12.2.2  Previous and next permutation

The set of n-tuples of an ordered set can be put in lexicographic order, where the tuple (a₁,a₂,…,a_n) comes before (b₁,b₂,…,b_n) exactly when for some k (possibly k=0), a_i=b_i for i=1,…,k−1 and a_k<b_k. For example, the list of all permutations of size 3 in lexicographic order is: (0,1,2), (0,2,1), (1,0,2), (1,2,0), (2,0,1), (2,1,0).

The prevperm and nextperm commands find the preceding and succeeding permutation.

• prevperm takes p, a permutation.
• prevperm(p) returns the previous permutation in lexicographic order, or undef if there is no previous permutation.
• nextperm takes p, a permutation.
• nextperm(p) returns the next permutation in lexicographic order, or undef if there is no next permutation.

Examples