When calculating the midpoint in binary search, two approach are commonly used:

1. mid = left + (right - left) / 2 - This method prevents integer overflow by first cmoputing the interval length
2. mid = (left + right) / 2 - This simpler form may cause overflow with large values

The first approach is recommended for safety.

For boundary detection, we use inclusive boundss with additional range checks:

Left Boundary Search Implementation:

class BoundaryFinder {
    int findLeftEdge(int[] data, int key) {
        int low = 0;
        int high = data.length - 1;
        
        while (low <= high) {
            int center = low + (high - low) / 2;
            
            if (data[center] == key) {
                high = center - 1;
            } else if (data[center] < key) {
                low = center + 1;
            } else {
                high = center - 1;
            }
        }
        
        if (low >= data.length || data[low] != key) {
            return -1;
        }
        
        return low;
    }
}

Right Boundary Search Implementation:

class BoundaryFinder {
    int findRightEdge(int[] data, int key) {
        int low = 0;
        int high = data.length - 1;
        
        while (low <= high) {
            int center = low + (high - low) / 2;
            
            if (data[center] == key) {
                low = center + 1;
            } else if (data[center] < key) {
                low = center + 1;
            } else {
                high = center - 1;
            }
        }
        
        if (high < 0 || data[high] != key) {
            return -1;
        }
        
        return high;
    }
}