Trying to understand the question(well spaced points ?) better
What is the correct output if the sorted array as 1, 2, 3, 4 ,5 ,6 and C is 3? 


Let us try. How about (1,2,3)? Too closely together. We should push away 3. (1,2,6) looks more far apart. Hmm, (1,2) is not good. (1, 3, 6) is the best.  


  What about if the sorted array as 1, 10, 11, 12, 23, 24, 25 and C is 3 ?


We should include the smallest and biggest numbers, 1 and 25. Then we should choose a number as close to the middle as possible. (1,12,25).

...

Let us analyze $\min_{i,j  \in S,i\ne j} |i-j|$. Suppose $S=\{a_1, a_2, \cdots, a_C\}$, where $a_k\le a_{k+1}$. Then
$$\min_{i,j  \in S,i\ne j} |i-j|=\min_{1\le k\lt C}|a_{k+1}-a_k|$$
since the difference between two non-adjacent numbers $a_k$ and $a_{k+t}$ must be greater than the difference between $a_k$ and $a_{k+1}$.

So the minimum difference among numbers in $S$ seems in "reverse proportion" to the difference between the adjacent or nearby numbers of the given array.

I will leave the above as a hint. Hopefully it is enough for you to figure out the rest.