Write a recursive algorithm for binary search

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Write a recursive algorithm for binary search

This search algorithm works on the principle of divide and conquer. For this algorithm to work properly, the data collection should be in the sorted form. Binary search looks for a particular item by comparing the middle most item of the collection. If a match occurs, then the index of item is returned.

If the middle item is greater than the item, then the item is searched in the sub-array to the left of the middle item. Otherwise, the item is searched for in the sub-array to the right of the middle item.

This process continues on the sub-array as well until the size of the subarray reduces to zero. How Binary Search Works? For a binary search to work, it is mandatory for the target array to be sorted. We shall learn the process of binary search with a pictorial example.

The following is our sorted array and let us assume that we need to search the location of value 31 using binary search. So, 4 is the mid of the array.

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Now we compare the value stored at location 4, with the value being searched, i. We find that the value at location 4 is 27, which is not a match. As the value is greater than 27 and we have a sorted array, so we also know that the target value must be in the upper portion of the array.

We compare the value stored at location 7 with our target value The value stored at location 7 is not a match, rather it is more than what we are looking for. So, the value must be in the lower part from this location. Hence, we calculate the mid again.

This time it is 5. We compare the value stored at location 5 with our target value. We find that it is a match. We conclude that the target value 31 is stored at location 5.

Binary search halves the searchable items and thus reduces the count of comparisons to be made to very less numbers.The Fibonacci sequence is a sequence F n of natural numbers defined recursively.

write a recursive algorithm for binary search

F 0 = 0 F 1 = 1 F n = F n-1 + F n-2, if n>1. Task. Write a function to generate the n th Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow and are mostly used as an exercise in recursion).

Binary search is a fast search algorithm with run-time complexity of Ο(log n). This search algorithm works on the principle of divide and conquer. For this algorithm to work properly, the data collection should be in the sorted form.

In computer science, binary 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.

[4] [5] Binary search compares the target value to the middle element of the array. A binary search divides a range of values into halves, and continues to narrow down the field of search until the unknown value is found.

It is the classic example of a "divide and conquer" algorithm. A binary search tree is a binary tree data structure that works based on the principle of binary search. The records of the tree are arranged in sorted order, and each record in the tree can be searched using an algorithm similar to binary search, taking on average logarithmic time.

In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ()) is an unambiguous specification of how to solve a class of feelthefish.comthms can perform calculation, data processing and automated reasoning tasks..

As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function.

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