# 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. 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? 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.

## Pseudocode

It is done when the list is empty. Created using Runestone 2.I really want to be able to write a much cleaner and efficient binary search algorithm, an alternative to what I've coded. I have seen examples of how recursion is used such as when doing factorial with numbers which I understand.

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 heartoftexashop.com time complexity of above algorithm is O(n).

Another approach to perform the same task is using Binary Search.

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Binary Search: Search a sorted array by. Binary search algorithm. Generally, to find a value in unsorted array, we should look through elements of an array one by one, until searched value is found. Stanford CS Education Library: this article introduces the basic concepts of binary trees, and then works through a series of practice problems with solution code in C/C++ and Java.

Binary trees have an elegant recursive pointer structure, so they make a good introduction to recursive pointer algorithms. If the item we are searching for is less than the middle item, we can simply perform a binary search of the left half of the original list. Likewise, if the item is greater, we can perform a binary search of the right half. Either way, this is a recursive call to the binary search function passing a smaller list.

 Binary Search Trees I The trick is to pick a midpoint near the center of the array, compare the data at that point with the data being searched and then responding to one of three possible conditions: Recursion is used in this algorithm because with each pass a new array is created by cutting the old one in half. JAVA EXAMPLE PROGRAMS Binary Tree PreOrder Traversal in Java - Recursion and Iteration Example Unlike linked list and array which can only be traversed linearly, there are several ways to traverse a binary tree. Binary Search Implementation Using C# Implement Binary search in java using recursive algorithm. A binary search or half-interval search algorithm finds the position of a specified value the input "key" within a sorted array. How Binary Search Works? Algorithm[ edit ] Binary search works on sorted arrays. Binary Tree PreOrder Traversal in Java - Recursion and Iteration Example Algorithm example[ edit ] An animation of the quicksort algorithm sorting an array of randomized values.

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 | Recursive & Iterative Implementation