Final answer:
Iteration is the repetition of a set of instructions in a loop, while recursion is a function calling itself to divide problems into sub-problems. Recursive backtracking is a problem-solving strategy that uses recursion to try multiple paths, backtracking if a solution path fails. Algorithms provide a step-by-step procedure, whereas heuristics offer a general guide to problem-solving.
Step-by-step explanation:
To distinguish between the problem-solving methods of iteration, recursion, and recursive backtracking, it is important to understand their definitions and applications.
Iteration vs Recursion
Iteration involves repeating a set of instructions until a certain condition is met. A typical example is a loop structure in programming that executes the same block of code multiple times. Recursion, on the other hand, is a method where a function calls itself in order to divide a problem into smaller, more manageable sub-problems. It often involves a base case to stop the recursive calls.
Recursion vs Recursive Backtracking
While recursion is simply a function calling itself, recursive backtracking is a more specific application of recursion. It involves trying out different alternatives to find a solution, and if the current path doesn't lead to a solution, it "backtracks" to the previous state and tries a different path. This is commonly used in puzzles and search algorithms where multiple solutions are possible.
When applying these problem-solving strategies, one must also be aware of identifying knowns and unknowns, ensuring that the solution is reasonable, and using a step-by-step approach or tools like the TI-83, 83+, or 84 calculators.
In general, an algorithm is a step-by-step set of operations to be performed for a given task, while a heuristic is a general problem-solving framework or mental shortcut that is useful for making judgments and decisions.