Code at boundary conditions

I am new to codechef.I am unable to solve problems in even the easy levels.

There are always some runtime errors because i cannot allocate an data structure(array) with this much elements and so on.So by brute force method u can’t develop a solution for these problems.
So what are the pre-requisites that i should study.I was solving lowest sum problem at easy level.I got a runtime error because of you can’t declare array with large number of elements like 100000 in C.

So i mean to say though i understand the problem statement and code it,my code works for small test cases but they are unable to satisfy the boundary ones.
So,how do i need to transform my approach so that my code works for boundary conditions and what are pre-requisites for that.
Sometime i also read the approach the below link of the problem like i did in the lowest sum and i was unable to understand the approach too.

Also can anybody take an easy example problem whose input data is large enough that u can’t declare an array statically or dynamically and the approach used?

Ok i would take the example.
eg.Lowest sum at easy level.

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