Leetcode 75. Sort Colors

https://leetcode.com/problems/sort-colors/

Medium

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]

Follow up:

• A rather straight forward solution is a two-pass algorithm using counting sort.
  First, iterate the array counting number of 0's, 1's, and 2's, then overwrite array with total number of 0's, then 1's and followed by 2's.
• Could you come up with a one-pass algorithm using only constant space?

---

• Dutch national flag problem。类似快排的three-way-partition。用三个指针，保证0 <= i <= j <= n <= len(array) - 1，i 是小于middle的元素的最大下标，n是大于middle的元素的最小下标，j是当前元素下标。最终划分成 [0, i], (i, n), [n, len(array) - 1]。
• Python O(n) 1 pass in-place solution with explanation - LeetCode Discuss
  • https://leetcode.com/problems/sort-colors/discuss/26481/Python-O(n)-1-pass-in-place-solution-with-explanation
• Dutch national flag problem - Wikipedia
  • https://en.wikipedia.org/wiki/Dutch_national_flag_problem

class Solution:
    def sortColors(self, nums: List[int]) -> None:
        """
        Do not return anything, modify nums in-place instead.
        """
        
        def three_way_partition(nums, middle):
            i, j, n = 0, 0, len(nums) - 1
            
            while j <= n:
                if nums[j] < middle:
                    nums[i], nums[j] = nums[j], nums[i]
                    i += 1
                    j += 1
                elif nums[j] > middle:
                    nums[j], nums[n] = nums[n], nums[j]
                    n -= 1
                else:
                    j += 1
        
        three_way_partition(nums, 1)