HARD NC#79 Backtracking
51. N-Queens
📖 Problem
The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other. Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •Recursive function frames
- •Push/pop state undo
- •Pruning branches early
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Backtracking reasoning pattern
- •Apply Recursion reasoning pattern
💡 Approach
- → Use backtracking to try each valid queen position
- → Track used columns and diagonals to avoid attacks
- → For each row, try placing queen at each column
- → Skip invalid positions (conflicts)
- → Time: O(N!), Space: O(N) for recursion stack
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •Use backtracking to try each valid queen position
- •Track used columns and diagonals to avoid attacks
- •For each row, try placing queen at each column
Common Pitfalls
- •Skip invalid positions (conflicts)
- •Time: O(N!), Space: O(N) for recursion stack
🧪 Test Cases
Hidden tests on submit: 1
Test Case 1
Not run Input:
solveNQueens(4); Expected:
[[".Q..","...Q","Q...","..Q."], ["..Q.","Q...","...Q",".Q.."]] Test Case 2
Not run Input:
solveNQueens(1); Expected:
[["Q"]] Test Case 3
Not run Input:
solveNQueens(3); Expected:
[] 📝 Code Editor
📤 Output