How does the stooge sort algorithm work?

The Stooge Sort algorithm is a recursive sorting algorithm that works by dividing the array into thirds and recursively sorting them.

Stooge Sort is a relatively inefficient sorting algorithm, with a time complexity of O(n^2.7095...), making it less practical for large data sets. However, it's a good example of a recursive sorting algorithm and can be useful for teaching purposes.

The algorithm begins by dividing the array into three equal parts. If the array cannot be divided equally into three, the middle part overlaps with the first and last part. The algorithm then recursively sorts the first two-thirds of the array, followed by the last two-thirds, and finally, it sorts the first two-thirds again. This process is repeated until the array is fully sorted.

Here's a step-by-step breakdown of how the Stooge Sort algorithm works:

1. If the value at the start of the array is greater than the value at the end, swap them.
2. If there are 3 or more elements in the array, then:
a. Calculate one third of the array size, let's call this 'm'.
b. Recursively Stooge Sort the first 2/3 of the array (from index 0 to index 2m).
c. Recursively Stooge Sort the last 2/3 of the array (from index m to end).
d. Recursively Stooge Sort the first 2/3 of the array again (from index 0 to index 2m).

The algorithm continues to divide the array into thirds and sort them until the entire array is sorted. Despite its inefficiency, the Stooge Sort algorithm is a good example of a divide and conquer strategy in computer science. It's also a fun and interesting way to explore recursion, a fundamental concept in computer science.