New Algorithms for Generation of Combinations in Lexicographical Order

Generating r-combinations of the set N={1, 2, …, n} in lexicographical order has been an interest for researchers in the field of computer science and combinatorial optimization. This study provides three new algorithms for generating these r-combinations in lexicographical order for the given n and r. The first two of these algorithms generate all the combinations by using a backtracking process. The third algorithm directly generates the k-th sequence in the lexicographical order by using a hash function. All these algorithms perform an efficient running time compared to the well-known methods used in literature