Develop a merge implementation that reduces the extra space requirement to max(M, N/M), based on the following idea: Divide the array into N/M blocks of size M (for simplicity in this description, assume that N is a multiple of M). Then, (i) considering the blocks as items with their first key as the sort key, sort them using selection sort; and (ii) run through the array merging the first block with the second, then the second block with the third, and so forth.

Consider a hallway in a building, with N equally sized rooms, numbered 1,..., N. Several meetings are planned, which require different numbers of adjacent rooms. You are given a list of meeting requests with the number of rooms need for each. The requests are represented by the array r[1, ..., k]. For example, meeting j requires r[j] adjacent rooms. You are offered a programmatic tool, which requires n steps to partition a set of n rooms, to accommodate two meeting requests of sizes s1 and s2, where s1+s2 = N.  Describe an algorithm that receives a set of meeting requests s1, s2, ..., etc., and calculates the rooms allocations in the least number of steps. Formally prove that the algorithm is correct and that the solution it provides requires the lowest cost (in computational steps). Explain your solution with a concrete example. There was a similar question, but I did not understand the answer the expert gave.  It had almost no details, and I could not follow it.

Given two sorted arrays of distinct elements. There is only 1 difference between the arrays. First array has one element extra added in between. Find the index of the extra element. Example 1: Input: N = 7 A[] {2,4,6,8,9,10,12} = B[] = {2,4,6,8,10,12} Output: 4 Explanation: In the second array, 9 is missing and it's index in the first array is 4.

Write a bottom-up mergesort that makes use of the array's order by carrying out the following steps each time it needs to locate two arrays to merge: locate the first element in an array that is smaller than its predecessor, then locate the next, and finally merge them to form a sorted subarray. Consider the array size and the number of maximal ascending sequences in the array while analysing the running time of this method.