Q. You are given a rod of length 5 and the prices of each length are as follows:
length price

1 2

2 5

3 6

4 9

5 9

What is the maximum value that you can get after cutting the rod and selling the pieces?

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Q. Consider the brute force implementation of the rod cutting problem in which all the possible cuts are found and the maximum value is calculated. What is the time complexity of this brute force implementation?

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Q. You are given a rod of length 10 and the following prices.
length price

1 2

2 5

3 6

4 9

5 9

6 17

7 17

8 18

9 20

10 22

Which of these pieces give the maximum price?

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Q. For every rod cutting problem there will be a unique set of pieces that give the maximum price.

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Q. You are given an array of elements where each array element represents the MAXIMUM number of jumps that can be made in the forward direction from that element. You have to find the minimum number of jumps that are required to reach the end of the array. Which of these methods can be used to solve the problem?

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Q. Consider the following array:
{1, 3, 5, 8, 9, 2, 6, 7, 6}

What is the minimum number of jumps required to reach the end of the array?

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Q. For a given array, there can be multiple ways to reach the end of the array using minimum number of jumps.

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Q. For any array, given that at most one element is non-zero, it is ALWAYS possible to reach the end of the array using minimum jumps.

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Q. The Knapsack problem is an example of ____________

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Q. Which of the following methods can be used to solve the Knapsack problem?

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Q. You are given a knapsack that can carry a maximum weight of 60. There are 4 items with weights {20, 30, 40, 70} and values {70, 80, 90, 200}. What is the maximum value of the items you can carry using the knapsack?

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Q. Which of the following problems is equivalent to the 0-1 Knapsack problem?

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Q. What is the time complexity of the brute force algorithm used to solve the Knapsack problem?

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Q. The 0-1 Knapsack problem can be solved using Greedy algorithm.

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Q. Which of the following methods can be used to solve the matrix chain multiplication problem?

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Q. Which of the following is the recurrence relation for the matrix chain multiplication problem where mat[i-1] * mat[i] gives the dimension of the ith matrix?

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Q. Consider the two matrices P and Q which are 10 x 20 and 20 x 30 matrices respectively. What is the number of multiplications required to multiply the two matrices?

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Q. Consider the matrices P, Q and R which are 10 x 20, 20 x 30 and 30 x 40 matrices respectively. What is the minimum number of multiplications required to multiply the three matrices?

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Q. Consider the matrices P, Q, R and S which are 20 x 15, 15 x 30, 30 x 5 and 5 x 40 matrices respectively. What is the minimum number of multiplications required to multiply the four matrices?

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Q. Consider the brute force implementation in which we find all the possible ways of multiplying the given set of n matrices. What is the time complexity of this implementation?

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