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Let's do this question.

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An array is monotonic if it is either monotone increasing or monotone decreasing.

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An array is monotone increasing if all its elements from left to right are non-decreasing, an array

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is monotone decreasing if all its elements from left to right are non-increasing.

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

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All right, so this is the question at hand.

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Let's try to understand this over here.

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This is a mathematical concept.

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When we say that an array is monotonic.

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Now an array is monotonic if it's either monotone increasing or monotone decreasing.

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So let's understand these two.

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So this is monotone increasing and this is monotone decreasing.

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Now if an array is monotone increasing then it means that when we go from left to right the elements

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are non decreasing.

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For example let's take an example like one.

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And then you have um two.

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And then you have three right over here.

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When you go from 1 to 2 that is you're going from left to right.

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Right.

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So the elements are non decreasing.

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So we can say that this is monotone increasing.

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Now why is it mentioned over here as non decreasing.

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Now let's say we add an element three over here.

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Now over here we can see that these two elements are equal right.

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So it's not increasing.

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But still because it is non-decreasing right.

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From 3 to 3 it's not decreasing.

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Right.

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So it's non decreasing.

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Therefore we can say that this array over here is still monotone increasing.

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Now what about monotone decreasing.

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Let's take an example.

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Again we take a simple example.

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Let's say we have 321.

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Now in this case when we go from left to right right.

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So the elements are non increasing.

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So from 3 to 2 the the value is not increasing right.

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And similarly from 2 to 1 the value is not increasing.

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So the elements are non increasing.

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Again we add an element over here.

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Let's say we have one over here.

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In this case when we go from 1 to 1 the value is not decreasing.

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It's equal right.

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But then it is not increasing.

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So that's why we can say that this array over here is also monotone decreasing.

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All right.

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So we have understood the question.

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We have understood what we mean with monotone increasing and monotone decreasing.

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Now the question says that we are given an array.

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And then we have to do some operations.

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And we have to identify whether the given array is monotonic.

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That means whether it is monotone increasing or monotone decreasing.

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And if it is, we have to return true, else we have to return false.

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So that's the question now in the interview when you get this question, always feel free to ask clarifying

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questions so that you thoroughly understand the question and you and the interviewer are on the same

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page.

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Now, what are some possible questions possibly you could ask?

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Is an empty array monotonic?

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And let's say that the interviewer says yes, an empty array is monotonic.

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All right.

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Now another question could be is an array with only one integer monotonic.

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And again let's say the interviewer replies yes, this array is monotonic.

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All right.

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So again, as of now we have understood the question.

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We have understood what is monotonic increasing and monotone decreasing.

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And we have done clarifying any kind of question or doubt you have all right now at the At.

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Then as a next step, let's go ahead and write test cases.

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And remember, you can always take the help of the interviewer whenever you write test cases.

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But over here it's pretty straightforward.

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So let's go ahead and write a few test cases.

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Now if the array which is given to us is one, two, three, then over here we can see that the elements

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are non-decreasing.

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Right.

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So I'm just writing end over here.

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It's non-decreasing.

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So yes we can say that this array over here is monotonic or it is monotonic increasing.

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Right.

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So if the value is monotonic increasing it should be just non-decreasing.

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Now what if we are given the array 321.

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In this case we can see that the array over here is non-increasing right as we go from left to right

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it's not increasing.

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So therefore it is monotonic decreasing.

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Right.

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So yes over here also we would be returning true.

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Now if the array which is given to us is one two, two.

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In this case also it will be true.

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Right?

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It will be monotonic because in this case it's monotonic increasing right.

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Again it's monotonic increasing because it is non-decreasing.

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When you go from 2 to 2 again it's not decreasing.

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So it's non-decreasing.

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That's why it's monotonic increasing.

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And we return true.

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Now let's take one more example.

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What if we have 333.

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In this case also it will be true.

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Right.

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So we have got a fair understanding and about the edge cases.

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We had asked clarifying questions.

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Right.

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So if you are given let's say an array with only one element, then we will return true.

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And if you are given an empty array in that case also we will return true.

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Now all of these cases were true.

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What would an example be of a false case?

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For example, if you have two, two, three and one, you can see as we go from left to right till here

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it was monotonic right.

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It was monotonic because it was non decreasing.

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But then when we came from 3 to 1 it decreased right.

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So when we take this array.

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The.

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It is not monotonic, right?

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It's neither non-increasing nor non-decreasing.

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So we return false.

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So we have got a good understanding of the question.

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Now in the next video, let's go ahead and think through how we are going to solve this.