# Binary search program in data structure

The drawbacks of sequential search can be eliminated by using Binary search algorithm. In binary search, it halves the size of the list to search in each iterations. It is faster then Linear search. Binary search requires sorted data to operate on since the data may not be contiguous like the pages of a book.

We cannot guess which quarter of the data the required item may be in. So we divide the list in the center each time. Typical example of binary search is searching for a page in a book. Suppose you were searching for page 6 in book of 20 pages.

You would first open it at random towards the later half of the book. If the page is less than 6, you would open at a page to the right, it is greater than 6 you would open at a page to the left, repeating the process till page 6 was found. As you can see, by the first instinctive search, you dramatically reduced the number of pages to search.

If the search takes the right path, there is a higher chance that the search will make the maximum number of comparisons. An internal path is any path from the root to an existing node. This is because internal paths represent the elements that the search algorithm compares to the target.

The lengths of these internal paths represent the number of iterations after the root node. Adding the average of these lengths to the one iteration at the root yields the average case. It turns out that the tree for binary search minimizes the internal path length. Knuth proved that the external path length the path length over all nodes where both children are present for each already-existing node is minimized when the external nodes the nodes with no children lie within two consecutive levels of the tree.

When each subtree has a similar number of nodes, or equivalently the array is divided into halves in each iteration, the external nodes as well as their interior parent nodes lie within two levels. It follows that binary search minimizes the number of average comparisons as its comparison tree has the lowest possible internal path length. The time complexity for this variation grows slightly more slowly, but at the cost of higher initial complexity.

Linear search has lower initial complexity because it requires minimal computation, but it quickly outgrows binary search in complexity. A modification to the half-interval search binary search method. Communications of the ACM. Journal of the ACM. Procedure is described at p. Lower bounds for intersection searching and fractional cascading in higher dimension PDF. Upper and Lower Bounds". Retrieved 28 March Journal of Computer and System Sciences.

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In Linear search algorithm searching begins with searching every element of the list till the required record is found. If the list is quite huge, then this approach is not optimal. The drawbacks of sequential search can be eliminated by using Binary search algorithm. In binary search, it halves the size of the list to search in each iterations. It is faster then Linear search. Binary search requires sorted data to operate on since the data may not be contiguous like the pages of a book.

We cannot guess which quarter of the data the required item may be in. So we divide the list in the center each time. Typical example of binary search is searching for a page in a book. Suppose you were searching for page 6 in book of 20 pages. You would first open it at random towards the later half of the book.