The previous slide established that an algorithm must satisfy criteria like Finiteness and Definiteness. Translating a computational task into a proven method that meets these strict standards requires a structured, iterative design process. The lifecycle of developing a reliable, high-performance algorithm involves four critical stages, moving from an abstract idea to a concrete program that meets a predicted time complexity $O(f(n))$.

  • 1. Problem Definition:
    • Defining the exact relationship between the input (e.g., array $A$ of size $n$) and the desired output (e.g., finding target $t$, or sorting $A$).
    • This stage clarifies all constraints and operational expectations.
  • 2. Algorithm Design & Analysis:
    • Developing the high-level computational strategy (e.g., greedy approach, brute force, divide and conquer).
    • Crucially, this is where we analyze the theoretical cost, determining the worst-case time complexity $O(f(n))$ before writing code.
  • 3. Implementation:
    • Translating the abstract design into executable, unambiguous code (like the selection_sort function we examined).
  • 4. Testing, Validation, and Refinement:
    • Running the implementation (e.g., on Search_Array_A) to verify correctness and measure its actual performance against the predicted $O(f(n))$.

Algorithm Development Lifecycle

Stage Key Activity Output
Problem Definition Clarify I/O & constraints Formal specification
Design & Analysis Develop strategy & predict cost Pseudocode & $O(f(n))$
Implementation Translate design to code Working program
Testing & Refinement Verify correctness & measure speed Validated code