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generateParentheses

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Problem

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

"((()))", "(()())", "(())()", "()(())", "()()()"

Solution

Brute force, backtrack and prune impossible branch

memoize current left and right parentheses count (as parameters) for fast condition eval