Understanding dutch national flag sort algorithm

Now that we have explored the significance, advantages, and limitations of the Dutch National Flag sort, we can turn our attention to understanding the algorithm behind it. In the following section, we will examine how the algorithm works step by step and see how it efficiently organizes elements into their respective partitions.

Algorithm

The Dutch National Flag algorithm is designed to sort an array containing only three distinct values (commonly 0, 1, and 2) by partitioning the array into three sections and expanding them as the algorithm progresses. The algorithm uses three pointers, all 0 indexed, to keep track of the boundaries between the sections (in the bullets below, n is the size of the input array).

• The `left` pointer is set to `0` and marks the boundary of the section containing elements equal to `0`.
• The `mid` pointer is set to `0` and is used to traverse the array.
• The `right` pointer is set to `n - 1` and marks the boundary of the section containing the elements equal to `2`.

At any point during execution, the array maintains the following structure:

• Elements from index `0` to `left - 1` are all `0s` (sorted smallest section).
• Elements from index `left` to `mid - 1` are all `1s` (sorted middle section).
• Elements from index `mid` to `right` are unsorted.
• Elements from index `right + 1` to `n - 1` are all `2s` (sorted largest section).