Computational Method, Method or algorithm that can be carried out by a computer to solve a problem Eg. This can be considered when deciding how, or whether, a problem can be solved algorithmically., Computable Problem, Problem for which an algorithm exists that can produce a solution in a finite amount of time Eg. finding the largest value in a finite list is computable because an algorithm can solve it., Non-computable Problem, Problem for which no algorithm exists that can always produce a solution Eg. the general halting problem cannot be solved by an algorithm for every possible program and input., Tractable Problem, Problem that can be solved computationally in a reasonable amount of time Eg. This can be considered when deciding how, or whether, a problem can be solved algorithmically., Intractable Problem, Problem for which a solution may exist but cannot generally be found in a reasonable amount of time as problem size grows Eg. This can be considered when deciding how, or whether, a problem can be solved algorithmically., Halting Problem, Problem of determining for every possible program and input whether that program will eventually stop; no algorithm can solve this for all cases Eg. there is no algorithm that can always decide whether every possible program will eventually stop., Heuristic, Rule or approximation used to find a good solution efficiently without guaranteeing the optimal solution Eg. A* can use straight-line distance to the destination as a heuristic., Backtracking, Problem-solving method that builds a solution incrementally and abandons a path when it cannot lead to a valid solution Eg. a maze solver can follow a path and return to an earlier junction when it reaches a dead end., Brute Force, Solving a problem by systematically trying all possible candidate solutions until one is found Eg. a program could try every possible four-digit PIN from 0000 to 9999., Divide and Conquer, Breaking a problem into smaller sub-problems, solving them and combining their results Eg. merge sort divides a list into smaller sub-lists before combining them., Recursion, Technique where a subroutine calls itself to solve smaller instances of a problem Eg. factorial(5) can call factorial(4), which calls factorial(3), until a base case is reached., Base Case, Condition that stops further recursive calls Eg. factorial(0) = 1 can stop further recursive calls.

A Level P2: Computational Methods and Problem Classification - Mr Gopal

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