How do you solve Monotonic Array on LeetCode?

Monotonic Array (LeetCode #896) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: An array can be monotonic if it is either non-decreasing or non-increasing.

What is the brute force solution for Monotonic Array?

The brute force approach for Monotonic Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every pair of elements in the array to determine if the entire array is either increasing or decreasing. This is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Monotonic Array?

Monotonic Array uses the following concepts: Array. The recommended patterns to study are: Array.

What are the interview tips for Monotonic Array?

Clarify the definition of monotonic arrays before starting your solution. Consider edge cases, such as arrays with only one element or arrays with all equal elements. Explain your thought process clearly while coding to show your understanding.

What are common mistakes when solving Monotonic Array?

Students often forget to check both increasing and decreasing conditions. Some might assume the array must be strictly increasing or decreasing, missing equal elements.

#896

Monotonic Array

Easy

ArrayArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

The optimal solution uses a single pass through the array to determine if it is monotonic. This is efficient and leverages the fact that we only need to check the relationship between adjacent elements.

⚙️

Algorithm

4 steps

1Step 1: Initialize two flags, isIncreasing and isDecreasing, to true.
2Step 2: Loop through the array from the first to the second last element.
3Step 3: Compare each element with the next one; if any element is greater than the next, set isIncreasing to false, and if any element is less than the next, set isDecreasing to false.
4Step 4: After the loop, return true if either isIncreasing or isDecreasing is true.

solution.py9 lines

1def isMonotonic(nums):
2    isIncreasing = True
3    isDecreasing = True
4    for i in range(len(nums) - 1):
5        if nums[i] > nums[i + 1]:
6            isIncreasing = False
7        if nums[i] < nums[i + 1]:
8            isDecreasing = False
9    return isIncreasing or isDecreasing

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the array. The space complexity is O(1) as we are using a constant amount of space for the flags.

1An array can be monotonic if it is either non-decreasing or non-increasing.
2The optimal solution leverages the relationship between adjacent elements to minimize checks.

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