What is the recurrence for the maximum subarray problem and why?
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In class we discussed an approach that yields a Θ(n) algorithm for solving the maximum subarray problem. This approach incrementally calculates the maximum subarray for A[1..j] that uses A[j], and then uses that value to calculate the maximum subarray for A[1..j+1] that uses A[j+1]. The answer is the maximum of all those n calculated values. Write pseudocode for a version of this algorithm that instead works from the right side of the array to the left. That is, it calculates...
Implement the maximum-subarray problem using brute-force approach taking Θ(n2)Θ(n2) time.
Give an algorithm that finds the maximum size subarray that is increas- ing (the entries may not be contiguous. It may be any set but you need to keep the order.). In the above array the maximum non contiguous increasing subset is 1, 2, 4, 6, 8, 9, 14, 16, 30 that forms an increasing sequence. There are no other array provided in this question, thank you
How to design an algorithm using recursion to find number of subarray contains all 0 in an array which only contains 0 or 1? For example, we have array 00, so we return 1, if we have an array 0100, we return 2. Assume the size of array >=1. How to find the recurrence relation of the algorithm? And how to express the recurrence relation as a function of n.
Convert the pseudocode into a C++ function Decrease-by-Half Algorithm We can solve the same problem using a decrease-by-half algorithm. This algorithm is based on the following ideas: In the base case, n 1 and the only possible solution is b 0, e 1 In the general case, divide V into a left and rnight half; then the maximum subarray can be in one of three places: o entirely in the left half; o entirely in the right half; or o...
explain why the recurrence relation for number of ternary strings of length n contains "01" 7. (10 points) Extra credit: Explain why the recurrence relation for number of ternary strings of length n that contain "01" is bn = 3n-1-bn-2 +31-2?
Assume a modification of the divide-and-conquer solution in which the Find-Max-Crossing-Subarray call is always omitted. Provide the most basic example array for which the modified algorithm would fail. Explain why it fails.
What does it mean to solve a recurrence relation? Solve the recurrence relation a_n = 2na_n-1 where a_o = 1.
Rod-cutting problem Design a dynamic programming algorithm for the following problem. Find the maximum total sale price that can be obtained by cutting a rod of n units long into integer-length pieces if the sale price of a piece i units long is pi for i = 1, 2, . . . , n. What are the time and space efficiencies of your algorithm? Code or pseudocode is not needed. Just need theoretical explanation with dynamic programming with recurrence relation...
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