# Meta Binary Search | One-Sided Binary Search

• Difficulty Level : Medium
• Last Updated : 27 Apr, 2021

Meta binary search (also called one-sided binary search by Steven Skiena in The Algorithm Design Manual on page 134) is a modified form of binary search that incrementally constructs the index of the target value in the array. Like normal binary search, meta binary search takes O(log n) time.

Examples:

```Input: [-10, -5, 4, 6, 8, 10, 11], key_to_search = 10
Output: 5

Input: [-2, 10, 100, 250, 32315], key_to_search = -2
Output: 0```

The exact implementation varies, but the basic algorithm has two parts:

1. Figure out how many bits are necessary to store the largest array index.
2. Incrementally construct the index of the target value in the array by determining whether each bit in the index should be set to 1 or 0.

Approach:

1. Store number of bits to represent the largest array index in variable lg.
2. Use lg to start off the search in a for loop.
3. If the element is found return pos.
4. Otherwise, incrementally construct an index to reach the target value in the for loop.
5. If element found return pos otherwise -1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of above approach`` ` `#include ``#include ``#include ``using` `namespace` `std;`` ` `// Function to show the working of Meta binary search``int` `bsearch``(vector<``int``> A, ``int` `key_to_search)``{``    ``int` `n = (``int``)A.size();``    ``// Set number of bits to represent largest array index``    ``int` `lg = log2(n-1)+1; `` ` `    ``//while ((1 << lg) < n - 1)``        ``//lg += 1;`` ` `    ``int` `pos = 0;``    ``for` `(``int` `i = lg ; i >= 0; i--) {``        ``if` `(A[pos] == key_to_search)``            ``return` `pos;`` ` `        ``// Incrementally construct the``        ``// index of the target value``        ``int` `new_pos = pos | (1 << i);`` ` `        ``// find the element in one``        ``// direction and update position``        ``if` `((new_pos < n) && (A[new_pos] <= key_to_search))``            ``pos = new_pos;``    ``}`` ` `    ``// if element found return pos otherwise -1``    ``return` `((A[pos] == key_to_search) ? pos : -1);``}`` ` `// Driver code``int` `main(``void``)``{`` ` `    ``vector<``int``> A = { -2, 10, 100, 250, 32315 };``    ``cout << ``bsearch``(A, 10) << endl;`` ` `    ``return` `0;``}`` ` `// This implementation was improved by Tanin`

## Java

 `//Java implementation of above approach ``import` `java.util.Vector;``import` `com.google.common.math.BigIntegerMath;``import` `java.math.*;`` ` `class` `GFG {`` ` `// Function to show the working of Meta binary search ``    ``static` `int` `bsearch(Vector A, ``int` `key_to_search) {``        ``int` `n = (``int``) A.size();``        ``// Set number of bits to represent largest array index``        ``int` `lg = BigIntegerMath.log2(BigInteger.valueOf(n-``1``),RoundingMode.UNNECESSARY) + ``1``;``  ` `        ``//while ((1 << lg) < n - 1) {``        ``//    lg += 1;``        ``//}`` ` `        ``int` `pos = ``0``;``        ``for` `(``int` `i = lg - ``1``; i >= ``0``; i--) {``            ``if` `(A.get(pos) == key_to_search) {``                ``return` `pos;``            ``}`` ` `            ``// Incrementally construct the ``            ``// index of the target value ``            ``int` `new_pos = pos | (``1` `<< i);`` ` `            ``// find the element in one ``            ``// direction and update position ``            ``if` `((new_pos < n) && (A.get(new_pos) <= key_to_search)) {``                ``pos = new_pos;``            ``}``        ``}`` ` `        ``// if element found return pos otherwise -1 ``        ``return` `((A.get(pos) == key_to_search) ? pos : -``1``);``    ``}`` ` `// Driver code ``    ``static` `public` `void` `main(String[] args) {``        ``Vector A = ``new` `Vector();``        ``int``[] arr = {-``2``, ``10``, ``100``, ``250``, ``32315``};``        ``for` `(``int` `i = ``0``; i < arr.length; i++) {``            ``A.add(arr[i]);``        ``}``        ``System.out.println(bsearch(A, ``10``));``    ``}``}`` ` `// This code is contributed by 29AjayKumar``// This implementation was improved by Tanin`

