# Write a recursive algorithm for binary search

O 1 In computer sciencebinary search, also known as half-interval search,  logarithmic search,  or binary chop,  is a search algorithm that finds the position of a target value within a sorted array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. Either that is the item we are looking for or it is not. Either way, we are done. The maximum number of comparisons is logarithmic with respect to the number of items in the list.

One additional analysis issue needs to be addressed. In the recursive solution shown above, the recursive call, binarySearch alist[: The analysis that we did above assumed that the slice operator takes constant time. However, we know that the slice operator in Python is actually O k. This means that the binary search using slice will not perform in strict logarithmic time.

## JAVA EXAMPLE PROGRAMS

Luckily this can be remedied by passing the list along with the starting and ending indices. The indices can be calculated as we did in Listing 3. We leave this implementation as an exercise. Even though a binary search is generally better than a sequential search, it is important to note that for small values of n, the additional cost of sorting is probably not worth it. In fact, we should always consider whether it is cost effective to take on the extra work of sorting to gain searching benefits. If we can sort once and then search many times, the cost of the sort is not so significant. However, for large lists, sorting even once can be so expensive that simply performing a sequential search from the start may be the best choice.

Suppose you have the following sorted list [3, 5, 6, 8, 11, 12, 14, 15, 17, 18] and are using the recursive binary search algorithm. Which group of numbers correctly shows the sequence of comparisons used to find the key 8. A 11, 5, 6, 8 Looks like you might be guilty of an off-by-one error.

Remember the first position is index 0. B 12, 6, 11, 8 Binary search starts at the midpoint and halves the list each time.

C 3, 5, 6, 8 Binary search does not start at the beginning and search sequentially, its starts in the middle and halves the list after each compare.

D 18, 12, 6, 8 It appears that you are starting from the end and halving the list each time. Which group of numbers correctly shows the sequence of comparisons used to search for the key 16?

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A 11, 14, 17 Looks like you might be guilty of an off-by-one error. B 18, 17, 15 Remember binary search starts in the middle and halves the list. C 14, 17, 15 Looks like you might be off by one, be careful that you are calculating the midpont using integer arithmetic.

D 12, 17, 15 Binary search starts at the midpoint and halves the list each time. It is done when the list is empty. Created using Runestone 2.Binary Search: The non-recursive binary search on the left is a function you've seen before.

It maintains a range between two variables low high. This range is cut roughly in half at each step of the algorithm. Binary Search: The non-recursive binary search on the left is a function you've seen before.

It maintains a range between two variables low high. This range is cut roughly in half at each step of the algorithm. Binary Search Algorithm and its Implementation. In our previous tutorial we discussed about Linear search algorithm which is the most basic algorithm of searching which has some disadvantages in terms of time complexity, so to overcome them to a level an algorithm based on dichotomic (i.e.

selection between two distinct alternatives) divide and conquer technique is used i.e. Binary search. Given a sorted array arr[] of n elements, write a function to search a given element x in arr[]. A simple approach is to do linear ph-vs.com time complexity of above algorithm is O(n).

Another approach to perform the same task is using Binary Search. Binary Search: Search a sorted array by. Description: Write a program to reverse a number using numeric operations. Below example shows how to reverse a number using numeric operations. Binary Search Algorithm | Recursive & Iterative Implementation Given a sorted array of integers and a target value, find out if a target exists in the array or not in .

Data Structures and Algorithms Binary Search Tree