[LeetCode] 769. Max Chunks To Make Sorted 可排序的最大块数

Given an array arr that 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:

• arr will have length in range [1, 10].
• arr[i] will be a permutation of [0, 1, ..., arr.length - 1].

给一个长度为n的数组，里面的数字是[0, n-1]范围内的所有数字的枚举中的一中。将其分成若干块儿，要求分别给每一小块儿排序，再组合到一起，等于原数组的有序排列，问最多能分多少块。

跟45. Jump Game II那题很像，我们需要维护一个最远能到达的位置，这里的每个数字相当于那道题中的跳力，只有当我们刚好到达最远点的时候，就可以把之前断成一个新的块儿了。

解法：

The basic idea is to use max[] array to keep track of the max value until the current position, and compare it to the sorted array (indexes from 0 to arr.length - 1). If the max[i] equals the element at index i in the sorted array, then the final count++.

e.g: 

original: 0, 2, 1, 4, 3, 5, 7, 6
max: 0, 2, 2, 4, 4, 5, 7, 7
sorted: 0, 1, 2, 3, 4, 5, 6, 7
index: 0, 1, 2, 3, 4, 5, 6, 7
The chunks are: 0 | 2, 1 | 4, 3 | 5 | 7, 6

Java:

public int maxChunksToSorted(int[] arr) {
        if (arr == null || arr.length == 0) return 0;
        
        int[] max = new int[arr.length];
        max[0] = arr[0];
        for (int i = 1; i < arr.length; i++) {
            max[i] = Math.max(max[i - 1], arr[i]);
        }
        
        int count = 0;
        for (int i = 0; i < arr.length; i++) {
            if (max[i] == i) {
                count++;
            }
        }
        
        return count;
    }

Java:

public int maxChunksToSorted(int[] arr) {
        if (arr == null || arr.length == 0) return 0;
        
        int count = 0, max = 0;
        for (int i = 0; i < arr.length; i++) {
            max = Math.max(max, arr[i]);
            if (max == i) {
                count++;
            }
        }
        
        return count;
    }

Python:

class Solution(object):
    def maxChunksToSorted(self, arr):
        """
        :type arr: List[int]
        :rtype: int
        """
        expectSum = 0
        cnt = 0
        realSum = 0
        
        for i in range(len(arr)):
            if arr[i] + realSum == expectSum:
                cnt += 1
                realSum = 0
                if i + 1 < len(arr):
                    expectSum = i + 1
            else:
                realSum += arr[i]
                if i + 1 < len(arr):
                    expectSum += i + 1
        
        return cnt

Python:

def maxChunksToSorted(self, arr):
        curMax = -1
        res = 0
        for i, v in enumerate(arr):
            curMax = max(curMax, v)
            if curMax == i:
                res += 1
        return res

Python:

def maxChunksToSorted(self, arr):
        return sum(max(arr[:i + 1]) == i for i in range(len(arr)))

C++:

class Solution {
public:
    int maxChunksToSorted(vector<int>& arr) {
        int res = 0, n = arr.size(), mx = 0;
        for (int i = 0; i < n; ++i) {
            mx = max(mx, arr[i]);
            if (mx == i) ++res;
        }
        return res;
    }
};

　　

类似题目：

[LeetCode] 768. Max Chunks To Make Sorted II 可排序的最大块数 II

[LeetCode] 45. Jump Game II 跳跃游戏 II

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