Nothing special here. It’s just a blog post for summarising my algorithm learning course. Although this was already taught in the University, I remember nothing about it because I haven’t touched it for the long time.

# Quick Sort - Duplicate Keys Problem

• Quick Sort goes quadratic unless partitioning stops on equal keys!
• ~½N2 compares when all keys equal.
• B A A B A B B B C C C
• A A A A A A A A A A A
• Solve by using 3-way partitioning

# 3-way Partitioning

Partition array into 3 parts so that:

• Entries between lt and gt equal to partition item v
• No larger entries to left of lt
• No smaller entries to right of gt • Let v be partitioning item a[lo]
• Scan i from left to right.
• (a[i] < v): exchange a[lt] with a[i]; increment both lt and i
• (a[i] > v): exchange a[gt] with a[i]; decrement gt
• (a[i] == v): increment i

# Java Implementation

private static void sort(Comparable[] a, int lo, int hi) {
if (hi <= lo) return;
int lt = lo, gt = hi;
Comparable v = a[lo];
int i = lo;
while (i <= gt)
{
int cmp = a[i].compareTo(v);
if (cmp < 0) exch(a, lt++, i++);
else if (cmp > 0) exch(a, i, gt--);
else i++;
}
sort(a, lo, lt - 1);
sort(a, gt + 1, hi);
} Quick Sort with 3-way partitioning is even shorter (and harder to imagine). I gave one compliment to the brain that could thought of those above solutions.