In-situ associative permuting

The technique of in-situ associative permuting is introduced which is an association of in-situ permuting and in-situ inverting. It is suitable for associatively permutable permutations of {1, 2, . . . , n} where the elements that will be inverted are negative and stored in order relative to each other according to their absolute values. Let K[1 . . . n] be an array of n integer keys each in the range [1, n], and it is allowed to modify the keys in the range [−n, n]. If the integer keys are rearranged such that one of each distinct key having the value i is moved to the ith position of K, then the resulting arrangement (will be denoted by K ) can be transformed in-situ into associatively permutable permutation π using only log n additional bits. The associatively permutable permutation π not only stores the ranks of the keys of K but also uniquely represents K . Restoring the keys