How does the pancake sort algorithm function?

The pancake sort algorithm sorts a list by repeatedly flipping sections of it to move elements into their correct positions.

The pancake sort algorithm is a comparison sort that uses a unique approach to sort a list of elements. It's named after the process of sorting a stack of pancakes in order of size using a spatula, where the spatula can be inserted at any point in the stack and used to flip all pancakes above it. Similarly, in the pancake sort algorithm, we can 'flip' any prefix of the array.

The algorithm begins by finding the maximum element in the list and flipping the section of the list from the start to this element. This brings the maximum element to the front of the list. The entire list is then flipped, moving the maximum element to its correct position at the end of the list. This process is repeated for the rest of the list, excluding the last element each time as it is already in its correct position.

For example, consider the list [3, 1, 4, 1]. The maximum element is 4, so we flip the first three elements to get [4, 1, 3, 1]. Then we flip the entire list to get [1, 3, 1, 4]. Now the maximum element is in its correct position. We repeat this process for the rest of the list, excluding the last element each time.

The pancake sort algorithm is not often used in practice as it is less efficient than other sorting algorithms. Its time complexity is O(n²), which means it takes considerably longer to sort large lists compared to algorithms like quicksort or mergesort. However, it is a fun and interesting algorithm that demonstrates a different approach to sorting. It's also a great way to understand the concept of in-place sorting, as it only requires a small, constant amount of extra space to perform the sort.