Problem Description
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.
Key Insights
- An array is monotonic increasing if each element is less than or equal to the next.
- An array is monotonic decreasing if each element is greater than or equal to the next.
- We can determine if an array is monotonic by checking the differences between consecutive elements.
- The algorithm needs to traverse the array just once to check for monotonicity, ensuring efficiency.
Space and Time Complexity
Time Complexity: O(n) - where n is the length of the array, as we need to check each pair of adjacent elements. Space Complexity: O(1) - we only use a constant amount of extra space for variables.
Solution
To determine if the array is monotonic, we can iterate through the array and compare each element with the next one. We will maintain two flags: one for checking if the array is increasing and another for checking if it is decreasing. If we find any violation of these conditions, we can immediately return false. If we complete the iteration without finding any violations, we return true.