Why use binary search if there's ternary search?
I recently heard about ternary search in which we divide an array into 3 parts and compare. Here there will be two comparisons but it reduces the array to n/3. Why don't people use this much?
Answer
Actually, people do use k-ary trees for arbitrary k.
This is, however, a tradeoff.
To find an element in a k-ary tree, you need around k*ln(N)/ln(k) operations (remember the change-of-base formula). The larger your k is, the more overall operations you need.
The logical extension of what you are saying is "why don't people use an N-ary tree for N data elements?". Which, of course, would be an array.