Given an array A[0 : n−1] of n integers, compute the maximum sum of non-empty consecutive subsequence present in the array. For example, if the input is A = [3, 2, 5, 1, 6], then the output max sum is 17 (the corresponding maximum sum consecutive subsequence is [3, 2, 5, 1, 6]. If the input is A = [−2, 11, −4, 13, −5, −2], then the output max sum is 20 (the corresponding maximum sum consecutive subsequence is [11, −4, 13]. (a) Given input A[0 : n − 1] and n, design a divide-and-conquer algorithm which outputs the maximum sum of non-empty consecutive subsequence in the array. You only need to output the sum value and do not need to output the exact subsequence. [We are expecting a brief justification for the intuitive idea of the algorithm and the pseudocode of the algorithm.] (b) Let T(n) be the runtime of your algorithm when the input size is n. Establish the recurrence relation of T(n) for your algorithm, and then solve the recurrence relation to provide the big-O runtime of your algorithm. [You can use any method to solve the recurrence relation.]
Given an array A[0 : n−1] of n integers, compute the maximum sum of non-empty consecutive subsequence present in the array.
For example, if the input is A = [3, 2, 5, 1, 6], then the output max sum is 17 (the corresponding maximum sum consecutive subsequence is [3, 2, 5, 1, 6]. If the input is A = [−2, 11, −4, 13, −5, −2], then the output max sum is 20 (the corresponding maximum sum consecutive subsequence is [11, −4, 13].
(a) Given input A[0 : n − 1] and n, design a divide-and-conquer
(b) Let T(n) be the runtime of your algorithm when the input size is n. Establish the recurrence relation of T(n) for your algorithm, and then solve the recurrence relation to provide the big-O runtime of your algorithm. [You can use
any method to solve the recurrence relation.]
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