Example - n = 3
Input
3
Output
['((()))', '(()())', '(())()', '()(())', '()()()']
All 5 valid combinations for 3 pairs.
Full lesson preview
Generate well-formed parentheses
Produce all combinations of n pairs of well-formed parentheses using recursion and backtracking.
Python practice13 minRecursion & BacktrackingIntermediateLast updated March 27, 2026
Problem statement
Given n pairs of parentheses, generate all combinations of well-formed parentheses. Use recursion/backtracking to explore placement of '(' and ')' while preserving validity (never place more ')' than '(' at any prefix). Return the combinations as a list of strings in the order produced by standard backtracking (always try to place '(' before ')').
Task
Implement a backtracking generator that returns all valid parentheses strings for n pairs, ensuring deterministic ordering.
Examples
Input format
A single integer n (number of pairs).
Output format
A list of strings representing all valid parentheses combinations.
Constraints
0 <= n <= 8. Return combinations in the order produced by backtracking that always attempts '(' before ')'.
Samples
Sample 1
Input
2
Output
['(())', '()()']
Two valid combinations for 2 pairs.