LC896. Monotonic Array

Problem Description

LeetCode Problem 896: An array is monotonic if it is either monotone increasing or monotone decreasing.

An array nums is monotone increasing if for all i <= j, nums[i] <= nums[j]. An array nums is monotone decreasing if for all i <= j, nums[i] >= nums[j].

Given an integer array nums, return true if the given array is monotonic, or false otherwise.

Clarification

• < vs <= (strictly monotonic?)
• either increase or decrease

Assumption

Solution

Approach

Start from the basic definition where

• Monotonic increase: \(nums[i + 1] >= nums[i]\) for all \(i\). For strictly monotonic, use >.
• Monotonic decrease: \(nums[i + 1] <= nums[i]\) for all \(i\). For strictly monotonic, use <.

Python

class Solution:
    def isMonotonic(self, nums: List[int]) -> bool:
        isMonotonicIncrease = True
        isMonotonicDecrease = True
        for i in range(len(nums) - 1):
            if nums[i] > nums[i + 1]:
                isMonotonicIncrease = False

            if nums[i] < nums[i + 1]:
                isMonotonicDecrease = False

            if not isMonotonicIncrease and not isMonotonicDecrease:
                break

        return isMonotonicIncrease or isMonotonicDecrease

Complexity Analysis

• Time complexity: \(O(n)\)
  In the worst case, need to go through the whole array.
• Space complexity: \(O(1)\)
  Use a pointer and limited local variables.

Test