The Four Core Patterns of Backtracking
Understanding Backtracking Patterns
Backtracking can be applied to a wide variety of problems, but most of them follow one of these four core patterns.
Each pattern represents a different way of thinking about and applying backtracking to solve problems.
Sudoku Solver Pattern
Graph Coloring Pattern
Learning Objective
Understand the core patterns of backtracking and how they can be applied to solve different types of problems.
The Four Core Patterns of Backtracking
While backtracking can be applied to many different problems, most backtracking solutions follow one of these four core patterns. Understanding these patterns will help you recognize when and how to apply backtracking to new problems.
Board Configuration Problems
Problems involving placing objects on a board while satisfying certain constraints.
Examples: N-Queens, Knight's Tour
Constraint Satisfaction Problems
Problems where solutions must satisfy a set of constraints.
Examples: Sudoku, Crossword Puzzles
Combinatorial Problems
Problems involving finding combinations or permutations with specific properties.
Examples: Combination Sum, Subset Sum
Graph Problems
Problems involving traversing or modifying graphs.
Examples: Graph Coloring, Hamiltonian Path
Choosing the Right Pattern
When faced with a problem that might be solved using backtracking, ask yourself these questions to identify the most appropriate pattern:
For N-Queens Pattern
"Am I placing objects on a board where their positions affect each other?"
For Sudoku Solver Pattern
"Am I filling in values that must satisfy multiple constraints simultaneously?"
For Combination Sum Pattern
"Am I looking for combinations of elements that satisfy a specific condition?"
For Graph Coloring Pattern
"Am I assigning values to connected entities where adjacent entities must have different values?"