[Verse 1] Started with recursion, but the stack was bleeding slow Same calculations running everywhere I go Fibonacci sequence got me trapped inside a loop Calculate the same damn numbers, watch performance droop Cache becomes my savior, dictionary in my hand Store results forever, make this algorithm grand First call hits the function, checks if we computed yet If it's in our lookup table, grab the value, place your bet [Chorus] Memo-ize, memo-ize, cache what you calculate Store the past, make it last, optimization fate Base case zero, base case one, foundation stones are laid Build the tower from below, let the memory cascade Memo-ize, memo-ize, trade your space for speed Dynamic programming flow, efficiency guaranteed [Verse 2] Initialize the storage, dictionary starts empty Check the key existence before we go and tempt thee If the value's sitting there, return without delay Otherwise compute it fresh, then tuck the result away Recursive calls still happen, but only once per number Previous calculations sleep, no need to wake their slumber Linear time complexity, exponential death is gone Memoization transformation got the algorithm strong [Chorus] Memo-ize, memo-ize, cache what you calculate Store the past, make it last, optimization fate Base case zero, base case one, foundation stones are laid Build the tower from below, let the memory cascade Memo-ize, memo-ize, trade your space for speed Dynamic programming flow, efficiency guaranteed [Bridge] From exponential nightmare to linear progression clean Memory consumption grows but computation's lean Top-down approach with storage, recursive elegance preserved Bottom-up alternative but this keeps structure served [Outro] Cache the calculations, let the memory do its dance Fibonacci memoized, giving algorithms a chance Dictionary holds the answers, lookup faster than the wind Optimization mastery, let the learning now begin
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