Ignore small subarrays. Run experiments to compare the following strategy for dealing with small subarrays with the approach described in Exercise Simply ignore the small subarrays in quicksort, then run a single insertion sort after the quicksort completes. Note : You may be able to estimate the size of your computer’s cache memory with these experiments, as the performance of this method is likely to degrade when the array does not fit in the cache.
Exercise
Cutoff to insertion sort. Implement quicksort with a cutoff to insertion sort for subarrays with less than M elements, and empirically determine the value of M for which quicksort runs fastest in your computing environment to sort random arrays of N doubles, for N = 103, 104, 105, and 106. Plot average running times for M from 0 to 30 for each value of M. Note : You need to add a three-argument sort() method to algorithm 2.2 for sorting subarrays such that the call Insertion.sort(a, lo, hi) sorts the subarray a[1o..hi].
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