The Data Structure dictates the architectural constraints and potential operational costs $O(f(n))$. To realize those complexities, we must apply a specific, detailed Algorithm.

An algorithm is the recipe used to solve a computational problem. It operates on data structures by defining the precise steps required to transform an input into a desired output.

To be successful, any algorithm must satisfy five key criteria:

  • Input & Output: It must take zero or more inputs and produce at least one output.
  • Definiteness: Every step must be clear and unambiguous.
  • Finiteness: It must terminate after a finite number of steps, regardless of the size of $n$.
  • Effectiveness: Every operation must be simple and practical to execute.

Formal Definition

An Algorithm is a well-defined, finite sequence of unambiguous computational steps designed to transform an input (like array $A$ of size $n$) into a desired output (e.g., a sorted version of $A$, or finding the index of target $t$).