What is the Next Permutation Algorithm?

In technical interviews, questions regarding permutations often arise, particularly about generating the next permutation in lexicographical order. Understanding this concept is essential for developers, as it not only tests algorithmic skills but also critical thinking. Let’s explore how to find the next permutation in detail.

A permutation of a sequence is simply a rearrangement of its elements. The next permutation is the next lexicographical arrangement of these elements. If the sequence is sorted in descending order, it represents the largest possible permutation. The next permutation will return the smallest possible permutation if the current one is the largest.

Here is the essential algorithm for finding the next permutation of an array of integers:

1. Identify the longest non-increasing suffix: Start from the end of the array and find the first pair of elements where the order breaks. Let’s call the index of this first element i-1, where i is the index of the first decrease.

2. Handle the case where the entire array is non-increasing: If no such index exists (i.e., the entire array is non-increasing), reverse the entire array to get the smallest permutation.

3. Find the successor to pivot: If the previous step didn't apply, identify the successor to the pivot (the element at index i-1). This is done by finding the smallest element larger than the pivot in the suffix.

4. Swap: Swap the pivot with the successor found from the previous step.

5. Reverse the suffix: Finally, reverse the suffix starting from index i.

Here is how the code looks in Python:

PythonCopy code

This code effectively implements the steps outlined and generates the next permutation in place. It runs in linear time, O(n), since each step processes the array with a few passes. It’s efficient and suitable for competitive programming and coding interviews alike.