Find possible parenthesizing

Given an input n write a program to generate all possible parenthesizing.

For ex: if n=3, then following is the result

((()))
(())()
()()()
(()())
()(())

Number of such elements is represented as Catalan Number. For more details, see http://en.wikipedia.org/wiki/Catalan_number

A similar problem asks to find all possible permutations of given elements with following two variations:

1. There might be repetitions
2. All elements are unique

Stack with findMin() in O(1) worst case

Implement a data structure which provides all stack operations in O(1)(e.g. push(), pop()) and also provides findMin() in O(1) in worst case.

Difference b/w Collection and Collections

Collections provide you views (annoymous class instances) for read-only

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m = n & (d - 1); where d= (1 << k)

Find if the given integer is even or odd

Use of division is not permissible.