Leetcode #2945: Find Maximum Non-decreasing Array Length
In this guide, we solve Leetcode #2945 Find Maximum Non-decreasing Array Length in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given a 0-indexed integer array nums. You 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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Stack, Queue, Array, Binary Search, Dynamic Programming, Monotonic Queue, Monotonic Stack
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums = [5,2,2]
Output: 1
Explanation: This array with length 3 is not non-decreasing.
We have two ways to make the array length two.
First, choosing subarray [2,2] converts the array to [5,4].
Second, choosing subarray [5,2] converts the array to [7,2].
In these two ways the array is not non-decreasing.
And if we choose subarray [5,2,2] and replace it with [9] it becomes non-decreasing.
So the answer is 1.
Python Solution
class Solution:
def findMaximumLength(self, nums: List[int]) -> int:
n = len(nums)
s = list(accumulate(nums, initial=0))
f = [0] * (n + 1)
pre = [0] * (n + 2)
for i in range(1, n + 1):
pre[i] = max(pre[i], pre[i - 1])
f[i] = f[pre[i]] + 1
j = bisect_left(s, s[i] * 2 - s[pre[i]])
pre[j] = i
return f[n]
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.