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Hi everyone, I hope you have thought about how to solve this on your own.

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Now let's look at how to solve this together.

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The first method is the brute force method.

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All right so let's look at this method over here.

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For this let's take a sample input.

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Let's say the input is minus three one two and seven.

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So we have this array as input.

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Notice that this is sorted.

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All right.

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Now the brute force method is that we just square each element and put it in a new array.

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Right.

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So that uh after doing that what would be the array.

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The array would be 914 and 49.

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Right.

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We are just squaring each element and putting it in a new array.

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So minus three square is nine, one square is one, two square is four and seven square is 49.

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Now notice that this array over here is not sorted now.

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So the next step would be that we have to sort this array.

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And once we sort this array we will get the required output which is 149 and 49.

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Now this is very simple but it does not have the best space and time complexity.

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Now let's look at the space and time complexity of this solution.

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Now over here notice that we have traversed the array.

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And we have squared each element and put it in a new array.

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Right.

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So we have traversed it one time.

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Let's say this array has n elements.

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So the time complexity of this operation is O of n right.

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We are just traversing it one time.

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Now after this we have to sort right.

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We have to sort the given array to get from here to here right now.

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Any good sort is has a time complexity of o of n log n for example, quicksort, etc..

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Right.

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So the total time complexity of this algorithm therefore is equal to o of n log n.

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Now you could say that it is O of n log n plus n right o of n log n plus n.

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Yes, we can say that.

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But again this simplifies to n log n.

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Why is that so?

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Because n log n is greater than n right in.

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In the logarithm section we have seen that already n log n is greater than n.

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Now if n log n is greater than n, you can either just remove this and you're just left with n log n,

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or you can think of it in this way instead of n, let's replace it with n log n.

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So when we add these two, we get two n log n.

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And then this is a constant.

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So we can remove the constant.

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And again we are getting n log n.

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So the time complexity of the brute force method is n log n.

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Now what about the space complexity of this solution over here?

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Notice that we have made a new array with n elements.

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So we have consumed some space.

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Therefore the space complexity of this algorithm is O of n right.

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This will have n elements.

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If the input array has n elements, the new array also will have n elements.

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So the space complexity is O of n.

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All right.

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So we have seen that the time complexity is O of n log n and the space complexity is O of n.

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Now this is the brute force method.

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We will see in the next video how we can do better than this.