Explore the cosmos of optimization! Master Fractional, 0/1, and Unbounded Knapsack problems through an interstellar adventure.
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Greedy (sorting by value/weight ratio) works perfectly for Fractional Knapsackbecause we can take partial items. But for 0/1 Knapsack, greedy can fail! Example: items with weights [10, 20, 30] and values [60, 100, 120] with capacity 50. Greedy takes item 1 (ratio 6.0) leaving no room for better combinations, while DP finds items 2+3 = 220 value!