# Uniform Binary Search

Uniform Binary Search is an optimization of Binary Search algorithm when many searches are made on same array or many arrays of same size. In normal binary search, we do arithmetic operations to find the mid points. Here we precompute mid points and fills them in lookup table. The array look-up generally works faster than arithmetic done (addition and shift) to find the mid point.

Examples:

```Input : array={1, 3, 5, 6, 7, 8, 9}, v=3
Output : Position of 3 in array = 2

Input :array={1, 3, 5, 6, 7, 8, 9}, v=7
Output :Position of 7 in array = 5
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The algorithm is very similar to Binary Search algorithm, The only difference is a lookup table is created for an array and the lookup table is used to modify the index of the pointer in the array which makes the search faster . Instead of maintaining lower and upper bound the algorithm maintains an index and the index is modified using the lookup table.

## C++

 `// C++ implemenatation of above approach ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `MAX_SIZE = 1000; ` ` `  `// lookup table ` `int` `lookup_table[MAX_SIZE]; ` ` `  `// create the lookup table ` `// for an array of length n ` `void` `create_table(``int` `n) ` `{ ` `    ``// power and count variable ` `    ``int` `pow` `= 1; ` `    ``int` `co = 0; ` `    ``do` `{ ` `        ``// multiply by 2 ` `        ``pow` `<<= 1; ` ` `  `        ``// initialize the lookup table ` `        ``lookup_table[co] = (n + (``pow` `>> 1)) / ``pow``; ` `    ``} ``while` `(lookup_table[co++] != 0); ` `} ` ` `  `// binary search ` `int` `binary(``int` `arr[], ``int` `v) ` `{ ` `    ``// mid point of the array ` `    ``int` `index = lookup_table - 1; ` ` `  `    ``// count ` `    ``int` `co = 0; ` ` `  `    ``while` `(lookup_table[co] != 0) { ` ` `  `        ``// if the value is found ` `        ``if` `(v == arr[index]) ` `            ``return` `index; ` ` `  `        ``// if value is less than the mid value ` `        ``else` `if` `(v < arr[index]) ` `            ``index -= lookup_table[++co]; ` ` `  `        ``// if value is greater than the mid value ` `        ``else` `            ``index += lookup_table[++co]; ` `    ``} ` `} ` ` `  `// main function ` `int` `main() ` `{ ` ` `  `    ``int` `arr[] = { 1, 3, 5, 6, 7, 8, 9 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` ` `  `    ``// create the lookup table ` `    ``create_table(n); ` ` `  `    ``// print the position of the array ` `    ``cout << ``"Position of 3 in array = "`  `         ``<< binary(arr, 3) << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implemenatation of above approach  ` `class` `GFG ` `{ ` `     `  `    ``static` `int` `MAX_SIZE = ``1000``;  ` `     `  `    ``// lookup table  ` `    ``static` `int` `lookup_table[] = ``new` `int``[MAX_SIZE];  ` `     `  `    ``// create the lookup table  ` `    ``// for an array of length n  ` `    ``static` `void` `create_table(``int` `n)  ` `    ``{  ` `        ``// power and count variable  ` `        ``int` `pow = ``1``;  ` `        ``int` `co = ``0``;  ` `        ``do`  `        ``{  ` `            ``// multiply by 2  ` `            ``pow <<= ``1``;  ` `     `  `            ``// initialize the lookup table  ` `            ``lookup_table[co] = (n + (pow >> ``1``)) / pow;  ` `        ``} ``while` `(lookup_table[co++] != ``0``);  ` `    ``}  ` `     `  `    ``// binary search  ` `    ``static` `int` `binary(``int` `arr[], ``int` `v)  ` `    ``{  ` `        ``// mid point of the array  ` `        ``int` `index = lookup_table[``0``] - ``1``;  ` `     `  `        ``// count  ` `        ``int` `co = ``0``;  ` `     `  `        ``while` `(lookup_table[co] != ``0``)  ` `        ``{  ` `     `  `            ``// if the value is found  ` `            ``if` `(v == arr[index])  ` `                ``return` `index;  ` `     `  `            ``// if value is less than the mid value  ` `            ``else` `if` `(v < arr[index])  ` `            ``{ ` `                ``index -= lookup_table[++co];  ` `                ``return` `index; ` `            ``} ` `             `  `            ``// if value is greater than the mid value  ` `            ``else` `            ``{ ` `                ``index += lookup_table[++co]; ` `                ``return` `index; ` `            ``} ` `        ``}  ` `        ``return` `index ; ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{  ` `     `  `        ``int` `arr[] = { ``1``, ``3``, ``5``, ``6``, ``7``, ``8``, ``9` `};  ` `        ``int` `n = arr.length;  ` `     `  `        ``// create the lookup table  ` `        ``create_table(n);  ` `     `  `        ``// print the position of the array  ` `        ``System.out.println( ``"Position of 3 in array = "` `+  ` `                                    ``binary(arr, ``3``)) ; ` `     `  `     `  `    ``}  ` `} ` ` `  `// This code is contributed by Ryuga `

