You are given an array nums of length n, where each element represents an object colored either red, white, or blue. The integers 0, 1, and 2 are used to represent red, white, and blue, respectively.

Sort the array in place so that all objects of the same color are grouped together, arranged in the order: red (0), white (1), and blue (2).

You must solve this problem without using any library sort function.

Note: Could you come up with a one pass algorithm using only constant extra space?

Constraints:

• $n$ $==$ colors.length

• $1 \leq$ $n$ $\leq 300$

• colors[i] is either 0, 1, or 2

The key intuition behind this problem is to use the Dutch National Flag algorithm, which partitions the array into three sections in a single pass using three pointers. We maintain a low pointer that tracks where the next $0$ should be placed, a high pointer that tracks where the next $2$ should be placed, and a mid pointer that scans through the array. As mid advances, every element it encounters is either swapped to the front (if it is $0$), left in place (if it is ...