# Queries for decimal values of subarrays of a binary array

• Difficulty Level : Medium
• Last Updated : 13 Jul, 2022

Given a binary array arr[], we to find the number represented by the subarray a[l..r]. There are multiple such queries.

Examples:

```Input :  arr[] = {1, 0, 1, 0, 1, 1};
l = 2, r = 4
l = 4, r = 5
Output : 5
3
Subarray 2 to 4 is 101 which is 5 in decimal.
Subarray 4 to 5 is 11 which is 3 in decimal.

Input : arr[] = {1, 1, 1}
l = 0, r = 2
l = 1, r = 2
Output : 7
3```

A Simple Solution is to compute decimal value for every given range using simple binary to decimal conversion. Here each query takes O(len) time where len is length of range.

An Efficient Solution is to do per-computations, so that queries can be answered in O(1) time.

The number represented by subarray arr[l..r] is arr[l]*+ arr[l+1]*….. + arr[r]*

1. Make an array pre[] of same size as of given array where pre[i] stores the sum of arr[j]*where j includes each value from i to n-1.
2. The number represented by subarray arr[l..r] will be equal to (pre[l] – pre[r+1])/.pre[l] – pre[r+1] is equal to arr[l]*+ arr[l+1]*+……arr[r]*. So if we divide it by , we get the required answer

Flowchart

Flowchart

Implementation:

## C++

 `// C++ implementation of finding number` `// represented by binary subarray` `#include ` `using` `namespace` `std;`   `// Fills pre[]` `void` `precompute(``int` `arr[], ``int` `n, ``int` `pre[])` `{` `    ``memset``(pre, 0, n * ``sizeof``(``int``));` `    ``pre[n - 1] = arr[n - 1] * ``pow``(2, 0);` `    ``for` `(``int` `i = n - 2; i >= 0; i--)` `        ``pre[i] = pre[i + 1] + arr[i] * (1 << (n - 1 - i));` `}`   `// returns the number represented by a binary` `// subarray l to r` `int` `decimalOfSubarr(``int` `arr[], ``int` `l, ``int` `r,` `                    ``int` `n, ``int` `pre[])` `{` `    ``// if r is equal to n-1 r+1 does not exist` `    ``if` `(r != n - 1)` `        ``return` `(pre[l] - pre[r + 1]) / (1 << (n - 1 - r));`   `    ``return` `pre[l] / (1 << (n - 1 - r));` `}`   `// Driver Function` `int` `main()` `{` `    ``int` `arr[] = { 1, 0, 1, 0, 1, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``int` `pre[n];` `    ``precompute(arr, n, pre);` `    ``cout << decimalOfSubarr(arr, 2, 4, n, pre) << endl;` `    ``cout << decimalOfSubarr(arr, 4, 5, n, pre) << endl;` `    ``return` `0;` `}`

## Java

 `// Java implementation of finding number` `// represented by binary subarray` `import` `java.util.Arrays;`   `class` `GFG {`   `    ``// Fills pre[]` `    ``static` `void` `precompute(``int` `arr[], ``int` `n, ``int` `pre[])` `    ``{` `        ``Arrays.fill(pre, ``0``);`   `        ``pre[n - ``1``] = arr[n - ``1``] * (``int``)(Math.pow(``2``, ``0``));` `        ``for` `(``int` `i = n - ``2``; i >= ``0``; i--)` `            ``pre[i] = pre[i + ``1``] + arr[i] * (``1` `<< (n - ``1` `- i));` `    ``}`   `    ``// returns the number represented by a binary` `    ``// subarray l to r` `    ``static` `int` `decimalOfSubarr(``int` `arr[], ``int` `l, ``int` `r,` `                               ``int` `n, ``int` `pre[])` `    ``{`   `        ``// if r is equal to n-1 r+1 does not exist` `        ``if` `(r != n - ``1``)` `            ``return` `(pre[l] - pre[r + ``1``]) / (``1` `<< (n - ``1` `- r));`   `        ``return` `pre[l] / (``1` `<< (n - ``1` `- r));` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``1``, ``0``, ``1``, ``0``, ``1``, ``1` `};` `        ``int` `n = arr.length;`   `        ``int` `pre[] = ``new` `int``[n];` `        ``precompute(arr, n, pre);`   `        ``System.out.println(decimalOfSubarr(arr,` `                                           ``2``, ``4``, n, pre));`   `        ``System.out.println(decimalOfSubarr(arr,` `                                           ``4``, ``5``, n, pre));` `    ``}` `}`   `// This code is contributed by Anant Agarwal.`

