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Hi, everyone.

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So in this video, we're going to solve this question, Woodgate Matrix.

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OK, so basically the government is basically engross and ammunition and what we have to do, so we

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have to rotate this matrix by 90 degrees in the clockwise direction.

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OK, so this is the clockwise direction and this is anticlockwise direction.

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OK, so basically we have to rotate the government by 90 degrees in the clockwise direction.

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OK, so let us consider some example.

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So let us consider this matrix.

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OK, so now that is rotated by 90 degree in the clockwise direction.

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OK, so initially this was like this.

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Now, after dating, so consider this line, so after dating this line with the 90 degree, so this

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line.

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That new line will be this one.

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OK, so if this is the old line, if you can rotated by the 90 degree in the clockwise Badakshan, so

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this line will become like this.

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OK.

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Now, let us rotate this line.

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So it will look like this, I have three and one.

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OK, so in this way, this line will become this.

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So this will be three and this will be one.

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Initially, this was three and this was one.

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OK, now let's rotate this lane to rotate in the clockwise direction by 90 degrees so it will become

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full comma, too.

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OK, so this is the new matrix, three one for Commodore.

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OK, so after rotating this matrix, this is the new matrix.

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OK, now US did this matrix.

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OK, so now let us rotate this matrix.

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So this is.

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One four seven, so after reading this line, so after reading this line in the clockwise direction

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where 90 degree, so this will be the new this will be the new line.

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So it will be seven for one seven four one, OK.

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Now, let us read this line.

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So this this will become basically eight, five and two.

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And this is nine, then six and then three.

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OK, so this is the new matrix.

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Simple.

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Now, let us read this matrix.

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OK, so what.

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The first rule.

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So.

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Let us rotate this lane.

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So it will be 15, then 13, then two and then five.

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The second will be basically 14, then three, then four and then one, that third row will be, well,

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six, eight and nine and the photo will be sixteen, then seven, then 10 and then 11.

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OK, so this is basically the new matrix, OK, this will be the new matrix, so what we have to do,

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so we have to convert this matrix, we have to convert the input matrix into the new matrix.

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OK, the matrix, which is rotated by 90 degrees in the clockwise direction.

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OK, OK, so now let's discuss how we can solve this equation.

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OK, so this is a very simple question.

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OK, so let us consider one example.

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So suppose this is the Matrix.

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One, two, three, then I have four or five, six and then I have seven, eight, nine.

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OK, so now rotate this matrix by 90 degree in the clockwise direction.

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So what with a new matrix.

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So new matrix will be basically seven for one, then eight five two and then nine six three.

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OK, so what will do?

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So our approach is very simple.

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I have to perform two step.

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So first step is basically take transpose of the given matrix and the second step is after transpose

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what we will do.

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Basically we will reverse each rule.

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OK, reverse each rule.

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OK, so how I come to know that after being transferred and then reversed.

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So this is basically observation.

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OK, so this is basically observation if you will see the examples carefully, if you will observe carefully.

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So I have to perform two steps.

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First, I would take transpose and then I have to reverse each rule.

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OK, so let us take its transpose.

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So first step is basically taking transpose so and transpose what we will do.

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We will swapper win column.

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OK, so transpose means basically you will swap rows and columns.

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So let us take the transfer so it will become one, two, three, then I have four, five, six, then

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I have seven, eight, nine.

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OK, so this was one, two, three.

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Now this is one, two, three.

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This is four, five, six.

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Now this is four, five, six.

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So this was seven, eight, nine.

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Now this is seven, eight, nine.

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OK, so transport's taking is very, very simple, but you have to do so.

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I have to strap Ruen column.

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OK, so if this was the rule.

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Now, make it clear if this was the second rule, make it second column, if this was the third rule,

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then make it third column.

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OK, very, very simple.

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We are just swapping rules and columns.

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OK, now the second step, basically, I have to reverse each rule.

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So now let's reverse this first rule.

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So it will become seven for one.

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Now let us reverse the second rule.

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So it will become eight five to reverse the third rule.

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So it will become nine six three.

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OK, and you can match.

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So they both have same.

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OK, so if you follow these two steps first taking place first and then reverse each row, we will be

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able to soil our question.

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OK, now let's take one more example if you want to understand it.

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OK, let's take one more example.

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So basically, let's take this one example, the example which is given in the question.

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OK.

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We just have to follow two steps, transpose and then reverse each.

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OK, so let us take the transpose.

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The first step, first step is basically taking the task force.

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Big task force means we're perusing columns.

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So if this is the first rule, I will make it first column.

