How is backtracking different from brute force?

Brute force enumerates every possible combination. Backtracking prunes the search by rejecting partial solutions that already violate constraints, so it explores far fewer states while still being guaranteed to find a valid solution if one exists.

What is the time complexity of N-Queens?

N-Queens has exponential worst-case complexity, roughly O(N!) without pruning. Constraint checks (no two queens share a row, column, or diagonal) prune most branches early, making real solving far faster than the worst case.

Where is backtracking used in practice?

Backtracking underpins constraint solvers, parsing, regular-expression matching, puzzle solvers (Sudoku), and combinatorial generation such as permutations and subsets. Many constraint-satisfaction problems are solved with backtracking plus heuristics.

All Tools›Algorithm›

Backtracking Visualizer

Free · No Server

Watch N-Queens, Sudoku, Rat in a Maze, and Knight’s Tour solved with backtracking — try, place, and undo animated on a board.

Backtracking Visualizer

Speed:

Step 0 / 367Decisions: 1

Try a queen at row 0, col 0.

Trying Placed Backtrack Solved

def solve(row, n, cols, d1, d2, board):
    if row == n:
        return True
    for c in range(n):
        if c in cols or (row-c) in d1 or (row+c) in d2:
            continue
        cols.add(c); d1.add(row-c); d2.add(row+c)
        if solve(row+1, n, cols, d1, d2, board):
            return True
        cols.discard(c); d1.discard(row-c); d2.discard(row+c)
    return False

About N-Queens

The N-Queens problem places N queens on an N×N board so that none attack each other. Backtracking tries each column per row, undoing a placement when it leads to a conflict.

Time (worst)	O(n!)
Space	O(n)

Real-world uses

Teaching backtracking and pruning
Constraint satisfaction problems
Parallel and distributed search benchmarks

What is Backtracking Visualizer?

The Backtracking Visualizer on AiTechWorlds animates how backtracking algorithms explore choices, hit dead ends, and undo decisions to find a valid solution. Backtracking is the engine behind many puzzles and constraint problems, but the recursive try-place-undo cycle is hard to follow in code. This tool animates N-Queens, Sudoku, Rat in a Maze, and the Knight's Tour on a board, showing each attempted placement, each rejection, and each undo as the algorithm searches. You can adjust board size and speed, or step through the recursion manually to see exactly when and why it backtracks. Everything runs in your browser — AiTechWorlds built this for CS students, interview candidates, and educators.

How to Use

1
Choose a problem
Pick N-Queens, Sudoku, Rat in a Maze, or Knight's Tour.
2
Configure the board
Set the board size or starting grid as the problem allows.
3
Run the solver
Press Solve to animate, or step through each placement and undo.
4
Watch placements and undos
Valid tries are placed; invalid ones are rejected and removed as it backtracks.
5
Reach the solution
Follow the search until a complete valid configuration is found.

Common Use Cases

Interview candidates learning backtracking and recursion patterns
CS students studying constraint-satisfaction problems
Educators demonstrating the try-place-undo cycle visually
Developers building intuition for pruning search spaces
Puzzle enthusiasts seeing how solvers work internally

Key Features

Animates N-Queens, Sudoku, Rat in a Maze, and Knight's Tour
Shows try, place, reject, and undo steps on a board
Adjustable board size and animation speed
Step-by-step recursion advance mode
Synced code view of the backtracking routine
Clear highlighting of dead ends and backtracks
100% browser-based

🔒

100% Private — No Server Required

All processing happens directly in your browser. No data is uploaded, stored, or transmitted to any server.

Frequently Asked Questions

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Last reviewed on June 18, 2026 by the AiTechWorlds Tools Team. All processing runs locally in your browser.

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AiTechWorlds

def solve(row, n, cols, d1, d2, board): if row == n: return True for c in range(n): if c in cols or (row-c) in d1 or (row+c) in d2: continue cols.add(c); d1.add(row-c); d2.add(row+c) if solve(row+1, n, cols, d1, d2, board): return True cols.discard(c); d1.discard(row-c); d2.discard(row+c) return False

What is Backtracking Visualizer?

How to Use

Choose a problem

Pick N-Queens, Sudoku, Rat in a Maze, or Knight's Tour.

Configure the board

Set the board size or starting grid as the problem allows.

Run the solver

Press Solve to animate, or step through each placement and undo.

Watch placements and undos

Valid tries are placed; invalid ones are rejected and removed as it backtracks.

Reach the solution

Follow the search until a complete valid configuration is found.