## Python3

 `# implementation of finding number` `# represented by binary subarray` `from` `math ``import` `pow`   `# Fills pre[]` `def` `precompute(arr, n, pre):` `    `  `    ``pre[n ``-` `1``] ``=` `arr[n ``-` `1``] ``*` `pow``(``2``, ``0``)` `    ``i ``=` `n ``-` `2` `    ``while``(i >``=` `0``):` `        ``pre[i] ``=` `(pre[i ``+` `1``] ``+` `arr[i] ``*` `                 ``(``1` `<< (n ``-` `1` `-` `i)))` `        ``i ``-``=` `1`   `# returns the number represented by ` `# a binary subarray l to r` `def` `decimalOfSubarr(arr, l, r, n, pre):` `    `  `    ``# if r is equal to n-1 r+1 does not exist` `    ``if` `(r !``=` `n ``-` `1``):` `        ``return` `((pre[l] ``-` `pre[r ``+` `1``]) ``/` `                ``(``1` `<< (n ``-` `1` `-` `r)))`   `    ``return` `pre[l] ``/` `(``1` `<< (n ``-` `1` `-` `r))`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``1``, ``0``, ``1``, ``0``, ``1``, ``1``]` `    ``n ``=` `len``(arr)`   `    ``pre ``=` `[``0` `for` `i ``in` `range``(n)]` `    ``precompute(arr, n, pre)` `    ``print``(``int``(decimalOfSubarr(arr, ``2``, ``4``, n, pre)))` `    ``print``(``int``(decimalOfSubarr(arr, ``4``, ``5``, n, pre)))`   `# This code is contributed by` `# Surendra_Gangwar`

## C#

 `// C# implementation of finding number` `// represented by binary subarray` `using` `System;`   `class` `GFG {`   `    ``// Fills pre[]` `    ``static` `void` `precompute(``int``[] arr, ``int` `n, ``int``[] pre)` `    ``{` `        ``for` `(``int` `i = 0; i < n; i++)` `            ``pre[i] = 0;`   `        ``pre[n - 1] = arr[n - 1] * (``int``)(Math.Pow(2, 0));` `        ``for` `(``int` `i = n - 2; i >= 0; i--)` `            ``pre[i] = pre[i + 1] + arr[i] * (1 << (n - 1 - i));` `    ``}`   `    ``// returns the number represented by ` `    ``// a binary subarray l to r` `    ``static` `int` `decimalOfSubarr(``int``[] arr, ``int` `l, ``int` `r,` `                                      ``int` `n, ``int``[] pre)` `    ``{` `        ``// if r is equal to n-1 r+1 does not exist` `        ``if` `(r != n - 1)` `            ``return` `(pre[l] - pre[r + 1]) / (1 << (n - 1 - r));`   `        ``return` `pre[l] / (1 << (n - 1 - r));` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[] arr = { 1, 0, 1, 0, 1, 1 };` `        ``int` `n = arr.Length;`   `        ``int``[] pre = ``new` `int``[n];` `        ``precompute(arr, n, pre);`   `        ``Console.WriteLine(decimalOfSubarr(arr,` `                                        ``2, 4, n, pre));`   `        ``Console.WriteLine(decimalOfSubarr(arr,` `                                        ``4, 5, n, pre));` `    ``}` `}`   `// This code is contributed by vt_m.`

## PHP

 `= 0; ``\$i``--)` `        ``\$pre``[``\$i``] = ``\$pre``[``\$i` `+ 1] + ``\$arr``[``\$i``] * ` `                           ``(1 << (``\$n` `- 1 - ``\$i``));` `}`   `// returns the number represented by ` `// a binary subarray l to r` `function` `decimalOfSubarr(&``\$arr``, ``\$l``, ``\$r``, ``\$n``, &``\$pre``)` `{` `    ``// if r is equal to n-1 r+1 does not exist` `    ``if` `(``\$r` `!= ``\$n` `- 1)` `        ``return` `(``\$pre``[``\$l``] - ``\$pre``[``\$r` `+ 1]) / ` `                    ``(1 << (``\$n` `- 1 - ``\$r``));`   `    ``return` `\$pre``[``\$l``] / (1 << (``\$n` `- 1 - ``\$r``));` `}`   `// Driver Code` `\$arr` `= ``array``(1, 0, 1, 0, 1, 1 );` `\$n` `= sizeof(``\$arr``);`   `\$pre` `= ``array_fill``(0, ``\$n``, NULL);` `precompute(``\$arr``, ``\$n``, ``\$pre``);` `echo` `decimalOfSubarr(``\$arr``, 2, 4, ``\$n``, ``\$pre``) . ``"\n"``;` `echo` `decimalOfSubarr(``\$arr``, 4, 5, ``\$n``, ``\$pre``) . ``"\n"``;`   `// This code is contributed by ita_c` `?>`

## Javascript

 ``

Output

```5
3```

Time complexity: O(n)
Auxiliary Space: O(n)

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