Compute The Middle Index

Java:

int left = ...;
int right = ...;
int middle = (right - left) / 2 + left;

Alternatively:

int middle = (left + right) / 2;

Proof:

(right - left) / 2 + left = (left + right) / 2
right - left + left * 2 = left + right
right + left = left + right 

The second method is much simpler to understand and compute.