Python Program to check if given array is Monotonic

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).

Examples:

Input : 6 5 4 4
Output : true

Input : 5 15 20 10
Output : false

Approach:
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:

Python3

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# Python3 program to find sum in Nth group
  
# Check if given array is Monotonic
def isMonotonic(A):
  
    return (all(A[i] <= A[i + 1] for i in range(len(A) - 1)) or
            all(A[i] >= A[i + 1] for i in range(len(A) - 1)))
  
# Driver program
A = [6, 5, 4, 4]
  
# Print required result
print(isMonotonic(A))
  
# This code is written by
# Sanjit_Prasad

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Output:

True

Time Complexity: O(N), where N is the length of array.



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