Given an array A containing n integers. The task is to check whether the array is Monotonic or not. An array is monotonic if it is either monotone increasing or monotone decreasing.
An array A is monotone increasing if for all i <= j, A[i] <= A[j]. An array A is monotone decreasing if for all i <= j, A[i] >= A[j].
Return “True” if the given array A is monotonic else return “False” (without quotes).
Input : 6 5 4 4 Output : true Input : 5 15 20 10 Output : false
An array is monotonic if and only if it is monotone increasing, or monotone decreasing. Since p <= q and q <= r implies p <= r. So we only need to check adjacent elements to determine if the array is monotone increasing (or decreasing), respectively. We can check each of these properties in one pass.
To check whether an array A is monotone increasing, we’ll check A[i] <= A[i+1] for all i indexing from 0 to len(A)-2. Similarly we can check for monotone decreasing where A[i] >= A[i+1] for all i indexing from 0 to len(A)-2.
Note: Array with single element can be considered to be both monotonic increasing or decreasing, hence returns “True“.
Below is the implementation of above approach:
Time Complexity: O(N), where N is the length of array.
- Python Program to check whether it is possible to make a divisible by 3 number using all digits in an array
- Python Program to check Armstrong Number
- Python program to check whether a number is Prime or not
- Python Program to Check Prime Number
- Python Program for Check if count of divisors is even or odd
- Python program to check if given string is vowel Palindrome
- Python Program for Check if all digits of a number divide it
- Python program to check if a string contains all unique characters
- Program to check if an array is bitonic or not
- Program to check if an array is palindrome or not using Recursion
- Program to check if an array is sorted or not (Iterative and Recursive)
- Python Program for GCD of more than two (or array) numbers
- Python Program to find sum of array
- Python Program for array rotation
- Python Program to Split the array and add the first part to the end
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.