An algorithm is a finite set of instructions, each of which has a clear, well-defined meaning and can be performed with a finite amount of effort in a finite amount of time.

Think of it as a recipe in a cookbook. You start with ingredients (inputs), follow a series of steps (logic), and end with a dish (outputs). In programming, we use algorithms to transform data into useful information.

Algorithm Essentials

Input: Zero or more supplied values
Output: At least one result produced
Precision: Steps are clear and unambiguous

Algorithm Criteria

Finite

The algorithm must terminate after a finite number of steps.

Definite

Each step must be precisely defined; action after each step must be clear.

Input

An algorithm has zero or more inputs taken from specified sets of objects.

Output

An algorithm has one or more outputs that have a relationship to the input.

Effectiveness

Each step must be basic enough to be performed exactly by a person with paper and pen.

Independent

Algorithm should be independent of any programming language or code.

Common Design Paradigms

Greedy Algorithm

Makes locally optimal choices without considering future consequences

Example:Dijkstra's algorithm, Prim's algorithm

Best used:When locally optimal choice leads to globally optimal solution

Divide and Conquer

Divides problem into smaller subproblems, solves recursively, then combines

Example:Quick sort, Merge sort, Binary search

Best used:When problem can be broken into similar smaller problems

Dynamic Programming

Solves overlapping subproblems by storing solutions in optimal structure

Example:Fibonacci series, Knapsack problem

Best used:When subproblems overlap and optimal substructure exists

Brute Force

Tries all possible solutions until finding the optimal one

Example:Linear search algorithm

Best used:When problem size is small or no better algorithm exists

Backtracking

Explores all possible solutions and backtracks when solution isn't optimal

Example:N-Queens problem, Sudoku solver

Best used:When need to find all solutions or constraint satisfaction problems

Branch and Bound

Systematically explores solution space with pruning of suboptimal branches

Example:Traveling salesman problem

Best used:For optimization problems where bounds can be computed

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