Recursive Generation of Subsets
Solve the problem of Programming Challenge 11 by using recursion. Do this by writing a recursive function that takes an integer parameter n and returns a list of all subsets of the set 1, 2 . . . , n.
11.Generation of Subsets
Adopt the following strategy to construct the list of all subsets of the set of the integers 1, 2, . . . n. Use an STL vector to represent a single subset of integers, and use an STL list of vectors to represent a list of subsets. Start with a list L0 of one empty vector; then L0 represents the list of all subsets of the empty set. Now suppose that you have created the list Lk-1 of all subsets of 1, 2, . . ., k-1. To form the list Lk of all subsets of 1, 2, . . . k create an empty list L, and then for each vector v in Lk-1, add both v and v [k] to L. Finally, set Lk to L. (Here by v [k] we mean the result of adding the integer k to the vector v.) Test your program for all values of n ≤4.
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