The worst case is achieved when the integers are equal. + E n ) n log ) This is approximately equal to + Running time of binary search. + + 8 , then ( 2 ( time. A k Binary search can be implemented only on a sorted list of items. ) 4 {\displaystyle T} {\displaystyle T(n)=1+{\frac {I(n)}{n}}} 1 2 [46], Binary search has been generalized to work on certain types of graphs, where the target value is stored in a vertex instead of an array element. It compactly stores a collection of bits, with each bit representing a single key within the range of keys. generate link and share the link here. ) queries. log 10 2 ⁡ Binary search can be used to perform exact matching and set membership (determining whether a target value is in a collection of values). L ) in every iteration. − Therefore, time complexity of binary search algorithm is O(log 2 n) which is very efficient. , {\displaystyle E(n)=I(n)+2n=\left[(n+1)\left\lfloor \log _{2}(n+1)\right\rfloor -2^{\left\lfloor \log _{2}(n+1)\right\rfloor +1}+2\right]+2n=(n+1)(\lfloor \log _{2}(n)\rfloor +2)-2^{\lfloor \log _{2}(n)\rfloor +1}}, Substituting the equation for [4][5] Binary search compares the target value to the middle element of the array. ) [42], Instead of calculating the midpoint, interpolation search estimates the position of the target value, taking into account the lowest and highest elements in the array as well as length of the array. 1 Looking at the performance analysis of the two algorithms, it can be seen clearly, that … [14], In the binary tree representation, a successful search can be represented by a path from the root to the target node, called an internal path. ⁡ ⁡ log Since 23 is the middle element. ⌋ + = ) 2 4 0 n n into the equation for 1 [56], The idea of sorting a list of items to allow for faster searching dates back to antiquity. {\displaystyle L