Given a square matrix of size Nxn where each cell is filled with a number between 9 and 9. A sub-square of size k is any set of k contiguous columns and k contiguous rows. For any sub-square, the sum of elements in its cells is called a sub-square sum. Given the Nx N square, write a program to find the maximum sub-square sum. Note that a 1 x 1 square (k=1) is not considered a sub-square.
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Answer:
Let the radius of circle be r and sides of square be a
According to question, we have
2πr+4a=k
a=
4
k−2πr
Sum of area will be
A=πr
2
+a
2
A=πr
2
+(
4
k−2πr
)
2
Now , we will calculate
dr
dA
dr
dA
=2πr+2(
16
k−2πr
)(−2π)
dr
dA
=0
at
r=
2(π+4)
k
Now,
dr
2
d
2
A
=2π+
2
π
2
>0
∴
at r=
2(π+4)
k
A has least value
then a=
(π+4)
k
putting the value of r in a=
4
k−2πr
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