Sort colors leetcode 75 arrays strings python

certainly! the "sort colors" problem is a classic algorithmic challenge that can be found on leetcode, specifically labeled as problem 75. the problem requires you to sort an array containing three distinct values that represent three different colors, which can be thought of as 0s, 1s, and 2s. the goal is to sort the array in a single pass with o(n) time complexity and o(1) space complexity.

### problem statement
given an array `nums` with `n` objects colored red, white, or blue, represented by integers `0`, `1`, and `2`, respectively, sort the array in-place so that objects of the same color are adjacent, with the colors in the order red, white, and blue.

### example

### approach
to solve this problem efficiently, we can use the dutch national flag algorithm, which uses three pointers:
1. `low`: to place the next `0`.
2. `mid`: to explore the array.
3. `high`: to place the next `2`.

### algorithm steps
1. initialize three pointers:
- `low` at the start of the array (index 0).
- `mid` also at the start of the array (index 0).
- `high` at the end of the array (index len(nums) - 1).

2. iterate through the array with the `mid` pointer:
- if `nums[mid]` is `0`, swap it with `nums[low]`, increment both `low` and `mid`.
- if `nums[mid]` is `1`, just increment `mid`.
- if `nums[mid]` is `2`, swap it with `nums[high]`, and decrement `high`. do not increment `mid` in this case since the swapped value from `high` needs to be evaluated.

3. continue until `mid` exceeds `high`.

### code example

### explanation of the code
- the function `sortcolors` takes a list `nums` as input.
- three pointers `low`, `mid`, and `high` are initialized.
- a `while` loop runs as long as `mid` is less than or equal to `high`.
- depending on the value at `nums[mid]`, we perform swaps or increments as described.
- after processing, the input list `nums` is sorted in-place.

### complexity analysis
- **time complexity**: o(n), where n is the number of elements in the a ...

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