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So this is five one nine 11.

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This is the second rule.

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Make it second column so it will become two four eight.

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And then this is the third rule.

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Make it third column.

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So 13, three, six and seven.

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This is the fourth rule.

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Make it fourth column.

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OK, so this will be 15, then 14, then 12 and then 16.

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OK, so after this, after the first step, what is the second step to second steps is reverse each

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rule.

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OK, we will reverse each rule.

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Every single rule will be reversed.

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OK, so now let's reverse this little so it will be basically 15, then 13, then two and then five,

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now reverse this rule.

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So this is 14, then three, then four, then one reversed this rule.

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So it is 12, then six, then eight, then nine.

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Now reverse this rule.

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So this will be 16, then seven, then 10 and then 11.

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OK, now you can match.

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OK, so they both have some.

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OK, they both have him, so basically our goal is going to be look very, very simple.

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First, I will write the code for taking the transpose, which is nothing, just rows and columns.

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And the second is basically I will reverse the Egil.

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OK, now what will be the time and the space complexity?

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So first, I am digging transport.

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So how much time it will take?

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So simply it will take into account the dimensions of the matrix that and so I have to go through each

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and every element.

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So it will take an enduring time and then I have to reverse each rule.

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OK, so what I will do, I will go through each and every rule and I will take the reverse.

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So bless and doing OK for reversing each rule.

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So basically, if you will add these two sort time complexities basically and square.

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And the space complexities basically are drawn, OK?

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We are we will not use any extra space.

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So this is the time and the space complexity for the solution.

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OK, digging transports and reversing each little.

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OK, so now let us write the code if you understood the logic.

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OK, so the government has basically passed by reference, OK, so we have to do changes in the government

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only we do not have to create new metrics.

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OK, we have to solve this question in place.

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So the meaning of this is basically the changes in the same metrics.

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OK, do not allocate any extra space.

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So now let us write the code.

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So first let us find out how many rules and columns are present.

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OK, so.

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Let's call it Immonen.

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OK, so this is basically tech, Start says.

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And what is and so this is metrics of zero Dorseys.

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Now, after finding out this is what you have to do, so basically first step, we have to take the

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transport.

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And passement means sabras in columns.

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OK, we will swap roles in columns, take the transpose.

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OK, so now let us write the code for taking the task force.

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Zero equals zero.

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Is M Andrew Placeless?

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Then column so column will start from the.

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Then Collum less than N and then column placeless.

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Now, what we have to do, so basically I have to strap rows and columns, so this is basically a matrix

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of.

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Column, Animatrix of column.

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OK, very simple.

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So basically at this point.

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Our task force is done now what we have to do.

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I have to reverse each second step.

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So the second step is basically.

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The reverse is true.

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OK, so what we'll do, I will go through each and every rule and I will reverse them.

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So I have to go through each and every rule, so I loop for going through each and every rule.

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Total Ambros out there.

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OK.

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Now, how to reverse so we know how to reverse.

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OK, so considering that now, if you want to give us an idea what we will do, it will take two point

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that you have a start point out here and you will pick and point out here.

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And similarly what you will do, you will start point and point to the starting point and move in this

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direction and move in this direction.

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So we will able to start placeless.

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I will do anything minus minus.

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I will continue.

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This thing will basically start is less than ideal and or you can write and will start this Lieutenant.

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OK.

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Now, let us create a start and end point, so the start point that will be at zero position.

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And that will be out basically and minus one politician, OK, and is the number of columns.

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Now, while it's this list than ideal Westwind, what do you have to do, you will slap.

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OK, so I have to step.

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Railways fixed, the value of roads fixed.

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OK, I'm reversing that.

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So start and similarly mattocks of is fixed basically and the column is variable, so it will be end.

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OK, I'm scrapping the start in the end.

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Point out what I will do.

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I'm I will do start placeless slightly.

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Move ahead.

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I will do end minus minus.

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OK, now our second step is also done.

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OK, so our first step taking transpose, our second step reversing the arrow.

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Now I think our goal will work fine.

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OK, now let us try to run our code and then we will try to submit.

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OK, so we are getting wrong on, so that means we did something wrong.

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Let's see.

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OK, so the mistake is basically.

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I forgot to initialize a rule.

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OK, so what is happening here is if you will see it carefully.

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So if this is the matrix, so I want my taxes, particularly one, two, three, then four, five,

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six, and then seven, eight, nine.

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OK, now let us take the transport.

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So it starts both will basically be one, two, three, then four, five, six, and then seven, eight

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and nine.