## Python3

 `# Python3 implemenatation of above approach ` ` `  `MAX_SIZE ``=` `1000` ` `  `# lookup table ` `lookup_table ``=` `[``0``] ``*` `MAX_SIZE ` ` `  `# create the lookup table ` `# for an array of length n ` `def` `create_table(n): ` `     `  `    ``# power and count variable ` `    ``pow` `=` `1` `    ``co ``=` `0` `    ``while` `True``: ` `         `  `        ``# multiply by 2 ` `        ``pow` `<<``=` `1` ` `  `        ``# initialize the lookup table ` `        ``lookup_table[co] ``=` `(n ``+` `(``pow` `>> ``1``)) ``/``/` `pow` `        ``if` `lookup_table[co] ``=``=` `0``: ` `            ``break` `        ``co ``+``=` `1` ` `  `# binary search ` `def` `binary(arr, v): ` `     `  `    ``# mid point of the array ` `    ``index ``=` `lookup_table[``0``] ``-` `1` ` `  `    ``# count ` `    ``co ``=` `0` ` `  `    ``while` `lookup_table[co] !``=` `0``: ` ` `  `        ``# if the value is found ` `        ``if` `v ``=``=` `arr[index]: ` `            ``return` `index ` ` `  `        ``# if value is less than the mid value ` `        ``elif` `v < arr[index]: ` `            ``co ``+``=` `1` `            ``index ``-``=` `lookup_table[co] ` ` `  `        ``# if value is greater than the mid value ` `        ``else``: ` `            ``co ``+``=` `1` `            ``index ``+``=` `lookup_table[co] ` ` `  `# main function ` `arr ``=` `[``1``, ``3``, ``5``, ``6``, ``7``, ``8``, ``9``] ` `n ``=` `len``(arr) ` ` `  `# create the lookup table ` `create_table(n) ` ` `  `# print the position of the array ` `print``(``"Position of 3 in array = "``, binary(arr, ``3``)) ` ` `  `# This code is contributed by divyamohan123 `

## C#

 `// C# implemenatation of above approach  ` `using` `System; ` `     `  `class` `GFG ` `{ ` `     `  `    ``static` `int` `MAX_SIZE = 1000;  ` `     `  `    ``// lookup table  ` `    ``static` `int` `[]lookup_table = ``new` `int``[MAX_SIZE];  ` `     `  `    ``// create the lookup table  ` `    ``// for an array of length n  ` `    ``static` `void` `create_table(``int` `n)  ` `    ``{  ` `        ``// power and count variable  ` `        ``int` `pow = 1;  ` `        ``int` `co = 0;  ` `        ``do` `        ``{  ` `            ``// multiply by 2  ` `            ``pow <<= 1;  ` `     `  `            ``// initialize the lookup table  ` `            ``lookup_table[co] = (n + (pow >> 1)) / pow;  ` `        ``} ``while` `(lookup_table[co++] != 0);  ` `    ``}  ` `     `  `    ``// binary search  ` `    ``static` `int` `binary(``int` `[]arr, ``int` `v)  ` `    ``{  ` `        ``// mid point of the array  ` `        ``int` `index = lookup_table - 1;  ` `     `  `        ``// count  ` `        ``int` `co = 0;  ` `     `  `        ``while` `(lookup_table[co] != 0)  ` `        ``{  ` `     `  `            ``// if the value is found  ` `            ``if` `(v == arr[index])  ` `                ``return` `index;  ` `     `  `            ``// if value is less than the mid value  ` `            ``else` `if` `(v < arr[index])  ` `            ``{ ` `                ``index -= lookup_table[++co];  ` `                ``return` `index; ` `            ``} ` `             `  `            ``// if value is greater than the mid value  ` `            ``else` `            ``{ ` `                ``index += lookup_table[++co]; ` `                ``return` `index; ` `            ``} ` `        ``}  ` `        ``return` `index ; ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main ()  ` `    ``{  ` `     `  `        ``int` `[]arr = { 1, 3, 5, 6, 7, 8, 9 };  ` `        ``int` `n = arr.GetLength(0);  ` `     `  `        ``// create the lookup table  ` `        ``create_table(n);  ` `     `  `        ``// print the position of the array  ` `    ``Console.WriteLine( ``"Position of 3 in array = "` `+  ` `                                    ``binary(arr, 3)) ; ` `     `  `     `  `    ``}  ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:

```Position of 3 in array = 1
```

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