Binary search is more commonly used than ternary search for a few key reasons:
Binary search has a simpler implementation. In each iteration, you only need to compare the target value to the middle element and decide whether to search the left or right half. Ternary search requires two comparisons to determine whether to search the left, middle, or right third[1][2].
Binary search has a better time complexity in the worst case. The number of comparisons in binary search is $\log_2 n$, while for ternary search it is $\log_3 n$. Since $\log_2 n < \log_3 n$ for all $n > 1$, binary search will always have a lower upper bound on the number of comparisons[1][3].
Binary search is more cache-efficient. By halving the search space each iteration, binary search accesses memory in a more contiguous manner compared to ternary search. This leads to better cache utilization on modern process...
