Let a[0 . . n] be an array of n + 1 natural numbers not exceeding n. let k < n be an integer such that the values of any two successive entries of a differ at most by k, i. e., |a[j] − a[j + 1]| ≤ k for all j ∈ {0, . . , n − 1}. 1. prove that there exist an index j such that |a[j] − j| ≤ (k + 1)/2. 2. given the number k, find an o(log n) divide and conquer algorithm that finds such an index.

Type the correct answer in each box. use numerals instead of words. the average number of subscribers to an online magazine each year from 2010 to 2015 is given in the table below. the average number of subscribers to the online magazine in 2010 was the percent increase in the average number of subscribers in 2011 to the average number of subscribers in 2012 was %. the maximum average number of subscribers to the online magazine in the years shown was