algorithms

A step-by-step procedure that transforms input into output in a finite number of operations. The foundation of all computation.

complexity

Big-O notation measures how an algorithm’s time or space grows with input size. Common classes: O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n) linearithmic, O(n^2) quadratic, O(2^n) exponential. Closely tied to complexity theory.

core families

• sorting: bubble, merge, quick, heap — ordering elements by key
• searching: binary search, depth-first, breadth-first
• graph algorithms: Dijkstra, A*, Bellman-Ford — pathfinding over data structures like graphs
• dynamic programming: breaking problems into overlapping subproblems, memoization
• greedy: locally optimal choices at each step
• divide and conquer: recursively splitting the problem, then merging solutions

relation to machines

An algorithm is independent of hardware. Its abstract form lives in automata theory; its concrete execution depends on compilers and operating systems.