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Welcome back.

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Let's now discuss how to code the is valid function for a box.

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In particular.

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Remember we had discussed the three rules which have to be satisfied for us to be able to fill a particular

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value at an empty cell.

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So basically the three rules were that that particular value should not be there in the same row, in

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the same column, and in the box, which is the box where that particular empty cell is located.

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Now the row check and the column check are pretty easy and straightforward.

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So we will just implement that in code.

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We can just use a for loop for this.

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But now let's go ahead and discuss how we can code the box check.

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Now logically it's pretty easy to think about this.

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We just need to ensure that if you are filling this cell, then whatever value we are going to fill

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over here should not have happened or occurred in the box in this box over here.

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But then how do we code this.

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So let's go ahead and discuss that.

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So over here we are given this board.

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And for a given row and column let's see how to check whether the value that we are considering is valid

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for the box.

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Which the row and column is part of.

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So for this, let's take an example.

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Let's say row is equal to two and column is equal to three.

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So the indices over here are 0 to 8.

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So row equal to two would be this row and column is equal to three.

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Is this column.

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So we are dealing with this particular empty cell.

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Now visually it's easy to see that it's part of this box over here.

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But then how do we do that as part of code.

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So let's make some space over here.

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Now notice that the values that we need or the combinations of row and column that we need to check

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the values already there in this box are rows 0 to 1 and column 3 to 5.

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So rows 0 to 1 and column 3 to 5.

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So all these combinations are required like for example 03040513.

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One, four, one five, two three, two four and two five.

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So now let's see how we can get these combinations.

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Now we will use again a for loop.

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And let's say we are iterating using a variable x that goes from zero up to eight.

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Now over here I'm going to write two expressions.

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Let's just see how this is useful.

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So the first expression over here is three into rows divided by three.

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And we are just taking the integer part when we are dividing plus x divided by three.

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Similarly three into column divided by three plus x modulo three.

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Now over here in this example, row is equal to two and column is equal to three.

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So when we do two divided by three we will get zero because we are just taking the integer part.

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We are getting 0.66.

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And we'll just take the integer part which is zero.

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And when we do three divided by three, we will get one.

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So let's write that over here.

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So this over here rows divided by three gives us zero.

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And then this is three by three which gives us one.

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And then one into three gives us three.

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So this whole part becomes three and three into zero is zero again.

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So this part over here is zero.

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And this part over here is three.

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Now let's quickly see what happens when x goes from 0 to 8.

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So when x is equal to zero.

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And one and two.

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Over here we have zero plus zero, which is zero.

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And then we have zero plus one by three.

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Again one by three is also zero.

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So zero by three is zero, one by three zero and two by three is zero.

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So for the values of zero, one and two we get zero, zero and zero when the values take the values

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from 3 to 5.

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Notice over here, three by three is one, four by three is one, and five by three is one.

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Because we're just taking the integer part.

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And zero plus one gives us one.

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So for three x equal to three four and five we get one one and one.

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And then for x is equal to six seven and eight six by three is two, seven by three is two and eight

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by three is two.

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So for the values of x from 6 to 8 we get two, two and two.

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Now what happens to columns when x is equal to zero?

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This part over here becomes zero modulo three which is equal to zero itself.

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So this three plus this zero gives us three.

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So when x is equal to zero we get the column as three.

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When x is equal to one, this part over here becomes one modulo three.

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Which is one itself and three.

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This three plus one gives us four.

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So when x is equal to one we get four.

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And when x is equal to two, we get two modulo three which is two and three plus two gives us five.

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Similarly, when x is equal to three, three modulo three is again zero.

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So notice that the pattern is repeating and three plus zero gives us three.

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And when x is equal to four again, for modulo three is equal to one and three plus one is equal to

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four.

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So you can see that this pattern is repeating.

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So again we'll get four over here.

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And then we'll get five again we'll get three four and 5467 and eight.

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Now notice that zero comma three is this position over here.

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Zero comma four is this position zero comma five is this position one comma three is over here.

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One comma.

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Four is over here, one comma, five is over here, and two comma three is over here, two comma four

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is over here.

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And two comma five is over here.

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So using this we were able to iterate through all the positions in the box at hand.

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So this over here is very useful.

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So three into rows by three plus x by three and three into columns by three plus x percentage or modulo

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three.

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If we can use this, we can just use a for loop where we are iterating through the values 0 to 8 to

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go through all the row column combinations which are part of the box at hand.

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So we will make use of this while we code out the solution.