All , I have a question for you . We are given a set of points in 2-D plane . we need to form a square centered at origin such that it has max perimeter and does not encloses any of those points . Can you answer this , or can you atleast refer me resources from where can i study this. your reply is greatly appreciated. kindly do not downvote this post, you can get answer if someone replies.

One possible solution is to binary search over the angle (rotate the square). Let $$$p$$$ be the nearest point to the origin. Let $$$\vec{p}$$$ be the position vector $$$p$$$. Let one angle be the angle the square points when the side is perpendicular to $$$\vec{p}$$$ and is touching $$$p$$$. The other angle is the angle the corner makes when the corner touches $$$p$$$. For an arbitrary angle between these two, the side length changes such that a side touches $$$p$$$.

can you provide me with a code for that ? a google link or so.

The code will be a little messy. Draw two squares, one with the corner touching $$$p$$$ (smallest square), and the other with the side touching $$$p$$$ (largest square possible). Now imagine rotating the smaller square to form the larger one while touching $$$p$$$. One of these intermediate squares is the most optimal square.

So, the

side touching psquare will be the largest if it touches the middle point of any side. And as we don't what the middle point can be, we need toBinary Searchright?In essence, yes. Point $$$p$$$ can be anywhere from the midpoint of the side to the corner. Binary search over the position of $$$p$$$.

Do the points and the square's co-ordinates have to be integers?

no

Can I have the problem link?

" kindly do not downvote this post". Weep bro weep..... Ro do tum ro do:p

You can represent your square boundaries by 4 points, ymin, ymax, xmin and xmax. Let's try to bound them.

For every point just relax these 4 points. Side of square should be absMin(ymix, ymax, xmin, xmax).

absMin(int...) is minimum over absolute values.