[Verse 1] Picture your suitcase, weight limit tight Every item's got value, gotta choose what's right Zero-one knapsack means take it or leave Can't split your grandmother's vintage TV Dynamic programming builds a grid so clean Rows are items, columns show the weight scene Each cell holds maximum value you can pack With that weight limit, no turning back [Chorus] Knapsack riddle, optimize the middle Value over weight, don't second-fiddle Zero-one or boundless, choices all around us DP table saves us, memory matrix claims us Max value, best weight, algorithm fate Knapsack riddle, optimize the middle [Verse 2] Recurrence relation breaks the spell If weight's too heavy, copy cell above, oh well If it fits inside, now here's the test Take it plus remainder or leave it, which is best Bottom-up approach fills every square Time complexity quadratic, handle with care Space is items times capacity bound Optimal substructure, treasure you've found [Chorus] Knapsack riddle, optimize the middle Value over weight, don't second-fiddle Zero-one or boundless, choices all around us DP table saves us, memory matrix claims us Max value, best weight, algorithm fate Knapsack riddle, optimize the middle [Verse 3] Unbounded version changes the game completely Same item multiple times, select so sweetly No quantity limits, infinite supply Coin change problems, same logic applies Inner loop goes forward, not reverse direction Previous calculations need protection One-dimensional array suffices here Space optimization crystal clear [Bridge] Backtrack the solution, trace your steps Which items made it past the checkpoint checks Start from bottom-right corner cell Follow the breadcrumbs, story to tell Practical applications everywhere you look Cargo loading, budget planning by the book Resource allocation, scheduling tasks Knapsack algorithm answers what it asks [Outro] From knapsack to the moon, optimization's tune DP memorization, computational salvation Zero-one or boundless, maximal value found Knapsack riddle solved, algorithm renowned
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