N Queens
Detailed guide and Python implementation for the 'N Queens' problem.
1. Concept Overview
The 'N Queens' problem is a key challenge in the Backtracking section.
This implementation focuses on medium-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for N Queens.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for N Queens carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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.
Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
Implement a function solveNQueens(n: int) -> list.
- •1 <= n <= 9
Examples
4
[[".Q..","...Q","Q...","..Q."],["..Q.","Q...",".Q..","...Q"]]
There are exactly 2 distinct solutions to the 4-queens puzzle.
1
[["Q"]]
A single queen on a 1x1 board is the only solution.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def solve_n_queens_opt(n: int) -> list[list[str]]:
col = set()
posDiag = set()
negDiag = set()
res = []
board = [["."] * n for _ in range(n)]
def backtrack(r):
if r == n:
res.append(["".join(row) for row in board])
return
for c in range(n):
if c in col or (r + c) in posDiag or (r - c) in negDiag:
continue
col.add(c)
posDiag.add(r + c)
negDiag.add(r - c)
board[r][c] = "Q"
backtrack(r + 1)
col.remove(c)
posDiag.remove(r + c)
negDiag.remove(r - c)
board[r][c] = "."
backtrack(0)
return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def solve_n_queens_brute(n: int) -> list[list[str]]:
res = []
board = [["."] * n for _ in range(n)]
def is_safe(r, c):
for i in range(r):
if board[i][c] == 'Q': return False
for j in range(n):
if board[i][j] == 'Q' and abs(i-r) == abs(j-c): return False
return True
def backtrack(r):
if r == n:
res.append(["".join(row) for row in board])
return
for c in range(n):
if is_safe(r, c):
board[r][c] = "Q"
backtrack(r + 1)
board[r][c] = "."
backtrack(0)
return resAlgorithm Pattern Checklist
When dealing with Backtracking data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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