## Python 3

 `# Python 3 implementation of ``# above approach`` ` `# Function to show the working``# of Meta binary search``import` `math``def` `bsearch(A, key_to_search):`` ` `    ``n ``=` `len``(A)``    ``# Set number of bits to represent``    ``lg ``=` `int``(math.log2(n``-``1``)) ``+` `1``;`` ` `    ``# largest array index``    ``#while ((1 << lg) < n - 1):``        ``#lg += 1`` ` `    ``pos ``=` `0``    ``for` `i ``in` `range``(lg ``-` `1``, ``-``1``, ``-``1``) :``        ``if` `(A[pos] ``=``=` `key_to_search):``            ``return` `pos`` ` `        ``# Incrementally construct the``        ``# index of the target value``        ``new_pos ``=` `pos | (``1` `<< i)`` ` `        ``# find the element in one``        ``# direction and update position``        ``if` `((new_pos < n) ``and` `            ``(A[new_pos] <``=` `key_to_search)):``            ``pos ``=` `new_pos`` ` `    ``# if element found return``    ``# pos otherwise -1``    ``return` `(pos ``if``(A[pos] ``=``=` `key_to_search) ``else` `-``1``)`` ` `# Driver code``if` `__name__ ``=``=` `"__main__"``:`` ` `    ``A ``=` `[ ``-``2``, ``10``, ``100``, ``250``, ``32315` `]``    ``print``( bsearch(A, ``10``))`` ` `# This implementation was improved by Tanin`` ` `# This code is contributed``# by ChitraNayal`

## C#

 `//C# implementation of above approach ``using` `System;``using` `System.Collections.Generic;`` ` `class` `GFG ``{`` ` `    ``// Function to show the working of Meta binary search ``    ``static` `int` `bsearch(List<``int``> A, ``int` `key_to_search)``    ``{``        ``int` `n = (``int``) A.Count;``        ``//int lg = 0;``        ``// Set number of bits to represent largest array index ``        ``int` `lg = (``int``)Math.Log(n-1, 2.0) + 1;``          ` `        ``// This is redundant and will cause error``        ``//while ((1 << lg) < n - 1)``        ``//{``        ``//    lg += 1;``        ``//}`` ` `        ``int` `pos = 0;``        ``for` `(``int` `i = lg - 1; i >= 0; i--)``        ``{``            ``if` `(A[pos] == key_to_search)``            ``{``                ``return` `pos;``            ``}`` ` `            ``// Incrementally construct the ``            ``// index of the target value ``            ``int` `new_pos = pos | (1 << i);`` ` `            ``// find the element in one ``            ``// direction and update position ``            ``if` `((new_pos < n) && (A[new_pos] <= key_to_search))``            ``{``                ``pos = new_pos;``            ``}``        ``}`` ` `        ``// if element found return pos otherwise -1 ``        ``return` `((A[pos] == key_to_search) ? pos : -1);``    ``}`` ` `    ``// Driver code ``    ``static` `public` `void` `Main()``    ``{``        ``List<``int``> A = ``new` `List<``int``>();``        ``int``[] arr = {-2, 10, 100, 250, 32315};``        ``for` `(``int` `i = 0; i < arr.Length; i++) ``        ``{``            ``A.Add(arr[i]);``        ``}``        ``Console.WriteLine(bsearch(A, 10));``    ``}``}`` ` `// This code is contributed by Rajput-Ji``// This implementation was improved by Tanin`

## PHP

 `= 0; ``\$i``--) ``    ``{``        ``if` `(``\$A``[``\$pos``] == ``\$key_to_search``)``            ``return` `\$pos``;`` ` `        ``// Incrementally construct the``        ``// index of the target value``        ``\$new_pos` `= ``\$pos` `| (1 << ``\$i``);`` ` `        ``// find the element in one``        ``// direction and update \$position``        ``if` `((``\$new_pos` `< ``\$n``) && ``            ``(``\$A``[``\$new_pos``] <= ``\$key_to_search``))``            ``\$pos` `= ``\$new_pos``;``    ``}`` ` `    ``// if element found return \$pos ``    ``// otherwise -1``    ``return` `((``\$A``[``\$pos``] == ``\$key_to_search``) ? ``                              ``\$pos` `: -1);``}`` ` `// Driver code``\$A` `= [ -2, 10, 100, 250, 32315 ];``\$ans` `= bsearch(``\$A``, 10, 5);``echo` `\$ans``;`` ` `// This code is contributed by AdeshSingh1``// This implementation was improved by Tanin``?>`

## Javascript

 ``
Output:
`1`

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