backtracking

Backtracking is the pattern behind permutations, subsets, N-queens, and constraint problems. The signal is the choose/explore/un-choose template plus pruning, and knowing exactly which knob separates permutations from combinations.

Generating then filtering is O(2^(2n)) and wasteful. Backtracking with two counters builds only valid strings by enforcing the balance rule at every step. Here is the template and why the pruning conditions are exactly right.