Permutations — Backtracking Patterns
The Permutations pattern applies when you need the Permutations technique within the Backtracking Patterns pattern. Its time complexity is O(n!) and space complexity O(n) recursion depth. It is used in 3 problems on Thita, including Next Permutation, Permutations and Permutation Sequence. Common variations are N-Queens / Constraint Satisfaction and Parentheses Generation.
Generate all permutations using backtracking. Handle duplicates and next permutation.
Permutations 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 a core technique: expect it to come up directly in interviews.
What Permutations 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 permutations, generate permutations, next permutation, permutation sequence, leetcode 46, leetcode 31.
How to practise Permutations on Thita.ai
Read the theory for Permutations, 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.
- 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.
- N-Queens / Constraint Satisfaction — Solve N-Queens and Sudoku using backtracking with constraint propagation.
- 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
Permutations 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.