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:
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. 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 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 repeatedly dividing the search interval in half. Begin with an interval covering the whole array.
Description: Write a program to reverse a number using numeric operations. Below example shows how to reverse a number using numeric operations.
This is a comprehensive catalog of quantum algorithms. If you notice any errors or omissions, please email me at [email protected] Recursive Binary Search Algorithm Given: The algorithm: Find the midpoint of the array; this will be the element at arr[size/2].
The midpoint divides the array into two smaller arrays: the lower half of the array consisting of elements 0 to midpoint - 1, and the upper half of the array consisting of elements midpoint to size - 1.
Interview question some engineer, asked me to write binary search in 2 ways, Also asked me to write binary search on a shifted array (10 20 1 2 3 4). 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.