Knapsack, Fractional Knapsack, Coin Change - Batch 1

What is the main objective of the 0/1 Knapsack problem?

• Minimize the weight of the knapsack

• Maximize the value of items in the knapsack

• Minimize the number of items in the knapsack

• Maximize the weight of items in the knapsack

Answer explanation

The main objective of the 0/1 Knapsack problem is to maximize the value of items in the knapsack.

In the 0/1 Knapsack problem, if the capacity of the knapsack is C and there are n items, what is the time complexity of the dynamic programming solution?

• O(n * C)

• O(n^2)

• O(C)

• O(n * log(C))

Answer explanation

The time complexity of the dynamic programming solution for the 0/1 Knapsack problem is O(n * C), where n is the number of items and C is the capacity of the knapsack.

Which of the following problems is suitable for the 0/1 Knapsack dynamic programming approach?

• Selecting items to maximize profit with a weight limit

• Selecting items to minimize cost without a weight limit

• Selecting items to maximize profit with no weight limit

• Selecting items to minimize profit with a weight limit

Answer explanation

Selecting items to maximize profit with a weight limit is suitable for the 0/1 Knapsack dynamic programming approach.

In the Fractional Knapsack problem, what is the strategy to maximize the value of the knapsack?

• Always include the item with the highest weight

• Always include the item with the highest value

• Include items based on the highest value-to-weight ratio

• Include items based on the lowest value-to-weight ratio

Answer explanation

Include items based on the highest value-to-weight ratio

Which algorithm is commonly used to solve the Fractional Knapsack problem?

• Dynamic Programming

• Greedy Algorithm

• Divide and Conquer

• Backtracking

Answer explanation

The Fractional Knapsack problem is commonly solved using the Greedy Algorithm.

If you are allowed to take fractions of items in the Fractional Knapsack problem, what is the time complexity of the greedy solution?

• O(n * log(n))

• O(n^2)

• O(n * C)

• O(n)

Answer explanation

The correct choice is O(n * log(n)) because sorting the items based on their value-to-weight ratio takes O(n * log(n)) time in the greedy solution.

In the Coin Change problem, what is the objective when given a set of coin denominations and a total amount?

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Answer explanation

The objective is to find the minimum number of coins needed to make up the total amount using the given denominations.

What is the time complexity of the dynamic programming solution for the Coin Change problem where n is the number of coin denominations and amount is the total amount?

• O(n * amount)

• O(n^2)

• O(amount^2)

• O(n + amount)

Answer explanation

The time complexity of the dynamic programming solution for the Coin Change problem is O(n * amount) where n is the number of coin denominations and amount is the total amount.

Which of the following approaches is not suitable for solving the Coin Change problem efficiently?

• Greedy Algorithm

• Dynamic Programming

• Recursive Approach

• Brute Force

Answer explanation

The Recursive Approach is not suitable for solving the Coin Change problem efficiently because it can lead to redundant calculations and exponential time complexity.

What is the key factor to consider in the Fractional Knapsack problem to maximize the value of the knapsack?

• Weight of the items

• Value of the items

• Weight-to-value ratio of the items

• Number of items

Answer explanation

Weight-to-value ratio of the items is the key factor to consider in the Fractional Knapsack problem to maximize the value of the knapsack.