median of three values strategy

Question

What is the median of three strategy to select the pivot value in quick sort?

I am reading it on the web, but I couldn\'t figure it out what exactly it is? And also

Answer 1

Think faster... C example....

int medianThree(int a, int b, int c) {
    if ((a > b) != (a > c)) 
        return a;
    else if ((b > a) != (b > c)) 
        return b;
    else
        return c;
}

This uses XOR like operator. So you would read:

• Is a greater than exclusively one of the others? return a
• Is b greater than exclusively one of the others? return b
• If none of above: return c

The median approach is faster because it would lead to more evenly partitioning in array, since the partitioning is based on the pivot value.

In the worst case scenario with a random pick or a fixed pick you would partition every array into an array containing just the pivot and another array with the rest, leading to an O(n²) complexity.

Using the median approach you make sure that won't happen, but instead you are introducing an overhead for calculating the median.

EDIT:

Benchmarks results show XOR is 32 times faster than Bigger even though I optimized Bigger a little:

You need to recall that XOR is actually a very basic operator of the CPU's Arithmetic Logic Unit (ALU), then although in C it may seen a bit hacky, under the hood it is compiling to the very efficient XOR assembly operator.