Max Chunks To Make Sorted Solution in Python

Problem Description

Welcome to the world of sorting, where we all dream of having our lives organized like a perfectly sorted array! The problem at hand, Max Chunks To Make Sorted, is like trying to sort your laundry into neat piles but realizing you can only fold certain chunks at a time. Imagine you have a pile of clothes (or an array) that you want to sort, but you can only take out certain chunks of clothes that are already in the right order. The challenge is to figure out how many chunks you can take out and sort before you have to deal with the chaos again.

In simpler terms, given an array of integers, you need to determine the maximum number of chunks you can split the array into such that when each chunk is sorted individually and then concatenated, the result is a sorted array. Sounds easy, right? Well, it’s like trying to convince your cat to take a bath—good luck with that!

Code Solution

class Solution:
    def maxChunksToSorted(self, arr: list[int]) -> int:
        ans = 0
        mx = -math.inf

        for i, a in enumerate(arr):
            mx = max(mx, a)
            if mx == i:
                ans += 1

        return ans

Approach Explanation

The approach used in the code is quite straightforward. We iterate through the array while keeping track of the maximum value encountered so far (mx). For each index i, if the maximum value equals the index, it means that all values from the start of the array to i can be sorted as a chunk. We then increment our chunk count (ans). This way, we efficiently determine how many chunks can be formed without needing to sort the entire array.

Time and Space Complexity

Complexity Type	Complexity
Time Complexity	O(n), where n is the length of the array. We traverse the array once.
Space Complexity	O(1), as we are using a constant amount of space for variables.

Real-World Example

Imagine you’re at a party, and everyone is dancing in their own little groups (chunks). If you want to make the dance floor look organized, you can only ask people from the same group to step out and dance in sync. If everyone in a group is in the right position, you can let them dance together. The more groups you can form, the more organized the dance floor becomes! This is essentially what the problem is asking you to do with the array.