How do you solve Find Maximum Non-decreasing Array Length on LeetCode?

Find Maximum Non-decreasing Array Length (LeetCode #2945) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Dynamic programming can significantly reduce the time complexity of problems involving sequences.

What is the time complexity of Find Maximum Non-decreasing Array Length?

The optimal solution for Find Maximum Non-decreasing Array Length runs in O(n) time and uses O(n) space. This complexity is efficient because we only make a single pass through the array, updating our dp array.

What is the brute force solution for Find Maximum Non-decreasing Array Length?

The brute force approach for Find Maximum Non-decreasing Array Length is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible subarray and calculating the maximum length of a non-decreasing array after replacing that subarray with its sum. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Find Maximum Non-decreasing Array Length?

Always clarify the problem requirements before diving into coding. Think about edge cases and test your solution against them. Explain your thought process as you code; it shows your understanding.

What are common mistakes when solving Find Maximum Non-decreasing Array Length?

Not considering edge cases like arrays that are already non-decreasing. Failing to properly initialize and update the dp array.

#2945

Find Maximum Non-decreasing Array Length

Hard

ArrayBinary SearchDynamic ProgrammingStackQueueMonotonic StackMonotonic QueueDynamic ProgrammingArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal approach uses dynamic programming to keep track of the maximum length of a non-decreasing array as we process each element. This allows us to efficiently determine the maximum length without checking every subarray.

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Algorithm

4 steps

1Step 1: Initialize a dp array where dp[i] represents the maximum length of a non-decreasing array ending at index i.
2Step 2: Iterate through the nums array and update dp[i] based on the previous values.
3Step 3: If nums[i] can extend the non-decreasing sequence from nums[i-1], update dp[i].
4Step 4: Return the maximum value in the dp array.

solution.py7 lines

1def maxNonDecreasingLength(nums):
2    n = len(nums)
3    dp = [1] * n
4    for i in range(1, n):
5        if nums[i] >= nums[i - 1]:
6            dp[i] = dp[i - 1] + 1
7    return max(dp)

ℹ

Complexity note: This complexity is efficient because we only make a single pass through the array, updating our dp array.

1Dynamic programming can significantly reduce the time complexity of problems involving sequences.
2Understanding how to build up solutions incrementally is key to mastering DSA.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.