Q. What is the space complexity of the naive method used to find the maximum sub-array sum in an array containing n elements?

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Q. What is the time complexity of the divide and conquer algorithm used to find the maximum sub-array sum?

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Q. What is the space complexity of the divide and conquer algorithm used to find the maximum sub-array sum?

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Q. Find the maximum sub-array sum for the following array:
{3, 6, 7, 9, 3, 8}

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Q. Kadane’s algorithm is used to find ____________

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Q. Kadane’s algorithm uses which of the following techniques?

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Q. For which of the following inputs would Kadane’s algorithm produce the CORRECT output?

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Q. For which of the following inputs would Kadane’s algorithm produce a WRONG output?

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Q. What is the time complexity of Kadane’s algorithm?

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Q. What is the space complexity of Kadane’s algorithm?

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Q. The longest increasing subsequence problem is a problem to find the length of a subsequence from a sequence of array elements such that the subsequence is sorted in increasing order and it’s length is maximum. This problem can be solved using __________

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Q. Find the longest increasing subsequence for the given sequence:
{10, -10, 12, 9, 10, 15, 13, 14}

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Q. Find the length of the longest increasing subsequence for the given sequence:
{-10, 24, -9, 35, -21, 55, -41, 76, 84}

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Q. For any given sequence, there will ALWAYS be a unique increasing subsequence with the longest length.

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Q. The number of increasing subsequences with the longest length for the given sequence are:
{10, 9, 8, 7, 6, 5}

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Q. In the brute force implementation to find the longest increasing subsequence, all the subsequences of a given sequence are found. All the increasing subsequences are then selected and the length of the longest subsequence is found. What is the time complexity of this brute force implementation?

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Q. Given a rod of length n and the selling prices of all pieces smaller than equal to n, find the most beneficial way of cutting the rod into smaller pieces. This problem is called the rod cutting problem. Which of these methods can be used to solve the rod cutting problem?

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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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