Unbounded Binary Search

Given a monotonically increasing function f(x), find the value of x where f(x) becomes positive for the first time. In other words, find a positive integer x such that f(x-1), f(x-2),… are negative and f(x+1), f(x+2),… are positive.

Find the odd occurring element in log(n) time

Given an array of integers where every element appears even number of times except one element which appears odd number of times, find that odd occurring element in O(log(n)) time and constant space.

Search in a nearly sorted array in log(n) time

Given a nearly sorted array such that each of the N elements may be misplaced by no more than one position from the correct sorted order, efficiently search a given element in it. Report if the element is not present in the input array.