Explain the difference between the 0/1 Knapsack Problem and the Fractional Knapsack Problem.
- In the 0/1 Knapsack Problem, items cannot be broken down; they must be taken either entirely or not at all, whereas in the Fractional Knapsack Problem, items can be broken down into fractions, allowing for a more flexible approach to selecting items.
- The 0/1 Knapsack Problem allows for items to be repeated multiple times in the knapsack, whereas the Fractional Knapsack Problem does not allow repetition of items.
- The 0/1 Knapsack Problem involves selecting items to maximize value without exceeding the weight capacity of the knapsack, whereas the Fractional Knapsack Problem involves selecting fractions of items to maximize value, with no weight constraint.
- The 0/1 Knapsack Problem is solved using dynamic programming, whereas the Fractional Knapsack Problem is solved using greedy algorithms.
The main difference between the 0/1 Knapsack Problem and the Fractional Knapsack Problem lies in the treatment of items. In the 0/1 Knapsack Problem, items cannot be broken down, whereas in the Fractional Knapsack Problem, items can be divided into fractions, allowing for a more flexible approach to selecting items based on their value-to-weight ratio.
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