leetcode75 Sort Colors

"""
Given an array 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.
Here, we will use the integers 0, 1, and 2 to represent the color red, white, and blue respectively.
Note: You are not suppose to use the library's sort function for this problem.
Example:
Input: [2,0,2,1,1,0]
Output: [0,0,1,1,2,2]
"""
"""
绝世好题：提供了四种解法
传送门：https://blog.csdn.net/qq_17550379/article/details/80499816
1.计数排序
2.三路快排(回顾liuyubobobo的视频第三章6-9)
3.适合此题的三路排序算法
4.三指针
"""
"""
解法一：计数排序
"""
class Solution1:
    def sortColors(self, nums):
        """
        Do not return anything, modify nums in-place instead.
        """
        count = [0, 0, 0]
        for i in nums:
            assert(i >= 0 and i <= 2)
            #python assert断言是声明布尔值必须为真的判定，如果发生异常就说明表达式为假。
            #可以理解assert断言语句为raise-if-not，用来测试表示式，其返回值为假，就会触发异常。
            count[i] += 1
        index = 0
        for i, num in enumerate(count):
            for j in range(num):
                nums[index] = i
                index += 1

"""
解法二：快速排序(三路)，没有随机标兵点
"""
class Solution2:
    def sortColors(self, nums: List[int]) -> None:
        """
        Do not return anything, modify nums in-place instead.
        """
        self._sortColors(nums, 0, len(nums)-1) #bug 没写-1
    def _sortColors(self, nums, l, r):
        if r <= l:
            return
        pivot = l #标定点
        lt = l #[l+1, lt] <val
        i = l+1 #[lt+1,gt-1] = val
        gt = r+1 #[gt, r] > val
        while i < gt:
            if nums[i] < nums[pivot]:
                lt += 1
                nums[i], nums[lt] = nums[lt], nums[i]
                i += 1
            elif nums[i] > nums[pivot]:
                gt -= 1
                nums[i], nums[gt] = nums[gt], nums[i]  #注意与后面的交换不需要再加i
            else:
                i += 1
        nums[pivot], nums[lt] = nums[lt], nums[pivot]
        self._sortColors(nums, l, lt-1) #快排交换放在了lt的位置
        self._sortColors(nums, gt, r)

"""
解法三：适合此题的三路排序算法
"""
class Solution3:
    def sortColors(self, nums):
        """
        Do not return anything, modify nums in-place instead.
        """
        zero = -1
        i = 0 #从0开始向后遍历
        two = len(nums)
        while i < two:
            if nums[i] == 1:
                i += 1
            elif nums[i] == 2:
                two -= 1
                nums[two], nums[i] = nums[i], nums[two]
            else:
                zero += 1
                nums[zero], nums[i] = nums[i], nums[zero]
                i += 1 #!!! forget
"""
解法四：用三个指针
i，j，k分别指向最后一个0，1，2
"""
class Solution4:
    def sortColors(self, nums):
        """
        Do not return anything, modify nums in-place instead.
        """
        i, j, k = -1, -1, -1 #i，j，k分别指向最后一个0，1，2
        for m in range(len(nums)):
            if nums[m] == 0:
                k += 1         #bug python中写成 nums[++k] 是无效的
                nums[k] = 2
                j += 1
                nums[j] = 1
                i += 1
                nums[i] = 0
            elif nums[m] == 1:
                k += 1
                nums[k] = 2
                j += 1
                nums[j] = 1
            else:
                k += 1
                nums[k] = 2