N-Queens / Constraint Satisfaction — Backtracking 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
- Heap (Priority Queue) Patterns — Top K elements, K-way merge, two heaps for median, and scheduling.
- Greedy Patterns — Interval scheduling, jump games, stock trading, and task scheduling.
- Dynamic Programming (DP) Patterns — Fibonacci, Kadane, knapsack, LCS, LIS, edit distance, grid paths, and word break.
- Graph Traversal Patterns (DFS & BFS) — DFS/BFS traversal, topological sort, shortest paths, Union-Find, and MST.
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.