Algorithms and program structure

An algorithm is a recipe: a finite sequence of unambiguous steps that turns input into output and is guaranteed to stop. A program is one expression of an algorithm, written in a particular language for a particular machine. The distinction matters because the hard thinking happens at the algorithm level — deciding what steps solve the problem — while the program is the translation. The same sorting algorithm exists in Python, C and pseudocode, and learning the algorithm transfers while learning one language's syntax largely does not.

Programs are built from a small number of constructs, and the count is genuinely small: a value, a variable to hold it, a way to choose between paths, a way to repeat, and a way to name a block of steps so it can be reused. Everything else is convenience. This is why the syllabus of a first programming course reads expressions, conditionals, functions, loops — that really is the whole vocabulary.

The construct that reliably confuses is the variable. In mathematics, x = x + 1 is a contradiction. In a program it is an instruction: evaluate the right-hand side, then store the result in the box named on the left. A variable is a named storage location whose contents change over time, not an unknown to be solved for. The second thing worth internalising early is that running is not the same as working. A program with a logic error executes happily and produces confident nonsense, so testing against known answers — not the absence of an error message — is what establishes correctness.