A Solution of Average Time for Pure and Multiset Permutations

Two efficient techniques for evaluating the performance of candidate multiset permutation algorithms are introduced. We arrive at two formulas for simulating the average running time of multiset permutations for all N^N possible inputs with length N. One formula is for non-lexicographic permutations and the other is for lexicographic permutations. For lexicographic permutations, we use 2^N-1 representatives to generate the average time for all N^N possible inputs; and, for non-lexicographic permutations, we use much fewer than 2^N-1 representatives to generate the average time for all N^N possible inputs.