If my algorithm goes awry, the most important method which I believe is dry run using pen and paper. If it works fine but bug still exists then execute it for very simple and easy input and add some display statements in each module as "in module X". If this works. then gradually increase to boundary case inputs and find the illogical code which had made you stuck in debugging nightmare.

What I always end up doing is adding print statements or logging between parts of code where data changes until I can eventually isolate the problem to a line or function. It is helpful to manually know what to expect your data to look like at a given step and verify if that is in fact what it is like.

1. Reproduce the Bug: Ensure you can consistently reproduce the error with specific inputs. Isolate the problem to simplify debugging. 2. Understand the Algorithm: Revisit the logic of the algorithm step-by-step. Break it down and ensure you fully understand its expected behavior. 3. Add Debugging Statements: Insert print statements or use debugging tools to trace variable values, loop iterations, and decision branches. This helps pinpoint where the issue occurs. 4. Check Edge Cases: Test with edge cases and boundary inputs that might expose flaws in the logic (e.g., empty inputs, maximum constraints). 5. Simplify the Code: Temporarily remove unnecessary parts of the code to focus on the core logic. Simplifying helps isolate the bug.