Algorithms flashcards, generated for you.

A step-by-step procedure to solve a problem or compute a result, with a defined input and output.

The number of basic operations an algorithm performs relative to input size n, expressed using Big O notation.

The amount of additional memory an algorithm uses relative to input size n, excluding input storage.

Big O abstracts away constants and lower-order terms, revealing how runtime scales as input grows, making algorithms comparable across machines.

Algorithms often optimize for speed by using extra memory (caching, memoization) or minimize memory at the cost of repeated computation.

A greedy algorithm makes locally optimal choices at each step. It works only when the problem has optimal substructure and the greedy choice property (local optimality leads to global optimality).

Divide-and-conquer breaks problems into independent subproblems (no overlap); dynamic programming optimizes overlapping subproblems via memoization or tabulation.

Stable sort preserves the relative order of equal elements; unstable does not. Stability matters when sorting by multiple keys or maintaining original ordering context.

Merge sort: O(n log n) worst-case, stable, requires O(n) extra space. Quicksort: O(n log n) average, O(n²) worst-case, in-place, faster in practice. Choose based on whether you need guaranteed time or space efficiency.

NP-complete problems have no known polynomial-time solution; if one is found, all are solvable in polynomial time. For large instances, use approximation, heuristics, or constraint-based solutions rather than exhaustive search.