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Given a Fractional knapsack problem, the preferred way of solution strategy will be1 pointBrute ForceDynamicGreedyAny one of these

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Given a Fractional knapsack problem, the preferred way of solution strategy will be1 pointBrute ForceDynamicGreedyAny one of these

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Solution 1

The preferred way of solving a Fractional Knapsack problem is using the Greedy strategy.

Here's a step-by-step guide on how to solve it:

  1. First, calculate the ratio (value/weight) for each item in the knapsack.

  2. Sort all items based on their ratios in decreasing order. This means the item with the highest ratio should be considered first.

  3. Start picking items from the sorted list, starting from the first item. Keep adding as much of each item as possible until the total weight does not exceed the capacity of the knapsack.

  4. If adding the entire item exceeds the capacity, add a fraction of it so that the total weight equals the capacity of the knapsack.

  5. The total value of items in the knapsack is the solution to the problem.

This strategy works because the Greedy approach aims to make the optimal choice at each step as it attempts to find the overall optimal solution to the problem. In the Fractional Knapsack problem, the Greedy strategy provides an optimal solution.

This problem has been solved

Solution 2

The preferred way of solving a Fractional Knapsack problem is using the Greedy strategy.

Here's a step-by-step guide on how to solve it:

  1. First, calculate the ratio (value/weight) for each item in the knapsack.

  2. Sort all items based on their ratios in decreasing order. This means the item with the highest ratio should be considered first.

  3. Start picking items from the sorted list, starting from the first item. Keep adding them to the knapsack until there's no more room.

  4. If an item is too large to fit entirely into the knapsack, take as much as possible. This is possible because we're dealing with a fractional knapsack problem, which allows us to take fractions of items, not just whole items.

  5. The total value of items in the knapsack at the end is the maximum possible value we can get.

This strategy is called a Greedy strategy because we're always making the choice that seems best at the moment, i.e., picking the item with the highest value-to-weight ratio first.

This problem has been solved

Solution 3

The preferred way of solving a Fractional Knapsack problem is using the Greedy strategy.

Here's a step-by-step guide on how to solve it:

  1. First, calculate the ratio (value/weight) for each item in the knapsack.

  2. Sort all items by this ratio in decreasing order.

  3. Start picking items from the sorted list, starting from the item with the highest ratio.

  4. Continue picking items until you've either run out of items or the knapsack is full.

  5. If the knapsack is full before you've run out of items, and the next item in the list doesn't fit entirely, take as much of it as you can.

This strategy works because the Greedy approach aims to make the optimal choice at each step as it attempts to find the overall optimal solution. In the Fractional Knapsack problem, the Greedy strategy provides an optimal solution.

This problem has been solved

Solution 4

The preferred way of solving a Fractional Knapsack problem is by using a Greedy strategy.

Here's a step-by-step guide on how to solve it:

  1. First, calculate the ratio of values to weight for each item. This ratio is called 'value per unit weight'.

  2. Sort all items based on this ratio in decreasing order. This sorting is the key to the greedy approach used in this problem.

  3. Start taking items from the sorted list, starting from the item with the highest ratio. Keep adding items until you can't add the next item without exceeding the total weight capacity of the knapsack.

  4. If adding the next item exceeds the weight capacity, take a fraction of the item such that the total weight becomes exactly equal to the weight capacity.

  5. The maximum total value that can be accommodated in the knapsack is the sum of the values of items included in the knapsack.

This greedy approach ensures that we get the maximum total value in the knapsack.

This problem has been solved

Solution 5

The preferred way of solving a Fractional Knapsack problem is using the Greedy strategy.

Here's a step-by-step guide on how to solve it:

  1. First, calculate the ratio (value/weight) for each item in the knapsack.

  2. Sort all items based on their ratios in decreasing order. This means the item with the highest ratio should be considered first.

  3. Start picking items from the sorted list, starting from the first item. Keep adding them to the knapsack as long as the total weight doesn't exceed the capacity of the knapsack.

  4. If adding the next item completely would exceed the capacity, then add a fraction of it such that the knapsack becomes full.

  5. The total value of items in the knapsack is the solution to the problem.

This strategy works best for the Fractional Knapsack problem because it ensures that you're always choosing the item with the highest value-to-weight ratio, which leads to the optimal solution.

This problem has been solved

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