Backtracking builds a candidate solution one choice at a time and undoes choices that cannot lead to a valid answer.
How to reason about it
Start by identifying the state the method maintains and the operation that changes it. Then trace one small input by hand. This separates the invariant that makes the method correct from implementation details such as arrays, pointers, counters, or protocol messages.
Worked example
A maze solver marks a cell, explores a neighbor, and removes the mark when that path reaches a dead end.
Write down the state before and after each step. For a larger input, repeat the same transition rather than guessing from the final output. That habit makes edge cases visible and gives you a concrete basis for testing.
Trade-offs and common mistakes
Pruning only works when the rejection rule is sound; an overly aggressive rule can discard valid solutions.'
Choose this technique when its assumptions match the problem. State those assumptions explicitly, test an empty or boundary input, and compare the cost of the operation you perform most often with the memory or setup cost it introduces.
Takeaway
Backtracking: Explore and Undo Choices becomes easier to use once its invariant, input assumptions, and failure cases are clear. A small worked example is a useful first test; measurements and proofs should follow when the system grows.