check if array is sorted java

## Checking if an Array is Sorted in Java: A Comprehensive Tutorial

This tutorial will explore various methods to determine if an array is sorted in Java. We'll cover different types of arrays (integers, strings, custom objects), different sorting orders (ascending, descending), and analyze the time complexity of each approach.

**What does it mean for an array to be "sorted"?**

An array is considered "sorted" if its elements are arranged in a specific order. Common sorting orders include:

* **Ascending Order:** Each element is greater than or equal to the element preceding it (e.g., `[1, 2, 2, 3, 5]` is sorted in ascending order).
* **Descending Order:** Each element is less than or equal to the element preceding it (e.g., `[5, 3, 2, 2, 1]` is sorted in descending order).

**Basic Approaches for Integer Arrays**

Let's start with checking if an integer array is sorted in ascending order using a simple iterative approach.

**1. Iterative Approach (Ascending Order)**

**Explanation:**

1. **Null and Empty Check:** The function first checks if the array is `null` or has only one element. In both cases, we consider the array sorted, returning `true`. This prevents `NullPointerException` and handles trivial cases gracefully.
2. **Iteration:** The `for` loop iterates through the array, starting from the second element (index 1).
3. **Comparison:** Inside the loop, it compares the current element `arr[i]` with the previous element `arr[i - 1]`.
4. **Unsorted Condition:** If `arr[i]` is less than `arr[i - 1]`, it means the array is not sorted in ascending order. The function immediately returns `false`.
5. **Sorted Condition:** If the loop completes without finding any elements out of order, it means the array is sorted in ascending order. The function returns `true`.

**Time Complexity:** O(n) - The function iterates through the array once in the worst case.

**2. Iterative Approach (Descending Order)**

**Explanation:**

The logic is almost identical to the a ...

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