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Backtracking Fundamentals

Essential concepts and techniques for implementing backtracking algorithms.

Recursive exploration​

  • Systematic Search: Explore all possible solutions systematically
  • Decision Tree: Represent problem as tree of decisions
  • Depth-First: Explore each path completely before backtracking
  • State Space: All possible states of the problem

Pruning techniques​

  • Constraint Pruning: Eliminate branches that violate constraints
  • Bound Pruning: Eliminate branches that cannot lead to better solution
  • Heuristic Pruning: Use heuristics to guide search
  • Early Termination: Stop when solution is found
  • State Representation: How to represent current state
  • State Transitions: How to move from one state to another
  • Goal State: Desired final state
  • Path Cost: Cost of reaching current state

Constraint satisfaction​

  • Constraints: Rules that must be satisfied
  • Variable Assignment: Assigning values to variables
  • Constraint Propagation: Inferring new constraints
  • Consistency Checking: Verifying constraint satisfaction

Solution space​

  • Complete Solutions: All variables assigned values
  • Partial Solutions: Some variables assigned values
  • Solution Validation: Checking if solution is valid
  • Solution Optimization: Finding best solution among all valid solutions