=comb(n,k);
   do j=1 to ncomb+1;
      rc=lexcombi(n, k, of i[*]);
      do h=1 to k;
         c[h]=x[i[h]];
      end;
      put @4 j= @10 'i= ' i[*] +3 'c= ' c[*] +3 rc=;
   end;
run;

SAS writes the following output to the log:

   j=1   i= 1 2 3    c= ant bee cat    rc=1
   j=2   i= 1 2 4    c= ant bee dog    rc=3
   j=3   i= 1 2 5    c= ant bee ewe    rc=3
   j=4   i= 1 3 4    c= ant cat dog    rc=2
   j=5   i= 1 3 5    c= ant cat ewe    rc=3
   j=6   i= 1 4 5    c= ant dog ewe    rc=2
   j=7   i= 2 3 4    c= bee cat dog    rc=1
   j=8   i= 2 3 5    c= bee cat ewe    rc=3
   j=9   i= 2 4 5    c= bee dog ewe    rc=2
   j=10  i= 3 4 5    c= cat dog ewe    rc=1
   j=11  i= 3 4 5    c= cat dog ewe    rc=-1