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OK, so our first rule is basically one four seven.

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So this is one four seven.

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Then our second rule is basically to five, eight to five it then our third rule is basically three

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six nine.

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So this is the third rule.

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OK, basically what we are doing, our reverse function is not locking.

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OK, our rivers function is not working because you can see here I forgot to initialize it all with

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zero.

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OK, will be initialized with zero.

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So now let us do the correction.

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So will be initialized to zero.

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OK, now this is correct, after initially said over zero, so now Ladson.

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OK, so our court is working fine now let us strive to submit our good.

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OK, so our goal is working fine.

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Now, as discussed, what is the time Diamond, the space complexity, so we know the time complexity

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is basically order off and then you can say and square because it is a given that the dimensions are

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increasing, OK, and the space complexity is basically ordered offline.

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OK, now let's discuss some good examples.

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So here in discussion.

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Let us talk about some more informations.

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OK, so the given question is basically so if we have to rotate the metrics by 90 degrees clockwise

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direction, so that means plus 90.

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OK, so 90 degrees clockwise direction, so clockwise I'm taking place.

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OK, so we have to rotate by plus degree, rotate by plus 90 degrees.

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Then the approach is very simple.

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First, big the transport and then reverse each.

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OK, big transports and reverse each.

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Now, if the question is basically rotate by minus 90 degree, if this is the question, rotate by minus

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90 degrees or minus means in the anticlockwise direction.

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OK, so what I will do, I will take the transport.

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And then basically, I will reverse each column.

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OK, so instead of reversing each rule, I will reverse each column.

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Simple.

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Now if the question is basically rotate by plus 180 degrees, that means 180 degrees in the clockwise

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direction.

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So there are two ways to solve this question.

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OK, so the first rule is basically what I will do.

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So I will follow this approach.

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I will rotate by plus 90 degree.

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I will rotate where plus 90 degrees and I will perform this step two times.

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OK, I will perform the rotation by 90 degree two times, OK, rotation by 90 degrees two times.

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So it will be plus 180 degrees.

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Now, the second step basically is very simple.

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What we will do, you will reverse.

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So basically there are two ways.

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So this is the first.

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We rotate by 90 degrees two times.

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Secondly, to solve this question is basically reverse each rule.

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And also the first column was each row and reverse each column.

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OK, now the fourth type of problem can be I have to rotate by minus 180.

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That means 180 degrees in the anticlockwise direction.

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OK, so again, there are three steps to solve this problem.

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OK, so basically there are three ways to solve this problem.

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So first rate is basically what I will do.

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I will rotate by minus 90 degrees and I will do the rotation by minus 90 degrees two times.

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OK.

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I will rotate by minus 90 degrees and I will do it two times, so in total it will be minus 180 degree

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simple.

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Now, the second way is basically what you can do.

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You will reverse each column and then basically you will reverse each rule.

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OK, so this is the second we.

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The third way is basically rotate by minus 180 degree is basically the same as.

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Rotate by plus 180 degree.

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OK, so the AC.

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OK, so if you will rotate by minus 180 degrees or you will rotate way plus 180 degrees.

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Basically, they both are saying, OK, you can take an example to see yourself.

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OK, so these these are four types of problem.

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If you have to rotate by plus 90 degree that we have already solved, transpose and reverse each little

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second is basically minus 180 degrees, again, transposed to reverse each column.

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That is basically the third type of question can be rotate by plus 180 degrees.

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So the first rate is always this one plus nine to the rotation by plus 90 degree and make it two times.

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OK, the second one is basically you will reverse each rule and reverse each column and minus 180 degrees

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again, but from the rotation by minus 90 degrees two times or the second way to basically reverse each

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column, then reverse each row.

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And third, which is basically rotation by a minus 180 degree or rotation by plus 180 degree, they

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both are saying, OK, now plus means clockwise direction, minus Miss Anticlockwise Direction.

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OK.

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OK, so this is not anticlockwise, this is anticlockwise, OK, so I remembered.

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So this is not clockwise.

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This is not anticlockwise.

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Anticlockwise is this one.

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And similarly, so this is minus.

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So this is anticlockwise.

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OK, sorry, I'm very sorry.

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So this is minus decis anticlockwise.

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OK, finally, this is clockwise in the direction of glogg and this is anticlockwise opposite to the

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direction of Gloc.

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OK, so if you have any doubt in this question, you can ask me.

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OK, one more thing.

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The time, complexity and all the solution will be emon.

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And the space complexity will be open.

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OK, we are just traversing through each and every element.

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OK, so thank you.