769 Max Chunks To Make Sorted

769. Max Chunks To Make Sorted

1. Question

Given an arrayarrthat is a permutation of[0, 1, ..., arr.length - 1], we split the array into some number of "chunks" (partitions), and individually sort each chunk. After concatenating them, the result equals the sorted array.

What is the most number of chunks we could have made?

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.

Note:

• arrwill have length in range[1, 10].

• arr[i]will be a permutation of[0, 1, ..., arr.length - 1].

2. Implementation

思路: 根据题意，每个数和数组的index是一一对应，要想得到最多的chunk使得整个数组sorted, 我们只要从左到右扫一遍数组，得到当前最大的数，如果当前最大的数和当前的index相等，说明这个时候我们需要加一个chunk

class Solution {
    public int maxChunksToSorted(int[] arr) {
        int curMax = Integer.MIN_VALUE;
        int chunks = 0;

        for (int i = 0; i < arr.length; i++) {
            curMax = Math.max(curMax, arr[i]);
            if (curMax == i) {
                ++chunks;
            }
        }
        return chunks;
    }
}

3. Time & Space Complexity

时间复杂度O(n), 空间复杂度O(1)