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Design a divide and conquer algorithm that takes as input

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Case Study: Brito's youngest kid is learning the natural numbers. To practice, he writes a list of natural numbers, starting from the number 1. In doing so, he repeats exactly one, resulting in a list A of N numbers, such that there is exactly one repeated, and A is non decreasingly sorted. Help Brito figure out which number is repeated.

Question 1: Design a divide and conquer algorithm that takes as input a sorted array A, of length N, containing all the integers from 1 to N-1 exactly once, except for one which appears twice. Your algorithm should find the value of the only repeated element.

Question 2: Describe your algorithm in words (no pseudocode!) and justify its correctness. State and justify its runtime. Faster (and correct) in asymptotic Big O notation is worth more credit.

 

Reference no: EM133557343

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