i have a simple equation of two variables say x and y such that x + y < 10^5 (this is a sort of constraint that i must obey). x and y can take only integer values.

now all i want to do is to maximise the equation consisting of these two variables x and y.

SO I have an equation like :

Ax + By (which i want to maxmise)

with constraints : x + y <= 10^5

where x,y can take only integer values

I googled a bit and this seems to be the case of integer linear programming which they say that is easier as compared to linear programming.

I am not able to figure out the algorithm that i need to know to maximise the equation efficiently. A simple brute force is not at all desirable to me, so I need something cool.

can you help me in figuring out the algorithm that i need to learn.(a brief explanation would be appreciated)

i often find it hard to read other's code than to write mine own version of code but competitive programming is not just all about writing codes. i have often heard people that you learn a lot when you read other's code whether its when you are trying to learn something out of other's code or you are trying to hack a solution in any contest.

can you throw some light on how one can increase his ability to read totally unfamiliar code easily and understand the algorithm working behind it swiftly.

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