The set of n-tuples of an ordered set can be put in lexicographic order, where the tuple (a1,a2,…,an) comes before (b1,b2,…,bn) exactly when for some k (possibly k=0), ai=bi for i=1,…,k−1 and ak<bk. For example, the set of 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.
Example.
Input:
Output:
| ⎡ ⎣ | 0,2,3,1 | ⎤ ⎦ |
Example.
Input:
Output:
| ⎡ ⎣ | 0,3,1,2 | ⎤ ⎦ |