Max Chunks To Make Sorted

Problem 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.

Key Insights

• The problem involves partitioning an array into chunks that can be individually sorted to yield a sorted array when concatenated.
• The maximum number of chunks corresponds to the number of indices where the largest element seen so far is equal to the current index.
• By tracking the maximum value encountered as we iterate through the array, we can determine valid chunk boundaries.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we will utilize a single pass through the array while keeping track of the maximum value encountered up to the current index. We'll compare this maximum value with the current index. Whenever they are equal, it indicates a valid chunk boundary. By counting these boundaries, we can determine the maximum number of chunks.

1. Initialize a variable to track the maximum value seen so far.
2. Iterate through the array, updating the maximum value at each step.
3. When the maximum value equals the current index, we can increment our chunk count.
4. Finally, return the counted chunks.

Code Solutions