Limitation of Binary Search: -

(i)  The complexity of Binary search is O (log2 n). The complexity is similar irrespective of the position of the element, even if it is not present in the array.

(ii)  The algorithm supposes that one has direct access to middle element in the list on a sub list. This means that the list must be kept in some type of array. Unfortunately inserting an element in an array requires element to be moved down the list and deleting an element from an array needs element to be moved up the list.

(iii) The list must be sorted.