classmateswhat does this say about the difficulty of doing empirical timing studies perform study of shellsortusing different increments compare the version shown in section where each increment is half the previous onewith others in particulartry implementing "division by where the increments on list of length will be / / etc do other increment schemes work as well the implementation for mergesort given in section takes an array as input and sorts that array at the beginning of section there is simple pseudocode implementation for sorting linked list using mergesort implement both linked list-based version of mergesort and the array-based version of mergesortand compare their running times radix sort is typically implemented to support only radix that is power of two this allows for direct conversion from the radix to some number of bits in an integer key value for exampleif the radix is then -bit key will be processed in steps of bits each this can lead to more efficient implementation because bit shifting can replace the division operations shown in the implementation of section re-implement the radix sort code given in section to use bit shifting in place of division compare the running time of the old and new radix sort implementations it has been proposed that heapsort can be optimized by altering the heap' siftdown function call the value being sifted down siftdown does two comparisons per levelfirst the children of are comparedthen the winner is compared to if is too smallit is swapped with its larger child and the process repeated the proposed optimization dispenses with the test against insteadthe larger child automatically replaces xuntil reaches the bottom level of the heap at this pointx might be too large to remain in that position this is corrected by repeatedly comparing with its parent and swapping as necessary to "bubbleit up to its proper level the claim is that this process will save number of comparisons because most nodes when sifted down end up near the bottom of the tree anyway implement both versions of siftdownand do an empirical study to compare their running times