# Binsearch not updating

### Binsearch not updating

In its simplest form, binary search is used to quickly find a value in a sorted sequence (consider a sequence an ordinary array for now).We’ll call the sought value the target value for clarity. At each step, the algorithm compares the median value in the search space to the target value.

I will now present another level of abstraction which will allow us to solve more problems, make proving binary search solutions very easy and also help implement them.Trying to use binary search on a container such as a linked list makes little sense and it is better use a plain linear search instead.C ’s Standard Template Library implements binary search in algorithms lower_bound, upper_bound, binary_search and equal_range, depending exactly on what you need to do. You’re best off using library functions whenever possible, since, as you’ll see, implementing binary search on your own can be tricky. A sequence (array) is really just a function which associates integers (indices) with the corresponding values.By lovro–Topcoder Member Discuss this article in the forums Binary search is one of the fundamental algorithms in computer science.In order to explore it, we’ll first build up a theoretical backbone, then use that to implement the algorithm properly and avoid those nasty off-by-one errors everyone’s been talking about.The logarithm is an awfully slowly growing function.

In case you’re not aware of just how efficient binary search is, consider looking up a name in a phone book containing a million names.

We use the predicate to verify if a candidate solution is legal (does not violate some constraint) according to the definition of the problem.

What we can call the main theorem states that binary search can be used if and only if for all x in S, p(x) implies p(y) for all y This is a series of no answers followed by a series of yes answers, as we were expecting.

The power of binary search begins to show now: not only do we need at most O(log N) comparisons to find the target value, but we also do not need to evaluate the function more than that many times.

Additionally, in this case we aren’t restricted by practical quantities such as available memory, as was the case with arrays.

Binary search maintains a contiguous subsequence of the starting sequence where the target value is surely located. Based on the comparison and because the sequence is sorted, it can then eliminate half of the search space.

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