Backtracking — Algorithms

Backtracking Visualizer

N-Queens

Step 0 / 0

Speed 100ms

Step Progress 0 / 0

Recursion Depth 0

Pruned Branches 0

Status Ready

Empty

Placing / Active

Conflict / Pruned

Solution

Placed

Step Explanation

Select an algorithm and press Play to watch the search tree explore and backtrack.

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Pseudocode

Backtracking Algorithms

Backtracking Algorithm Catalog

2 algorithms in this category. Click any card for detailed analysis.

N-Queens

Unstable

N-Queens places n queens on an n×n board so that no two queens attack each other (no shared row, column, or diagonal). Backtracking places queens row by row and undoes placements that lead to dead ends.

Ideal Use: Use N-Queens to learn backtracking, constraint satisfaction, and the classic board-search pattern that generalizes to scheduling and puzzle solving.

Best

O(n!)

Worst

O(n!)

Space

O(n)

Implementation Difficulty

★ ★ ★ ☆ ☆ 3/5

Intermediate

Graph algorithm — interactive visualization

Inspect & Visualize

Sudoku Solver

Unstable

The Sudoku solver fills every empty cell with a digit 1-9 such that each row, column, and 3×3 box contains every digit exactly once. Backtracking fills cells in order and undoes choices that violate the constraints.

Ideal Use: Use the Sudoku solver to practice constraint-satisfaction backtracking — the same pattern powers cryptoarithmetic, regex backtracking, and constraint solvers.

Best

O(9^(n²))

Worst

O(9^(n²))

Space

O(n²)

Implementation Difficulty

★ ★ ★ ☆ ☆ 3/5

Intermediate

Graph algorithm — interactive visualization

Inspect & Visualize

Backtracking Complexity Matrix

Complexity & Performance Tradeoffs

Side-by-side comparison of Big-O time and space complexity characteristics across backtracking algorithms.

Algorithm	Best Time	Average Time	Worst Time	Space Complexity	Stability
N-Queens	O(n!)	O(n!)	O(n!)	O(n)	Unstable
Sudoku Solver	O(9^(n²))	O(9^(n²))	O(9^(n²))	O(n²)	Unstable