# Sort Colors - Dutch Flag Partitioning Problem

Given an array nums with n objects colored red, white, or blue, sort them **in-place **so that objects of the same color are adjacent, with the colors in the order red, white, and blue.

We will use the integers 0, 1, and 2 to represent the color red, white, and blue, respectively.

```
def sortColors(self, nums):
red, white, blue = 0, 0, len(nums)-1
while white <= blue:
if nums[white] == 0:
nums[red], nums[white] = nums[white], nums[red]
white += 1
red += 1
elif nums[white] == 1:
white += 1
else:
nums[white], nums[blue] = nums[blue], nums[white]
blue -= 1
```

## Related Problems

Given an array of **distinct** integers candidates and a target integer target, return *a list of all ***unique combinations*** of *candidates* where the chosen numbers sum to *target*.* You may return the combinations in **any order**.

The **same** number may be chosen from candidates an **unlimited number of times**. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you **must** take course bi first if you want to take course ai.

For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Given an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value.

If target is not found in the array, return [-1, -1].

You must write an algorithm with O(log n) runtime complexity.

Given an m x n integers matrix, return *the length of the longest increasing path in *matrix.

From each cell, you can either move in four directions: left, right, up, or down. You **may not** move **diagonally** or move **outside the boundary** (i.e., wrap-around is not allowed).