Find Maximum Non-decreasing Array Length

Problem Statement

We are given a 0-indexed integer array nums. We can perform any number of operations, where each operation involves selecting a subarray of the array and replacing it with the sum of its elements.

For example, if the given array is [1,3,5,6] and you select subarray [3,5], the array will convert to [1,8,6]. Return the maximum length of a non-decreasing array that can be made after applying operations. A subarray is a contiguous, non-empty sequence of elements within an array.

Example:

Input: [5,2,2]

Output: 1

Explanation:

The given array [5,2,2] is not non-decreasing. To find the maximum non-decreasing subarray, we consider two options:

• Choosing subarray [2,2] and replacing it with [5,4], resulting in [5,4], which is not non-decreasing.
• Choosing subarray [5,2] and replacing it with [7,2], resulting in [7,2], which is not non-decreasing.
• Choosing subarray [5,2,2] and replacing it with [9] resulting in [9], which is non-decreasing.
• Therefore, the maximum length of a non-decreasing subarray is 1, and the answer is 1.

Java Approach Using Dynamic programming

Output:

Code Explanation:

• The Above Java code aims to find the maximum length of a subarray with a sum not exceeding a given target. It utilizes dynamic programming and binary search.
• The algorithm maintains a prefix sum array to calculate subarray sums efficiently. The main loop iterates through the elements, updating the maximum length based on the current element and the previous subarray.
• It also uses binary search to find the optimal subarray ending at the current index. The final result is the maximum length of a subarray with a sum not exceeding the target.

Time Complexity:

• The time complexity of the provided code is O(N log N), where N is the length of the input array. This complexity arises from the binary search operation performed in each iteration of the main loop.

Space Complexity:

• The space complexity is O(N), as the code utilizes additional space to store the prefix sum array (pre) and the dynamic programming array (dp). The size of these arrays is proportional to the length of the input array.