Tukey’s ninther. Add to your implementation from exercise code to use the Tukey ninther to...

Tukey’s ninther. Add to your implementation from exercise code to use the Tukey ninther to compute the partitioning item—choose three sets of three items, take the median of each, then use the median of the three medians as the partitioning item. Also, add a cutoff to insertion sort for small subarrays.

Exercise

Fast 3-way partitioning. (J. Bentley and D. Mcllroy) Implement an entropy-optimal sort based on keeping items with equal keys at both the left and right ends of the subarray. Maintain indices p and q such that a[1o..p-1] and a[q+1..hi] are all equal to a[1o], an index i such that a[p..i-1] are all less than a[1o], and an index j such that a[j+1..q] are all greater than a[1o]. Add to the inner partitioning loop code to swap a[i] with a[p] (and increment p) if it is equal to v and to swap a[j] with a[q] (and decrement q) if it is equal to v before the usual comparisons of a[i] and a[j] with v. After the partitioning loop has terminated, add code to swap the items with equal keys into position. Note : This code complements the code given in the

text, in the sense that it does extra swaps for keys equal to the partitioning item’s key, while the code in the text does extra swaps for keys that are not equal to the partitioning item’s key.