Q. Given a one-dimensional array of integers, you have to find a sub-array with maximum sum. This is the maximum sub-array sum problem. Which of these methods can be used to solve the problem?

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Q. Find the maximum sub-array sum for the given elements.
{2, -1, 3, -4, 1, -2, -1, 5, -4}

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Q. Find the maximum sub-array sum for the given elements.
{-2, -1, -3, -4, -1, -2, -1, -5, -4}

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Q. What is the time 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 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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