Consider the following modification to Algorithm MERGESORT. We apply the algorithm on the input array A[1..n]...

 

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Consider the following modification to Algorithm MERGESORT. We apply the algorithm on the input array A[1..n] and continue the recursive calls until the size of a subinstance becomes relatively small, say m or less. At this point, we switch to Algorithm INSERTIONSORT and apply it on the small instance. So, the first test of the modified algorithm will look like the following: if high-low +1m then INSERTIONSORT (A[low..high]). What is the largest value of m in terms of n such that the running time of the modified algorithm will still be O(nlogn)? You may assume for simplicity that n is a power of 2. Consider the following modification to Algorithm MERGESORT. We apply the algorithm on the input array A[1..n] and continue the recursive calls until the size of a subinstance becomes relatively small, say m or less. At this point, we switch to Algorithm INSERTIONSORT and apply it on the small instance. So, the first test of the modified algorithm will look like the following: if high-low +1m then INSERTIONSORT (A[low..high]). What is the largest value of m in terms of n such that the running time of the modified algorithm will still be O(nlogn)? You may assume for simplicity that n is a power of 2.