[Verse 1] Started with a problem, need to solve it right Big O notation, that's my guiding light Linear time means one pass through the data Quadratic loops got me working much harder Hash tables hit constant time access Arrays indexed fast, no need to stress When I'm coding up solutions, gotta think it through Time complexity tells me what my algorithm's gonna do [Chorus] Big O, Big O, how fast will it go Linear log linear quadratic you know Space and time, space and time Optimize the code, make the runtime shine Implementation, got to get it right Memory usage, keep it tight Analyze before you write, analyze before you write [Verse 2] Binary search cuts the problem in half Logarithmic time, do the math Merge sort's divide and conquer style N log N runtime, worth the while Bubble sort's quadratic, that's too slow When the input grows, watch the runtime blow Cache locality matters when you're moving data Sequential access keeps the processor happier [Chorus] Big O, Big O, how fast will it go Linear log linear quadratic you know Space and time, space and time Optimize the code, make the runtime shine Implementation, got to get it right Memory usage, keep it tight Analyze before you write, analyze before you write [Bridge] Worst case average case best case too Amortized analysis tells you what to do Trade-offs everywhere between space and speed Dynamic programming for what you need Recursion's elegant but watch that stack Iteration's safer, got your back [Verse 3] Linked lists traverse in linear time Random access costs, that's the crime Trees can balance, keep height low AVL rotations, make it flow Graph algorithms, BFS and DFS Shortest path problems, Dijkstra's the best Choose your structure, match the use case Time complexity, that's the ace [Chorus] Big O, Big O, how fast will it go Linear log linear quadratic you know Space and time, space and time Optimize the code, make the runtime shine Implementation, got to get it right Memory usage, keep it tight Analyze before you write, analyze before you write [Outro] From constant time to exponential growth Understand the math, that's the oath Implementation's art, complexity's science Code with confidence, math compliance
← Dijkstra vs Other Path-Finding Algorithms | Bellman-Ford algorithm →