leetcode - 769. Max Chunks To Make Sorted

Description

You are given an integer array arr of length n that represents a permutation of the integers in the range [0, n - 1].

We split arr into some number of chunks (i.e., partitions), and individually sort each chunk. After concatenating them, the result should equal the sorted array.

Return the largest number of chunks we can make to sort the array.

Example 1:

Input: arr = [4,3,2,1,0]
Output: 1
Explanation:
Splitting into two or more chunks will not return the required result.
For example, splitting into [4, 3], [2, 1, 0] will result in [3, 4, 0, 1, 2], which isn't sorted.

Example 2:

Input: arr = [1,0,2,3,4]
Output: 4
Explanation:
We can split into two chunks, such as [1, 0], [2, 3, 4].
However, splitting into [1, 0], [2], [3], [4] is the highest number of chunks possible.

Constraints:

n == arr.length
1 <= n <= 10
0 <= arr[i] < n
All the elements of arr are unique.

Solution

The description itself is very hard to understand… So basically we will split the array into several chunks, and sort each chunk internally, then concatenate all the sorted chunks. If the concatenated array is sorted, like [0,1,2,3,4,5], then we get our result.

So to get the final result sorted, then for each number, it has to be in the chunk that covers its final position. For example, if 4 appears in position 1, then 4 needs to be in the chunk that starts from position 1 to position 4. So we could iterate from the left to the right, and keep a max_right to denote the right most position of the current chunk. If the number is larger than the right most position, we need to expand the chunk. When we are outside the chunk, update to use a new chunk (size = 1).

Time complexity: $o(n)$
Space complexity: $o(1)$

Code

class Solution:
    def maxChunksToSorted(self, arr: List[int]) -> int:
        max_right = -1
        res = 0
        for i, each_num in enumerate(arr):
            if i > max_right:
                max_right = each_num
                res += 1
            else:
                max_right = max(max_right, each_num)
        return res