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

LEXCOMBI(n, k, index-1, …, k)

Required 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.

Example

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