N-Queens / Constraint SatisfactionBacktracking Patterns

The N-Queens / Constraint Satisfaction pattern applies when you need the N-Queens / Constraint Satisfaction technique within the Backtracking Patterns pattern. Its time complexity is O(n!) and space complexity O(n) recursion depth. It is used in 2 problems on Thita, including N-Queens and Sudoku Solver. Common variations are Parentheses Generation and Subsets (Include/Exclude).

Solve N-Queens and Sudoku using backtracking with constraint propagation.

N-Queens / Constraint Satisfaction is one of the 7 subpatterns of the Backtracking Patterns pattern, which covers subsets, permutations, combinations, N-Queens, and word search. The whole pattern is about 3 hours of study. This subpattern is an important variation worth recognising on sight.

What N-Queens / Constraint Satisfaction covers

Master backtracking algorithms including subsets, permutations, combinations, N-Queens, and word search. Exhaustive search with pruning for constraint satisfaction. Problems in this subpattern are usually searched for as N-Queens, sudoku solver, constraint satisfaction, backtrack constraints, leetcode 51, leetcode 37.

How to practise N-Queens / Constraint Satisfaction on Thita.ai

Read the theory for N-Queens / Constraint Satisfaction, then work the problems attached to it in the browser editor. Your solution runs against the problem's test cases, and the AI coach offers a hint about the technique you are missing rather than a finished solution. Progress is tracked per subpattern, so the Backtracking Patterns tracker shows this one as covered once you have solved its problems.

Other subpatterns in Backtracking Patterns

  • Subsets (Include/Exclude) Generate all subsets using include/exclude decision pattern. Handle duplicates in subsets.
  • Permutations Generate all permutations using backtracking. Handle duplicates and next permutation.
  • Combination Sum Find combinations that sum to target using backtracking. Handle reuse and duplicates.
  • Word Search / Path Finding in Grid Search for words in grid using backtracking. Handle visited cells and path restoration.
  • Parentheses Generation Generate all valid parentheses combinations using backtracking with balance tracking.
  • Palindrome Partitioning Partition string into palindromic substrings using backtracking.

Related DSA patterns

Where to go next

N-Queens / Constraint Satisfaction is one lesson in a 16-pattern DSA course. If you are preparing end to end, work the interview-critical patterns first and use the pattern sheet as the checklist; if you are here for one technique, the Backtracking Patterns guide is the shortest path back to the rest of it.

Preparing this lesson and its course outline.