给定一个包含红色、白色和蓝色，一共 n 个元素的数组，原地对它们进行排序，使得相同颜色的元素相邻，并按照红色、白色、蓝色顺序排列。
此题中，我们使用整数 0、 1 和 2 分别表示红色、白色和蓝色。

进阶：
你可以不使用代码库中的排序函数来解决这道题吗？
你能想出一个仅使用常数空间的一趟扫描算法吗？

官方解法：https://leetcode-cn.com/problems/sort-colors/solution/yan-se-fen-lei-by-leetcode-solution/

解法一：单指针(32ms/14.8MB)

class Solution:
    def sortColors(self, nums: List[int]) -> None:
        n = len(nums)
        ptr = 0
        for i in range(n):
            if nums[i] == 0:
                nums[i], nums[ptr] = nums[ptr], nums[i]
                ptr += 1
        for i in range(ptr, n):
            if nums[i] == 1:
                nums[i], nums[ptr] = nums[ptr], nums[i]
                ptr += 1

解法二：双指针(32ms/14.9MB)

class Solution:
    def sortColors(self, nums: List[int]) -> None:
        n = len(nums)
        p0 = p1 = 0
        for i in range(n):
            if nums[i] == 1:
                nums[i], nums[p1] = nums[p1], nums[i]
                p1 += 1
            elif nums[i] == 0:
                nums[i], nums[p0] = nums[p0], nums[i]
                if p0 < p1:
                    nums[i], nums[p1] = nums[p1], nums[i]
                p0 += 1
                p1 += 1

解法三：双指针(20ms/14.9MB)

class Solution:
    def sortColors(self, nums: List[int]) -> None:
        n = len(nums)
        p0, p2 = 0, n - 1
        i = 0
        while i <= p2:
            while i <= p2 and nums[i] == 2:
                nums[i], nums[p2] = nums[p2], nums[i]
                p2 -= 1
            if nums[i] == 0:
                nums[i], nums[p0] = nums[p0], nums[i]
                p0 += 1
            i += 1

解法四：循环不变量（36ms/14.9MB）

from typing import List


class Solution:
    def sortColors(self, nums: List[int]) -> None:
        """
        Do not return anything, modify nums in-place instead.
        """

        # all in [0, zero) = 0
        # all in [zero, i) = 1
        # all in [two, len - 1] = 2

        def swap(nums, index1, index2):
            nums[index1], nums[index2] = nums[index2], nums[index1]

        size = len(nums)
        if size < 2:
            return

        zero = 0
        two = size

        i = 0

        while i < two:
            if nums[i] == 0:
                swap(nums, i, zero)
                i += 1
                zero += 1
            elif nums[i] == 1:
                i += 1
            else:
                two -= 1
                swap(nums, i, two)

力扣 (LeetCode)链接：https://leetcode-cn.com/leetbook/read/top-interview-questions-medium/xvg25c/