When implementing quicksort, if the array contains lots of duplicates, it maybe better
Chapter 7, Problem 7.28(choose chapter or problem)
When implementing quicksort, if the array contains lots of duplicates, it maybe better to perform a three-way partition (into elements less than, equal to,and greater than the pivot), to make smaller recursive calls. Assume three-waycomparisons, as provided by the compareTo method.a. Give an algorithm that performs a three-way in-place partition of an N-elementsubarray using only N 1 three-way comparisons. If there are d items equalto the pivot, you may use d additional Comparable swaps, above and beyond the two-way partitioning algorithm. (Hint: As i and j move toward each other,maintain five groups of elements as shown below):EQUAL SMALL UNKNOWN LARGE EQUALi jb. Prove that using the algorithm above, sorting an N-element array that containsonly d different values, takes O(dN) time.
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