combinatorics

For a set of the form A = {1, 2, 3, ..., n} . It is called partition of the set A , a set of k<=n elements which respect the following theorems: a) the union of all the partitions of A is A b) the intersection of 2 partitions of A is the empty set (they can't share the same elements). For example. A = {1, 2,... n} We have the partitions: {1, 2, 3} {1, 2} {3} {1, 3} {2} {2, 3} {1} {1} {2} {3} These theoretical concepts are presented in my algorithms textbook (by the way, this subchapter is part of the "Backtracking" chapter). I am supposed to find an algorithm to generate all the partitions of

Finding all the permutations of a string is by a well known Steinhaus–Johnson–Trotter algorithm. But if the string contains the repeated characters such as AABB, then the possible unique combinations will be 4!/(2! * 2!) = 6 One way of achieving this is that we can store it in an array or so and then remove the duplicates. Is there any simpler way to modify the Johnson algorithm, so that we never generate the duplicated permutations. (In the most efficient way) Use the following recursive algorithm: PermutList Permute(SymArray fullSymArray){ PermutList resultList=empty; for( each symbol A in